TSTP Solution File: NUM925+7 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM925+7 : 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 : n015.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 : Sun May 5 08:43:30 EDT 2024
% Result : Theorem 2.37s 0.77s
% Output : Refutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1206
% Syntax : Number of formulae : 3478 (1405 unt; 0 def)
% Number of atoms : 7254 (2536 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 5911 (2135 ~;2114 |; 425 &)
% ( 822 <=>; 411 =>; 0 <=; 4 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 724 ( 722 usr; 644 prp; 0-4 aty)
% Number of functors : 58 ( 58 usr; 21 con; 0-4 aty)
% Number of variables : 4314 (4252 !; 62 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14168,plain,
$false,
inference(avatar_sat_refutation,[],[f7000,f7005,f7010,f7015,f7020,f7025,f7030,f7035,f7040,f7045,f7050,f7055,f7060,f7065,f7070,f7075,f7080,f7085,f7090,f7095,f7100,f7105,f7110,f7115,f7120,f7125,f7130,f7135,f7140,f7145,f7150,f7155,f7160,f7165,f7170,f7175,f7180,f7185,f7190,f7195,f7200,f7205,f7210,f7215,f7220,f7225,f7230,f7235,f7240,f7245,f7250,f7255,f7260,f7265,f7270,f7275,f7280,f7285,f7290,f7295,f7300,f7305,f7310,f7315,f7320,f7325,f7330,f7335,f7340,f7345,f7350,f7355,f7360,f7365,f7370,f7375,f7380,f7385,f7390,f7395,f7400,f7405,f7410,f7415,f7420,f7425,f7430,f7435,f7440,f7445,f7450,f7455,f7460,f7465,f7470,f7475,f7480,f7485,f7490,f7495,f7500,f7505,f7510,f7515,f7520,f7525,f7530,f7535,f7540,f7545,f7550,f7555,f7560,f7565,f7570,f7575,f7580,f7585,f7590,f7595,f7600,f7605,f7610,f7615,f7620,f7625,f7630,f7635,f7640,f7645,f7650,f7655,f7660,f7665,f7670,f7675,f7680,f7685,f7690,f7695,f7700,f7705,f7710,f7715,f7720,f7725,f7730,f7735,f7740,f7745,f7750,f7755,f7760,f7765,f7770,f7775,f7779,f7783,f7787,f7791,f7795,f7799,f7804,f7811,f7822,f7827,f7832,f7837,f7842,f7847,f7852,f7857,f7862,f7867,f7872,f7877,f7882,f7887,f7892,f7897,f7902,f7907,f7912,f7917,f7922,f7926,f7930,f7934,f7939,f7944,f7948,f7952,f7959,f7970,f7975,f7979,f7983,f7988,f7992,f7996,f8000,f8004,f8008,f8012,f8016,f8020,f8024,f8028,f8033,f8037,f8041,f8045,f8060,f8069,f8073,f8077,f8081,f8085,f8089,f8093,f8097,f8101,f8105,f8109,f8113,f8117,f8121,f8125,f8129,f8133,f8153,f8168,f8172,f8176,f8180,f8184,f8188,f8192,f8196,f8200,f8204,f8208,f8212,f8216,f8220,f8224,f8228,f8232,f8236,f8240,f8244,f8248,f8252,f8256,f8260,f8264,f8268,f8273,f8277,f8282,f8287,f8292,f8296,f8300,f8306,f8332,f8424,f8494,f8498,f8502,f8506,f8510,f8514,f8518,f8522,f8526,f8530,f8534,f8538,f8542,f8546,f8550,f8581,f8635,f8649,f8653,f8657,f8661,f8665,f8669,f8673,f8677,f8681,f8686,f8690,f8694,f8698,f8702,f8706,f8710,f8714,f8718,f8722,f8727,f8731,f8735,f8739,f8743,f8747,f8751,f8755,f8759,f8763,f8767,f8771,f8775,f8779,f8783,f8787,f8792,f8798,f8803,f8807,f8814,f8818,f8822,f8826,f8852,f8948,f9013,f9019,f9023,f9027,f9031,f9035,f9039,f9043,f9047,f9051,f9056,f9060,f9141,f9152,f9157,f9162,f9167,f9172,f9177,f9181,f9185,f9189,f9193,f9197,f9201,f9205,f9209,f9213,f9217,f9221,f9225,f9229,f9233,f9237,f9241,f9245,f9249,f9253,f9257,f9261,f9265,f9269,f9274,f9278,f9282,f9286,f9290,f9294,f9298,f9302,f9306,f9310,f9314,f9319,f9323,f9327,f9331,f9335,f9339,f9343,f9347,f9351,f9355,f9359,f9383,f9387,f9391,f9395,f9399,f9403,f9407,f9411,f9415,f9419,f9443,f9447,f9451,f9456,f9461,f9465,f9469,f9473,f9477,f9482,f9651,f9749,f9794,f9799,f9803,f9807,f9811,f9815,f9819,f9823,f9827,f9831,f9835,f9839,f9843,f9848,f9852,f9857,f9862,f9867,f9871,f9875,f9879,f9883,f9887,f9891,f9895,f9902,f10075,f10081,f10085,f10089,f10093,f10097,f10104,f10108,f10112,f10116,f10120,f10124,f10128,f10132,f10136,f10140,f10145,f10149,f10153,f10157,f10161,f10165,f10169,f10173,f10177,f10181,f10185,f10190,f10194,f10198,f10203,f10213,f10218,f10228,f10233,f10275,f10279,f10284,f10323,f10327,f10331,f10335,f10340,f10344,f10354,f10622,f11028,f11136,f11140,f11144,f11148,f11152,f11156,f11160,f11164,f11168,f11172,f11176,f11181,f11185,f11189,f11193,f11197,f11201,f11205,f11209,f11213,f11217,f11221,f11226,f11230,f11234,f11238,f11243,f11299,f11303,f11307,f11311,f11316,f11321,f11373,f11378,f11382,f11386,f11643,f11956,f12000,f12004,f12008,f12012,f12016,f12020,f12024,f12028,f12032,f12036,f12040,f12044,f12048,f12052,f12056,f12060,f12064,f12068,f12072,f12076,f12080,f12084,f12088,f12092,f12096,f12100,f12104,f12108,f12113,f12119,f12127,f12134,f12140,f12144,f12148,f12152,f12157,f12161,f12165,f12169,f12246,f12326,f12330,f12334,f12338,f12342,f12346,f12350,f12354,f12358,f12362,f12366,f12370,f12374,f12378,f12383,f12387,f12391,f12395,f12399,f12403,f12407,f12411,f12415,f12419,f12423,f12428,f12432,f12436,f12440,f12444,f12448,f12452,f12456,f12460,f12464,f12468,f12473,f12477,f12481,f12485,f12489,f12494,f12501,f12506,f12515,f12519,f12523,f12527,f12531,f12535,f12539,f12543,f12584,f13413,f14027,f14033,f14037,f14041,f14045,f14049,f14053,f14057,f14061,f14065,f14069,f14073,f14117,f14122,f14128,f14137,f14144,f14152,f14156,f14161,f14167]) ).
fof(f14167,plain,
( spl63_155
| ~ spl63_262
| ~ spl63_623
| ~ spl63_625 ),
inference(avatar_split_clause,[],[f14102,f14030,f13410,f8289,f7767]) ).
fof(f7767,plain,
( spl63_155
<=> min = pls ),
introduced(avatar_definition,[new_symbols(naming,[spl63_155])]) ).
fof(f8289,plain,
( spl63_262
<=> pls = hAPP(nat,int,semiring_1_of_nat(int),nat_1(pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_262])]) ).
fof(f13410,plain,
( spl63_623
<=> min = hAPP(nat,int,semiring_1_of_nat(int),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_623])]) ).
fof(f14030,plain,
( spl63_625
<=> n = nat_1(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_625])]) ).
fof(f14102,plain,
( min = pls
| ~ spl63_262
| ~ spl63_623
| ~ spl63_625 ),
inference(forward_demodulation,[],[f14080,f13412]) ).
fof(f13412,plain,
( min = hAPP(nat,int,semiring_1_of_nat(int),n)
| ~ spl63_623 ),
inference(avatar_component_clause,[],[f13410]) ).
fof(f14080,plain,
( pls = hAPP(nat,int,semiring_1_of_nat(int),n)
| ~ spl63_262
| ~ spl63_625 ),
inference(superposition,[],[f8291,f14032]) ).
fof(f14032,plain,
( n = nat_1(pls)
| ~ spl63_625 ),
inference(avatar_component_clause,[],[f14030]) ).
fof(f8291,plain,
( pls = hAPP(nat,int,semiring_1_of_nat(int),nat_1(pls))
| ~ spl63_262 ),
inference(avatar_component_clause,[],[f8289]) ).
fof(f14161,plain,
( spl63_643
| ~ spl63_488
| ~ spl63_642 ),
inference(avatar_split_clause,[],[f14157,f14154,f11025,f14159]) ).
fof(f14159,plain,
( spl63_643
<=> ! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,minus_minus(int,one_one(int),min)),X1)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_643])]) ).
fof(f11025,plain,
( spl63_488
<=> one_one(int) = minus_minus(int,pls,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_488])]) ).
fof(f14154,plain,
( spl63_642
<=> ! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min)),X1)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_642])]) ).
fof(f14157,plain,
( ! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,minus_minus(int,one_one(int),min)),X1)
| ~ number_ring(X0) )
| ~ spl63_488
| ~ spl63_642 ),
inference(forward_demodulation,[],[f14155,f11027]) ).
fof(f11027,plain,
( one_one(int) = minus_minus(int,pls,min)
| ~ spl63_488 ),
inference(avatar_component_clause,[],[f11025]) ).
fof(f14155,plain,
( ! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min)),X1)
| ~ number_ring(X0) )
| ~ spl63_642 ),
inference(avatar_component_clause,[],[f14154]) ).
fof(f14156,plain,
spl63_642,
inference(avatar_split_clause,[],[f6080,f14154]) ).
fof(f6080,plain,
! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min)),X1)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f6079,f5453]) ).
fof(f5453,plain,
pls = plus_plus(int,pls,pls),
inference(definition_unfolding,[],[f3860,f3968]) ).
fof(f3968,plain,
! [X0] : bit0(X0) = plus_plus(int,X0,X0),
inference(cnf_transformation,[],[f1270]) ).
fof(f1270,plain,
! [X0] : bit0(X0) = plus_plus(int,X0,X0),
inference(rectify,[],[f176]) ).
fof(f176,axiom,
! [X19] : bit0(X19) = plus_plus(int,X19,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
fof(f3860,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f170]) ).
fof(f170,axiom,
pls = bit0(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
fof(f6079,plain,
! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,minus_minus(int,minus_minus(int,plus_plus(int,pls,pls),min),min)),X1)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f6078,f5453]) ).
fof(f6078,plain,
! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,minus_minus(int,minus_minus(int,plus_plus(int,plus_plus(int,pls,pls),plus_plus(int,pls,pls)),min),min)),X1)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f5548,f5502]) ).
fof(f5502,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,[],[f3969,f3966,f5445,f3968,f3966]) ).
fof(f5445,plain,
! [X0] : bit1(X0) = minus_minus(int,plus_plus(int,X0,X0),min),
inference(definition_unfolding,[],[f3962,f3966,f3968]) ).
fof(f3962,plain,
! [X0] : bit1(X0) = succ(bit0(X0)),
inference(cnf_transformation,[],[f1266]) ).
fof(f1266,plain,
! [X0] : bit1(X0) = succ(bit0(X0)),
inference(rectify,[],[f612]) ).
fof(f612,axiom,
! [X19] : bit1(X19) = succ(bit0(X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_succ__Bit0) ).
fof(f3966,plain,
! [X0] : succ(X0) = minus_minus(int,X0,min),
inference(cnf_transformation,[],[f1269]) ).
fof(f1269,plain,
! [X0] : succ(X0) = minus_minus(int,X0,min),
inference(rectify,[],[f875]) ).
fof(f875,axiom,
! [X19] : succ(X19) = minus_minus(int,X19,min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_diff__bin__simps_I2_J) ).
fof(f3969,plain,
! [X0] : succ(bit1(X0)) = bit0(succ(X0)),
inference(cnf_transformation,[],[f1271]) ).
fof(f1271,plain,
! [X0] : succ(bit1(X0)) = bit0(succ(X0)),
inference(rectify,[],[f613]) ).
fof(f613,axiom,
! [X19] : succ(bit1(X19)) = bit0(succ(X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_succ__Bit1) ).
fof(f5548,plain,
! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min))),X1)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f4237,f3968,f5445]) ).
fof(f4237,plain,
! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2385]) ).
fof(f2385,plain,
! [X0] :
( ! [X1] : plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1447]) ).
fof(f1447,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) ),
inference(rectify,[],[f635]) ).
fof(f635,axiom,
! [X1] :
( number_ring(X1)
=> ! [X15] : plus_plus(X1,X15,X15) = times_times(X1,number_number_of(X1,bit0(bit1(pls))),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_mult__2) ).
fof(f14152,plain,
spl63_641,
inference(avatar_split_clause,[],[f5986,f14150]) ).
fof(f14150,plain,
( spl63_641
<=> ! [X0] :
( one_one(int) = hAPP(nat,int,power_power(int,min),X0)
| min = hAPP(nat,int,power_power(int,min),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_641])]) ).
fof(f5986,plain,
! [X0] :
( one_one(int) = hAPP(nat,int,power_power(int,min),X0)
| min = hAPP(nat,int,power_power(int,min),X0) ),
inference(forward_demodulation,[],[f5985,f3874]) ).
fof(f3874,plain,
min = ti(int,min),
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
min = ti(int,min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OMin_res) ).
fof(f5985,plain,
! [X0] :
( one_one(int) = hAPP(nat,int,power_power(int,ti(int,min)),X0)
| min = hAPP(nat,int,power_power(int,min),X0) ),
inference(forward_demodulation,[],[f5984,f3970]) ).
fof(f3970,plain,
! [X0] : ti(int,X0) = number_number_of(int,X0),
inference(cnf_transformation,[],[f1272]) ).
fof(f1272,plain,
! [X0] : ti(int,X0) = number_number_of(int,X0),
inference(rectify,[],[f218]) ).
fof(f218,axiom,
! [X19] : ti(int,X19) = number_number_of(int,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_number__of__is__id) ).
fof(f5984,plain,
! [X0] :
( min = hAPP(nat,int,power_power(int,min),X0)
| one_one(int) = hAPP(nat,int,power_power(int,number_number_of(int,min)),X0) ),
inference(forward_demodulation,[],[f5983,f3874]) ).
fof(f5983,plain,
! [X0] :
( ti(int,min) = hAPP(nat,int,power_power(int,ti(int,min)),X0)
| one_one(int) = hAPP(nat,int,power_power(int,number_number_of(int,min)),X0) ),
inference(forward_demodulation,[],[f4037,f3970]) ).
fof(f4037,plain,
! [X0] :
( number_number_of(int,min) = hAPP(nat,int,power_power(int,number_number_of(int,min)),X0)
| one_one(int) = hAPP(nat,int,power_power(int,number_number_of(int,min)),X0) ),
inference(cnf_transformation,[],[f1332]) ).
fof(f1332,plain,
! [X0] :
( number_number_of(int,min) = hAPP(nat,int,power_power(int,number_number_of(int,min)),X0)
| one_one(int) = hAPP(nat,int,power_power(int,number_number_of(int,min)),X0) ),
inference(rectify,[],[f974]) ).
fof(f974,axiom,
! [X14] :
( number_number_of(int,min) = hAPP(nat,int,power_power(int,number_number_of(int,min)),X14)
| one_one(int) = hAPP(nat,int,power_power(int,number_number_of(int,min)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_neg__one__power) ).
fof(f14144,plain,
( spl63_640
| ~ spl63_204
| ~ spl63_520
| ~ spl63_625
| ~ spl63_639 ),
inference(avatar_split_clause,[],[f14139,f14134,f14030,f11314,f8010,f14141]) ).
fof(f14141,plain,
( spl63_640
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),nat_1(minus_minus(int,one_one(int),min)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_640])]) ).
fof(f8010,plain,
( spl63_204
<=> ! [X0] : times_times(nat,one_one(nat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_204])]) ).
fof(f11314,plain,
( spl63_520
<=> ! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(minus_minus(int,one_one(int),min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_520])]) ).
fof(f14134,plain,
( spl63_639
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),plus_plus(nat,one_one(nat),one_one(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_639])]) ).
fof(f14139,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),nat_1(minus_minus(int,one_one(int),min))))
| ~ spl63_204
| ~ spl63_520
| ~ spl63_625
| ~ spl63_639 ),
inference(forward_demodulation,[],[f14138,f14032]) ).
fof(f14138,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),nat_1(minus_minus(int,one_one(int),min))))
| ~ spl63_204
| ~ spl63_520
| ~ spl63_639 ),
inference(forward_demodulation,[],[f14136,f11325]) ).
fof(f11325,plain,
( plus_plus(nat,one_one(nat),one_one(nat)) = nat_1(minus_minus(int,one_one(int),min))
| ~ spl63_204
| ~ spl63_520 ),
inference(superposition,[],[f11315,f8011]) ).
fof(f8011,plain,
( ! [X0] : times_times(nat,one_one(nat),X0) = X0
| ~ spl63_204 ),
inference(avatar_component_clause,[],[f8010]) ).
fof(f11315,plain,
( ! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(minus_minus(int,one_one(int),min)))
| ~ spl63_520 ),
inference(avatar_component_clause,[],[f11314]) ).
fof(f14136,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),plus_plus(nat,one_one(nat),one_one(nat))))
| ~ spl63_639 ),
inference(avatar_component_clause,[],[f14134]) ).
fof(f14137,plain,
spl63_639,
inference(avatar_split_clause,[],[f5842,f14134]) ).
fof(f5842,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f5841,f5811]) ).
fof(f5811,plain,
zero_zero(nat) = nat_1(pls),
inference(forward_demodulation,[],[f3877,f3861]) ).
fof(f3861,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f171]) ).
fof(f171,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(f3877,plain,
zero_zero(nat) = nat_1(zero_zero(int)),
inference(cnf_transformation,[],[f505]) ).
fof(f505,axiom,
zero_zero(nat) = nat_1(zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_transfer__nat__int__numerals_I1_J) ).
fof(f5841,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),plus_plus(nat,one_one(nat),one_one(nat)))),
inference(forward_demodulation,[],[f5840,f5826]) ).
fof(f5826,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,minus_minus(int,pls,min),minus_minus(int,pls,min))),
inference(forward_demodulation,[],[f5460,f5453]) ).
fof(f5460,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min))),
inference(definition_unfolding,[],[f3895,f3968,f5445]) ).
fof(f3895,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f127]) ).
fof(f127,axiom,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
fof(f5840,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,plus_plus(int,minus_minus(int,pls,min),minus_minus(int,pls,min))))),
inference(forward_demodulation,[],[f5464,f5453]) ).
fof(f5464,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min))))),
inference(definition_unfolding,[],[f3917,f3968,f5445]) ).
fof(f3917,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f287]) ).
fof(f287,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_pos2) ).
fof(f14128,plain,
spl63_638,
inference(avatar_split_clause,[],[f5826,f14125]) ).
fof(f14125,plain,
( spl63_638
<=> plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,minus_minus(int,pls,min),minus_minus(int,pls,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_638])]) ).
fof(f14122,plain,
~ spl63_637,
inference(avatar_split_clause,[],[f5718,f14119]) ).
fof(f14119,plain,
( spl63_637
<=> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,zero_zero(real),zero_zero(real)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_637])]) ).
fof(f5718,plain,
~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,zero_zero(real),zero_zero(real)))),
inference(equality_resolution,[],[f4647]) ).
fof(f4647,plain,
! [X0] :
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,X0,X0)))
| zero_zero(real) != X0 ),
inference(cnf_transformation,[],[f3404]) ).
fof(f3404,plain,
! [X0] :
( ( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,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(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,X0,X0))) ) ),
inference(nnf_transformation,[],[f1760]) ).
fof(f1760,plain,
! [X0] :
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,X0,X0)))
<=> zero_zero(real) = X0 ),
inference(rectify,[],[f751]) ).
fof(f751,axiom,
! [X4] :
( ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),times_times(real,X4,X4)))
<=> zero_zero(real) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_not__real__square__gt__zero) ).
fof(f14117,plain,
spl63_636,
inference(avatar_split_clause,[],[f5327,f14115]) ).
fof(f14115,plain,
( spl63_636
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),X2))
| ti(int,X1) != plus_plus(int,X0,times_times(int,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_636])]) ).
fof(f5327,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),X2))
| ti(int,X1) != plus_plus(int,X0,times_times(int,X2,X3)) ),
inference(cnf_transformation,[],[f3642]) ).
fof(f3642,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(int,bool,zcong(X0,X1),X2))
| ! [X3] : ti(int,X1) != plus_plus(int,X0,times_times(int,X2,X3)) )
& ( ti(int,X1) = plus_plus(int,X0,times_times(int,X2,sK59(X0,X1,X2)))
| ~ hBOOL(hAPP(int,bool,zcong(X0,X1),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f3640,f3641]) ).
fof(f3641,plain,
! [X0,X1,X2] :
( ? [X4] : ti(int,X1) = plus_plus(int,X0,times_times(int,X2,X4))
=> ti(int,X1) = plus_plus(int,X0,times_times(int,X2,sK59(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
fof(f3640,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(int,bool,zcong(X0,X1),X2))
| ! [X3] : ti(int,X1) != plus_plus(int,X0,times_times(int,X2,X3)) )
& ( ? [X4] : ti(int,X1) = plus_plus(int,X0,times_times(int,X2,X4))
| ~ hBOOL(hAPP(int,bool,zcong(X0,X1),X2)) ) ),
inference(rectify,[],[f3639]) ).
fof(f3639,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(int,bool,zcong(X0,X1),X2))
| ! [X3] : ti(int,X1) != plus_plus(int,X0,times_times(int,X2,X3)) )
& ( ? [X3] : ti(int,X1) = plus_plus(int,X0,times_times(int,X2,X3))
| ~ hBOOL(hAPP(int,bool,zcong(X0,X1),X2)) ) ),
inference(nnf_transformation,[],[f2185]) ).
fof(f2185,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),X2))
<=> ? [X3] : ti(int,X1) = plus_plus(int,X0,times_times(int,X2,X3)) ),
inference(rectify,[],[f993]) ).
fof(f993,axiom,
! [X6,X41,X27] :
( hBOOL(hAPP(int,bool,zcong(X6,X41),X27))
<=> ? [X43] : ti(int,X41) = plus_plus(int,X6,times_times(int,X27,X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_zcong__iff__lin) ).
fof(f14073,plain,
spl63_635,
inference(avatar_split_clause,[],[f5169,f14071]) ).
fof(f14071,plain,
( spl63_635
<=> ! [X2,X0,X1] :
( hAPP(X2,fun(X2,bool),X0,X1) = hAPP(X2,fun(X2,bool),X0,ti(X2,X1))
| ~ order(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_635])]) ).
fof(f5169,plain,
! [X2,X0,X1] :
( hAPP(X2,fun(X2,bool),X0,X1) = hAPP(X2,fun(X2,bool),X0,ti(X2,X1))
| ~ order(X2) ),
inference(cnf_transformation,[],[f2978]) ).
fof(f2978,plain,
! [X0,X1,X2] :
( hAPP(X2,fun(X2,bool),X0,X1) = hAPP(X2,fun(X2,bool),X0,ti(X2,X1))
| ~ order(X2) ),
inference(ennf_transformation,[],[f2078]) ).
fof(f2078,plain,
! [X0,X1,X2] :
( order(X2)
=> hAPP(X2,fun(X2,bool),X0,X1) = hAPP(X2,fun(X2,bool),X0,ti(X2,X1)) ),
inference(rectify,[],[f74]) ).
fof(f74,axiom,
! [X0,X2,X1] :
( order(X1)
=> hAPP(X1,fun(X1,bool),X0,X2) = hAPP(X1,fun(X1,bool),X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_0_arg2) ).
fof(f14069,plain,
spl63_634,
inference(avatar_split_clause,[],[f5163,f14067]) ).
fof(f14067,plain,
( spl63_634
<=> ! [X2,X0,X1] :
( hAPP(X2,fun(X2,bool),X0,X1) = hAPP(X2,fun(X2,bool),X0,ti(X2,X1))
| ~ dvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_634])]) ).
fof(f5163,plain,
! [X2,X0,X1] :
( hAPP(X2,fun(X2,bool),X0,X1) = hAPP(X2,fun(X2,bool),X0,ti(X2,X1))
| ~ dvd(X2) ),
inference(cnf_transformation,[],[f2972]) ).
fof(f2972,plain,
! [X0,X1,X2] :
( hAPP(X2,fun(X2,bool),X0,X1) = hAPP(X2,fun(X2,bool),X0,ti(X2,X1))
| ~ dvd(X2) ),
inference(ennf_transformation,[],[f2072]) ).
fof(f2072,plain,
! [X0,X1,X2] :
( dvd(X2)
=> hAPP(X2,fun(X2,bool),X0,X1) = hAPP(X2,fun(X2,bool),X0,ti(X2,X1)) ),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X0,X2,X1] :
( dvd(X1)
=> hAPP(X1,fun(X1,bool),X0,X2) = hAPP(X1,fun(X1,bool),X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_2_arg2) ).
fof(f14065,plain,
spl63_633,
inference(avatar_split_clause,[],[f5124,f14063]) ).
fof(f14063,plain,
( spl63_633
<=> ! [X2,X0,X1] :
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X2,X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_633])]) ).
fof(f5124,plain,
! [X2,X0,X1] :
( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X2,X0,X1))
| hBOOL(X2) ),
inference(cnf_transformation,[],[f2934]) ).
fof(f2934,plain,
! [X0,X1,X2] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X2,X0,X1))
| hBOOL(X2) )
& ( hAPP(nat,int,semiring_1_of_nat(int),X0) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X2,X0,X1))
| ~ hBOOL(X2) ) ),
inference(ennf_transformation,[],[f2034]) ).
fof(f2034,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(X2)
=> hAPP(nat,int,semiring_1_of_nat(int),X1) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X2,X0,X1)) )
& ( hBOOL(X2)
=> hAPP(nat,int,semiring_1_of_nat(int),X0) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X2,X0,X1)) ) ),
inference(rectify,[],[f258]) ).
fof(f258,axiom,
! [X4,X5,X32] :
( ( ~ hBOOL(X32)
=> hAPP(nat,int,semiring_1_of_nat(int),X5) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X32,X4,X5)) )
& ( hBOOL(X32)
=> hAPP(nat,int,semiring_1_of_nat(int),X4) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X32,X4,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_int__if__cong) ).
fof(f14061,plain,
spl63_632,
inference(avatar_split_clause,[],[f5123,f14059]) ).
fof(f14059,plain,
( spl63_632
<=> ! [X2,X0,X1] :
( hAPP(nat,int,semiring_1_of_nat(int),X0) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X2,X0,X1))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_632])]) ).
fof(f5123,plain,
! [X2,X0,X1] :
( hAPP(nat,int,semiring_1_of_nat(int),X0) = hAPP(nat,int,semiring_1_of_nat(int),if(nat,X2,X0,X1))
| ~ hBOOL(X2) ),
inference(cnf_transformation,[],[f2934]) ).
fof(f14057,plain,
spl63_631,
inference(avatar_split_clause,[],[f4912,f14055]) ).
fof(f14055,plain,
( spl63_631
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(nat,bool,X0,X3))
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X3)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_631])]) ).
fof(f4912,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X3))
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X3)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f3485]) ).
fof(f3485,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ~ hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
| ( ~ hBOOL(hAPP(nat,bool,X0,sK48(X0,X1)))
& ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),sK48(X0,X1)) ) )
& ( ( ( hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
& ! [X3] :
( hBOOL(hAPP(nat,bool,X0,X3))
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X3) ) )
| ~ sP12(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f3483,f3484]) ).
fof(f3484,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,X2))
& ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X2) )
=> ( ~ hBOOL(hAPP(nat,bool,X0,sK48(X0,X1)))
& ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),sK48(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3483,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ~ hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
| ? [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,X2))
& ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X2) ) )
& ( ( ( hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
& ! [X3] :
( hBOOL(hAPP(nat,bool,X0,X3))
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X3) ) )
| ~ sP12(X0,X1) ) ),
inference(rectify,[],[f3482]) ).
fof(f3482,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ~ hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
| ? [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,X2))
& ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X2) ) )
& ( ( ( hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
& ! [X2] :
( hBOOL(hAPP(nat,bool,X0,X2))
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ) )
| ~ sP12(X0,X1) ) ),
inference(flattening,[],[f3481]) ).
fof(f3481,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ~ hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
| ? [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,X2))
& ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X2) ) )
& ( ( ( hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
& ! [X2] :
( hBOOL(hAPP(nat,bool,X0,X2))
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ) )
| ~ sP12(X0,X1) ) ),
inference(nnf_transformation,[],[f3218]) ).
fof(f3218,plain,
! [X0,X1] :
( sP12(X0,X1)
<=> ( ( hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
& ! [X2] :
( hBOOL(hAPP(nat,bool,X0,X2))
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f14053,plain,
spl63_630,
inference(avatar_split_clause,[],[f4579,f14051]) ).
fof(f14051,plain,
( spl63_630
<=> ! [X0] :
( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int)
| one_one(int) != abs_abs(int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_630])]) ).
fof(f4579,plain,
! [X0] :
( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int)
| one_one(int) != abs_abs(int,X0) ),
inference(cnf_transformation,[],[f3369]) ).
fof(f3369,plain,
! [X0] :
( ( one_one(int) = abs_abs(int,X0)
| ( ti(int,X0) != number_number_of(int,min)
& ti(int,X0) != one_one(int) ) )
& ( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int)
| one_one(int) != abs_abs(int,X0) ) ),
inference(flattening,[],[f3368]) ).
fof(f3368,plain,
! [X0] :
( ( one_one(int) = abs_abs(int,X0)
| ( ti(int,X0) != number_number_of(int,min)
& ti(int,X0) != one_one(int) ) )
& ( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int)
| one_one(int) != abs_abs(int,X0) ) ),
inference(nnf_transformation,[],[f1730]) ).
fof(f1730,plain,
! [X0] :
( one_one(int) = abs_abs(int,X0)
<=> ( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int) ) ),
inference(rectify,[],[f1055]) ).
fof(f1055,axiom,
! [X28] :
( one_one(int) = abs_abs(int,X28)
<=> ( ti(int,X28) = number_number_of(int,min)
| one_one(int) = ti(int,X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_abs__eq__1__iff) ).
fof(f14049,plain,
spl63_629,
inference(avatar_split_clause,[],[f4405,f14047]) ).
fof(f14047,plain,
( spl63_629
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),plus_plus(X0,X1,one_one(X0))))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_629])]) ).
fof(f4405,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),plus_plus(X0,X1,one_one(X0))))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f2583]) ).
fof(f2583,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),plus_plus(X0,X1,one_one(X0))))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f1595]) ).
fof(f1595,plain,
! [X0] :
( linordered_semidom(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),plus_plus(X0,X1,one_one(X0)))) ),
inference(rectify,[],[f278]) ).
fof(f278,axiom,
! [X1] :
( linordered_semidom(X1)
=> ! [X30] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X30),plus_plus(X1,X30,one_one(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_less__add__one) ).
fof(f14045,plain,
spl63_628,
inference(avatar_split_clause,[],[f4065,f14043]) ).
fof(f14043,plain,
( spl63_628
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),times_times(X0,X1,X1)))
| ~ linordered_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_628])]) ).
fof(f4065,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),times_times(X0,X1,X1)))
| ~ linordered_ring(X0) ),
inference(cnf_transformation,[],[f2276]) ).
fof(f2276,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),times_times(X0,X1,X1)))
| ~ linordered_ring(X0) ),
inference(ennf_transformation,[],[f1348]) ).
fof(f1348,plain,
! [X0] :
( linordered_ring(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),times_times(X0,X1,X1))) ),
inference(rectify,[],[f392]) ).
fof(f392,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X30] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),times_times(X1,X30,X30))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_zero__le__square) ).
fof(f14041,plain,
spl63_627,
inference(avatar_split_clause,[],[f4064,f14039]) ).
fof(f14039,plain,
( spl63_627
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X1)),zero_zero(X0)))
| ~ linordered_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_627])]) ).
fof(f4064,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X1)),zero_zero(X0)))
| ~ linordered_ring(X0) ),
inference(cnf_transformation,[],[f2275]) ).
fof(f2275,plain,
! [X0] :
( ! [X1] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X1)),zero_zero(X0)))
| ~ linordered_ring(X0) ),
inference(ennf_transformation,[],[f1347]) ).
fof(f1347,plain,
! [X0] :
( linordered_ring(X0)
=> ! [X1] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X1)),zero_zero(X0))) ),
inference(rectify,[],[f507]) ).
fof(f507,axiom,
! [X1] :
( linordered_ring(X1)
=> ! [X30] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),times_times(X1,X30,X30)),zero_zero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_not__square__less__zero) ).
fof(f14037,plain,
spl63_626,
inference(avatar_split_clause,[],[f4021,f14035]) ).
fof(f14035,plain,
( spl63_626
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),times_times(nat,X0,times_times(nat,X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_626])]) ).
fof(f4021,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),times_times(nat,X0,times_times(nat,X0,X0)))),
inference(cnf_transformation,[],[f1319]) ).
fof(f1319,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),times_times(nat,X0,times_times(nat,X0,X0)))),
inference(rectify,[],[f672]) ).
fof(f672,axiom,
! [X13] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X13),times_times(nat,X13,times_times(nat,X13,X13)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_le__cube) ).
fof(f14033,plain,
( spl63_625
| ~ spl63_236
| ~ spl63_347
| ~ spl63_616
| ~ spl63_623 ),
inference(avatar_split_clause,[],[f13987,f13410,f12521,f9169,f8182,f14030]) ).
fof(f8182,plain,
( spl63_236
<=> ! [X0] : nat_1(hAPP(nat,int,semiring_1_of_nat(int),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_236])]) ).
fof(f9169,plain,
( spl63_347
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_347])]) ).
fof(f12521,plain,
( spl63_616
<=> ! [X0] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls))
| nat_1(X0) = nat_1(pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_616])]) ).
fof(f13987,plain,
( n = nat_1(pls)
| ~ spl63_236
| ~ spl63_347
| ~ spl63_616
| ~ spl63_623 ),
inference(forward_demodulation,[],[f13979,f13945]) ).
fof(f13945,plain,
( n = nat_1(min)
| ~ spl63_236
| ~ spl63_623 ),
inference(superposition,[],[f8183,f13412]) ).
fof(f8183,plain,
( ! [X0] : nat_1(hAPP(nat,int,semiring_1_of_nat(int),X0)) = X0
| ~ spl63_236 ),
inference(avatar_component_clause,[],[f8182]) ).
fof(f13979,plain,
( nat_1(pls) = nat_1(min)
| ~ spl63_347
| ~ spl63_616 ),
inference(resolution,[],[f12522,f9171]) ).
fof(f9171,plain,
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),pls))
| ~ spl63_347 ),
inference(avatar_component_clause,[],[f9169]) ).
fof(f12522,plain,
( ! [X0] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls))
| nat_1(X0) = nat_1(pls) )
| ~ spl63_616 ),
inference(avatar_component_clause,[],[f12521]) ).
fof(f14027,plain,
spl63_624,
inference(avatar_split_clause,[],[f4018,f14025]) ).
fof(f14025,plain,
( spl63_624
<=> ! [X0] : ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),plus_plus(real,abs_abs(real,X0),one_one(real))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_624])]) ).
fof(f4018,plain,
! [X0] : ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),plus_plus(real,abs_abs(real,X0),one_one(real))),X0)),
inference(cnf_transformation,[],[f1316]) ).
fof(f1316,plain,
! [X0] : ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),plus_plus(real,abs_abs(real,X0),one_one(real))),X0)),
inference(rectify,[],[f1071]) ).
fof(f1071,axiom,
! [X9] : ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),plus_plus(real,abs_abs(real,X9),one_one(real))),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_abs__add__one__not__less__self) ).
fof(f13413,plain,
( ~ spl63_34
| spl63_623
| ~ spl63_140
| ~ spl63_156
| ~ spl63_179
| ~ spl63_467
| ~ spl63_493
| ~ spl63_622 ),
inference(avatar_split_clause,[],[f13105,f12581,f11150,f10179,f7889,f7772,f7692,f13410,f7162]) ).
fof(f7162,plain,
( spl63_34
<=> group_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_34])]) ).
fof(f7692,plain,
( spl63_140
<=> power(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_140])]) ).
fof(f7772,plain,
( spl63_156
<=> pls = zero_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_156])]) ).
fof(f7889,plain,
( spl63_179
<=> min = ti(int,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_179])]) ).
fof(f10179,plain,
( spl63_467
<=> ! [X2,X0,X1] :
( hAPP(nat,X2,X0,X1) = ti(X2,hAPP(nat,X2,X0,X1))
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_467])]) ).
fof(f11150,plain,
( spl63_493
<=> ! [X2,X0,X1] :
( ti(X0,X2) = ti(X0,X1)
| zero_zero(X0) != minus_minus(X0,X1,X2)
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_493])]) ).
fof(f12581,plain,
( spl63_622
<=> pls = minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),n),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_622])]) ).
fof(f13105,plain,
( min = hAPP(nat,int,semiring_1_of_nat(int),n)
| ~ group_add(int)
| ~ spl63_140
| ~ spl63_156
| ~ spl63_179
| ~ spl63_467
| ~ spl63_493
| ~ spl63_622 ),
inference(forward_demodulation,[],[f13104,f7891]) ).
fof(f7891,plain,
( min = ti(int,min)
| ~ spl63_179 ),
inference(avatar_component_clause,[],[f7889]) ).
fof(f13104,plain,
( ti(int,min) = hAPP(nat,int,semiring_1_of_nat(int),n)
| ~ group_add(int)
| ~ spl63_140
| ~ spl63_156
| ~ spl63_467
| ~ spl63_493
| ~ spl63_622 ),
inference(forward_demodulation,[],[f13103,f11034]) ).
fof(f11034,plain,
( ! [X0,X1] : hAPP(nat,int,X0,X1) = ti(int,hAPP(nat,int,X0,X1))
| ~ spl63_140
| ~ spl63_467 ),
inference(resolution,[],[f10180,f7694]) ).
fof(f7694,plain,
( power(int)
| ~ spl63_140 ),
inference(avatar_component_clause,[],[f7692]) ).
fof(f10180,plain,
( ! [X2,X0,X1] :
( ~ power(X2)
| hAPP(nat,X2,X0,X1) = ti(X2,hAPP(nat,X2,X0,X1)) )
| ~ spl63_467 ),
inference(avatar_component_clause,[],[f10179]) ).
fof(f13103,plain,
( ti(int,min) = ti(int,hAPP(nat,int,semiring_1_of_nat(int),n))
| ~ group_add(int)
| ~ spl63_156
| ~ spl63_493
| ~ spl63_622 ),
inference(trivial_inequality_removal,[],[f13102]) ).
fof(f13102,plain,
( pls != pls
| ti(int,min) = ti(int,hAPP(nat,int,semiring_1_of_nat(int),n))
| ~ group_add(int)
| ~ spl63_156
| ~ spl63_493
| ~ spl63_622 ),
inference(forward_demodulation,[],[f13097,f7774]) ).
fof(f7774,plain,
( pls = zero_zero(int)
| ~ spl63_156 ),
inference(avatar_component_clause,[],[f7772]) ).
fof(f13097,plain,
( pls != zero_zero(int)
| ti(int,min) = ti(int,hAPP(nat,int,semiring_1_of_nat(int),n))
| ~ group_add(int)
| ~ spl63_493
| ~ spl63_622 ),
inference(superposition,[],[f11151,f12583]) ).
fof(f12583,plain,
( pls = minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),n),min)
| ~ spl63_622 ),
inference(avatar_component_clause,[],[f12581]) ).
fof(f11151,plain,
( ! [X2,X0,X1] :
( zero_zero(X0) != minus_minus(X0,X1,X2)
| ti(X0,X2) = ti(X0,X1)
| ~ group_add(X0) )
| ~ spl63_493 ),
inference(avatar_component_clause,[],[f11150]) ).
fof(f12584,plain,
( ~ spl63_18
| spl63_622
| ~ spl63_95
| ~ spl63_156
| ~ spl63_232
| ~ spl63_247
| ~ spl63_279
| ~ spl63_367
| ~ spl63_570 ),
inference(avatar_split_clause,[],[f12552,f12324,f9251,f8536,f8226,f8165,f7772,f7467,f12581,f7082]) ).
fof(f7082,plain,
( spl63_18
<=> ring_11004092258visors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_18])]) ).
fof(f7467,plain,
( spl63_95
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_95])]) ).
fof(f8165,plain,
( spl63_232
<=> pls = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,pls,min),min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_232])]) ).
fof(f8226,plain,
( spl63_247
<=> ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_247])]) ).
fof(f8536,plain,
( spl63_279
<=> ! [X0] : minus_minus(int,X0,min) = plus_plus(int,X0,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_279])]) ).
fof(f9251,plain,
( spl63_367
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ ab_semigroup_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_367])]) ).
fof(f12324,plain,
( spl63_570
<=> ! [X2,X0,X1] :
( zero_zero(X0) != hAPP(nat,X0,power_power(X0,X2),X1)
| zero_zero(X0) = ti(X0,X2)
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_570])]) ).
fof(f12552,plain,
( pls = minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),n),min)
| ~ ring_11004092258visors(int)
| ~ spl63_95
| ~ spl63_156
| ~ spl63_232
| ~ spl63_247
| ~ spl63_279
| ~ spl63_367
| ~ spl63_570 ),
inference(forward_demodulation,[],[f12551,f7774]) ).
fof(f12551,plain,
( zero_zero(int) = minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),n),min)
| ~ ring_11004092258visors(int)
| ~ spl63_95
| ~ spl63_156
| ~ spl63_232
| ~ spl63_247
| ~ spl63_279
| ~ spl63_367
| ~ spl63_570 ),
inference(forward_demodulation,[],[f12550,f8600]) ).
fof(f8600,plain,
( ! [X0] : minus_minus(int,X0,min) = plus_plus(int,one_one(int),X0)
| ~ spl63_247
| ~ spl63_279 ),
inference(superposition,[],[f8537,f8227]) ).
fof(f8227,plain,
( ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0)
| ~ spl63_247 ),
inference(avatar_component_clause,[],[f8226]) ).
fof(f8537,plain,
( ! [X0] : minus_minus(int,X0,min) = plus_plus(int,X0,one_one(int))
| ~ spl63_279 ),
inference(avatar_component_clause,[],[f8536]) ).
fof(f12550,plain,
( zero_zero(int) = plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))
| ~ ring_11004092258visors(int)
| ~ spl63_95
| ~ spl63_156
| ~ spl63_232
| ~ spl63_367
| ~ spl63_570 ),
inference(forward_demodulation,[],[f12549,f9559]) ).
fof(f9559,plain,
( ! [X0,X1] : plus_plus(int,X0,X1) = ti(int,plus_plus(int,X0,X1))
| ~ spl63_95
| ~ spl63_367 ),
inference(resolution,[],[f9252,f7469]) ).
fof(f7469,plain,
( ab_semigroup_add(int)
| ~ spl63_95 ),
inference(avatar_component_clause,[],[f7467]) ).
fof(f9252,plain,
( ! [X2,X0,X1] :
( ~ ab_semigroup_add(X2)
| plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1)) )
| ~ spl63_367 ),
inference(avatar_component_clause,[],[f9251]) ).
fof(f12549,plain,
( zero_zero(int) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))
| ~ ring_11004092258visors(int)
| ~ spl63_156
| ~ spl63_232
| ~ spl63_570 ),
inference(trivial_inequality_removal,[],[f12548]) ).
fof(f12548,plain,
( pls != pls
| zero_zero(int) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))
| ~ ring_11004092258visors(int)
| ~ spl63_156
| ~ spl63_232
| ~ spl63_570 ),
inference(forward_demodulation,[],[f12544,f7774]) ).
fof(f12544,plain,
( pls != zero_zero(int)
| zero_zero(int) = ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))
| ~ ring_11004092258visors(int)
| ~ spl63_232
| ~ spl63_570 ),
inference(superposition,[],[f12325,f8167]) ).
fof(f8167,plain,
( pls = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,pls,min),min)))
| ~ spl63_232 ),
inference(avatar_component_clause,[],[f8165]) ).
fof(f12325,plain,
( ! [X2,X0,X1] :
( zero_zero(X0) != hAPP(nat,X0,power_power(X0,X2),X1)
| zero_zero(X0) = ti(X0,X2)
| ~ ring_11004092258visors(X0) )
| ~ spl63_570 ),
inference(avatar_component_clause,[],[f12324]) ).
fof(f12543,plain,
spl63_621,
inference(avatar_split_clause,[],[f6628,f12541]) ).
fof(f12541,plain,
( spl63_621
<=> ! [X0,X1] :
( nat_1(pls) = X1
| one_one(nat) = X0
| one_one(nat) != hAPP(nat,nat,power_power(nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_621])]) ).
fof(f6628,plain,
! [X0,X1] :
( nat_1(pls) = X1
| one_one(nat) = X0
| one_one(nat) != hAPP(nat,nat,power_power(nat,X0),X1) ),
inference(forward_demodulation,[],[f4928,f5811]) ).
fof(f4928,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,[],[f3495]) ).
fof(f3495,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,[],[f3494]) ).
fof(f3494,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,[],[f1941]) ).
fof(f1941,plain,
! [X0,X1] :
( one_one(nat) = hAPP(nat,nat,power_power(nat,X0),X1)
<=> ( zero_zero(nat) = X1
| one_one(nat) = X0 ) ),
inference(rectify,[],[f290]) ).
fof(f290,axiom,
! [X4,X16] :
( one_one(nat) = hAPP(nat,nat,power_power(nat,X4),X16)
<=> ( zero_zero(nat) = X16
| one_one(nat) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_exp__eq__1) ).
fof(f12539,plain,
spl63_620,
inference(avatar_split_clause,[],[f6607,f12537]) ).
fof(f12537,plain,
( spl63_620
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,X0,nat_1(pls)))
| sP12(X0,X1)
| ~ hBOOL(hAPP(nat,bool,X0,sK48(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_620])]) ).
fof(f6607,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,X0,nat_1(pls)))
| sP12(X0,X1)
| ~ hBOOL(hAPP(nat,bool,X0,sK48(X0,X1))) ),
inference(forward_demodulation,[],[f4917,f5811]) ).
fof(f4917,plain,
! [X0,X1] :
( sP12(X0,X1)
| ~ hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
| ~ hBOOL(hAPP(nat,bool,X0,sK48(X0,X1))) ),
inference(cnf_transformation,[],[f3485]) ).
fof(f12535,plain,
spl63_619,
inference(avatar_split_clause,[],[f6455,f12533]) ).
fof(f12533,plain,
( spl63_619
<=> ! [X0,X1] :
( ti(int,X0) = min
| ti(int,X0) = one_one(int)
| one_one(int) != times_times(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_619])]) ).
fof(f6455,plain,
! [X0,X1] :
( ti(int,X0) = min
| ti(int,X0) = one_one(int)
| one_one(int) != times_times(int,X0,X1) ),
inference(forward_demodulation,[],[f6454,f3874]) ).
fof(f6454,plain,
! [X0,X1] :
( ti(int,X0) = ti(int,min)
| ti(int,X0) = one_one(int)
| one_one(int) != times_times(int,X0,X1) ),
inference(forward_demodulation,[],[f4761,f3970]) ).
fof(f4761,plain,
! [X0,X1] :
( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int)
| one_one(int) != times_times(int,X0,X1) ),
inference(cnf_transformation,[],[f2803]) ).
fof(f2803,plain,
! [X0,X1] :
( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int)
| one_one(int) != times_times(int,X0,X1) ),
inference(flattening,[],[f2802]) ).
fof(f2802,plain,
! [X0,X1] :
( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int)
| one_one(int) != times_times(int,X0,X1) ),
inference(ennf_transformation,[],[f1846]) ).
fof(f1846,plain,
! [X0,X1] :
( one_one(int) = times_times(int,X0,X1)
=> ( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int) ) ),
inference(rectify,[],[f884]) ).
fof(f884,axiom,
! [X13,X14] :
( one_one(int) = times_times(int,X13,X14)
=> ( number_number_of(int,min) = ti(int,X13)
| one_one(int) = ti(int,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_pos__zmult__eq__1__iff__lemma) ).
fof(f12531,plain,
spl63_618,
inference(avatar_split_clause,[],[f6326,f12529]) ).
fof(f12529,plain,
( spl63_618
<=> ! [X0] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),nat_1(pls)))
| nat_1(pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_618])]) ).
fof(f6326,plain,
! [X0] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),nat_1(pls)))
| nat_1(pls) = X0 ),
inference(forward_demodulation,[],[f6325,f5811]) ).
fof(f6325,plain,
! [X0] :
( nat_1(pls) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat))) ),
inference(forward_demodulation,[],[f4598,f5811]) ).
fof(f4598,plain,
! [X0] :
( zero_zero(nat) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat))) ),
inference(cnf_transformation,[],[f3380]) ).
fof(f3380,plain,
! [X0] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat)))
| zero_zero(nat) != X0 )
& ( zero_zero(nat) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat))) ) ),
inference(nnf_transformation,[],[f1736]) ).
fof(f1736,plain,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat)))
<=> zero_zero(nat) = X0 ),
inference(rectify,[],[f700]) ).
fof(f700,axiom,
! [X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),zero_zero(nat)))
<=> zero_zero(nat) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_le__0__eq) ).
fof(f12527,plain,
spl63_617,
inference(avatar_split_clause,[],[f6310,f12525]) ).
fof(f12525,plain,
( spl63_617
<=> ! [X0] :
( nat_1(X0) != nat_1(pls)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_617])]) ).
fof(f6310,plain,
! [X0] :
( nat_1(X0) != nat_1(pls)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls)) ),
inference(forward_demodulation,[],[f6309,f5811]) ).
fof(f6309,plain,
! [X0] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls))
| nat_1(X0) != zero_zero(nat) ),
inference(forward_demodulation,[],[f4577,f3861]) ).
fof(f4577,plain,
! [X0] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),zero_zero(int)))
| nat_1(X0) != zero_zero(nat) ),
inference(cnf_transformation,[],[f3367]) ).
fof(f3367,plain,
! [X0] :
( ( nat_1(X0) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),zero_zero(int))) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),zero_zero(int)))
| nat_1(X0) != zero_zero(nat) ) ),
inference(nnf_transformation,[],[f1729]) ).
fof(f1729,plain,
! [X0] :
( nat_1(X0) = zero_zero(nat)
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),zero_zero(int))) ),
inference(rectify,[],[f413]) ).
fof(f413,axiom,
! [X33] :
( zero_zero(nat) = nat_1(X33)
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X33),zero_zero(int))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_nat__0__iff) ).
fof(f12523,plain,
spl63_616,
inference(avatar_split_clause,[],[f6197,f12521]) ).
fof(f6197,plain,
! [X0] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls))
| nat_1(X0) = nat_1(pls) ),
inference(forward_demodulation,[],[f6196,f3861]) ).
fof(f6196,plain,
! [X0] :
( nat_1(X0) = nat_1(pls)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),zero_zero(int))) ),
inference(forward_demodulation,[],[f4503,f5811]) ).
fof(f4503,plain,
! [X0] :
( nat_1(X0) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),zero_zero(int))) ),
inference(cnf_transformation,[],[f2698]) ).
fof(f2698,plain,
! [X0] :
( nat_1(X0) = zero_zero(nat)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),zero_zero(int))) ),
inference(ennf_transformation,[],[f1686]) ).
fof(f1686,plain,
! [X0] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),zero_zero(int)))
=> nat_1(X0) = zero_zero(nat) ),
inference(rectify,[],[f412]) ).
fof(f412,axiom,
! [X15] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X15),zero_zero(int)))
=> zero_zero(nat) = nat_1(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_nat__le__0) ).
fof(f12519,plain,
( spl63_615
| spl63_343
| ~ spl63_567 ),
inference(avatar_split_clause,[],[f12319,f12163,f9149,f12517]) ).
fof(f12517,plain,
( spl63_615
<=> ! [X0,X1] : sP15(X0,min,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_615])]) ).
fof(f9149,plain,
( spl63_343
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_343])]) ).
fof(f12163,plain,
( spl63_567
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| sP15(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_567])]) ).
fof(f12319,plain,
( ! [X0,X1] : sP15(X0,min,X1)
| spl63_343
| ~ spl63_567 ),
inference(resolution,[],[f12164,f9151]) ).
fof(f9151,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),min))
| spl63_343 ),
inference(avatar_component_clause,[],[f9149]) ).
fof(f12164,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| sP15(X0,X2,X1) )
| ~ spl63_567 ),
inference(avatar_component_clause,[],[f12163]) ).
fof(f12515,plain,
spl63_614,
inference(avatar_split_clause,[],[f6173,f12513]) ).
fof(f12513,plain,
( spl63_614
<=> ! [X0] :
( nat_1(pls) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_614])]) ).
fof(f6173,plain,
! [X0] :
( nat_1(pls) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),X0)) ),
inference(forward_demodulation,[],[f6172,f5811]) ).
fof(f6172,plain,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),X0))
| zero_zero(nat) = X0 ),
inference(forward_demodulation,[],[f4500,f5811]) ).
fof(f4500,plain,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
| zero_zero(nat) = X0 ),
inference(cnf_transformation,[],[f2694]) ).
fof(f2694,plain,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
| zero_zero(nat) = X0 ),
inference(ennf_transformation,[],[f1683]) ).
fof(f1683,plain,
! [X0] :
( zero_zero(nat) != X0
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0)) ),
inference(rectify,[],[f237]) ).
fof(f237,axiom,
! [X14] :
( zero_zero(nat) != X14
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_gr0I) ).
fof(f12506,plain,
( spl63_613
| ~ spl63_488
| ~ spl63_612 ),
inference(avatar_split_clause,[],[f12502,f12499,f11025,f12504]) ).
fof(f12504,plain,
( spl63_613
<=> ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,one_one(int),min))
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_613])]) ).
fof(f12499,plain,
( spl63_612
<=> ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min))
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_612])]) ).
fof(f12502,plain,
( ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,one_one(int),min))
| ~ number_semiring(X0) )
| ~ spl63_488
| ~ spl63_612 ),
inference(forward_demodulation,[],[f12500,f11027]) ).
fof(f12500,plain,
( ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min))
| ~ number_semiring(X0) )
| ~ spl63_612 ),
inference(avatar_component_clause,[],[f12499]) ).
fof(f12501,plain,
spl63_612,
inference(avatar_split_clause,[],[f6118,f12499]) ).
fof(f6118,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min))
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f6117,f5453]) ).
fof(f6117,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,plus_plus(int,pls,pls),min),min))
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f6116,f5453]) ).
fof(f6116,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,plus_plus(int,plus_plus(int,pls,pls),plus_plus(int,pls,pls)),min),min))
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f5561,f5502]) ).
fof(f5561,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min)))
| ~ number_semiring(X0) ),
inference(definition_unfolding,[],[f4344,f3968,f5445]) ).
fof(f4344,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls)))
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f2494]) ).
fof(f2494,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls)))
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f1537]) ).
fof(f1537,plain,
! [X0] :
( number_semiring(X0)
=> plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ),
inference(rectify,[],[f107]) ).
fof(f107,axiom,
! [X1] :
( number_semiring(X1)
=> plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_semiring__one__add__one__is__two) ).
fof(f12494,plain,
( spl63_611
| ~ spl63_488
| ~ spl63_610 ),
inference(avatar_split_clause,[],[f12490,f12487,f11025,f12492]) ).
fof(f12492,plain,
( spl63_611
<=> ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,one_one(int),min))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_611])]) ).
fof(f12487,plain,
( spl63_610
<=> ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_610])]) ).
fof(f12490,plain,
( ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,one_one(int),min))
| ~ number_ring(X0) )
| ~ spl63_488
| ~ spl63_610 ),
inference(forward_demodulation,[],[f12488,f11027]) ).
fof(f12488,plain,
( ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min))
| ~ number_ring(X0) )
| ~ spl63_610 ),
inference(avatar_component_clause,[],[f12487]) ).
fof(f12489,plain,
spl63_610,
inference(avatar_split_clause,[],[f6075,f12487]) ).
fof(f6075,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,pls,min),min))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f6074,f5453]) ).
fof(f6074,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,plus_plus(int,pls,pls),min),min))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f6073,f5453]) ).
fof(f6073,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,minus_minus(int,minus_minus(int,plus_plus(int,plus_plus(int,pls,pls),plus_plus(int,pls,pls)),min),min))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f5544,f5502]) ).
fof(f5544,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min)))
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f4231,f3968,f5445]) ).
fof(f4231,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls)))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2379]) ).
fof(f2379,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls)))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1441]) ).
fof(f1441,plain,
! [X0] :
( number_ring(X0)
=> plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X1] :
( number_ring(X1)
=> plus_plus(X1,one_one(X1),one_one(X1)) = number_number_of(X1,bit0(bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
fof(f12485,plain,
spl63_609,
inference(avatar_split_clause,[],[f5937,f12483]) ).
fof(f12483,plain,
( spl63_609
<=> ! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(nat,int,semiring_1_of_nat(int),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_609])]) ).
fof(f5937,plain,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(nat,int,semiring_1_of_nat(int),X0))),
inference(forward_demodulation,[],[f4019,f3861]) ).
fof(f4019,plain,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X0))),
inference(cnf_transformation,[],[f1317]) ).
fof(f1317,plain,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X0))),
inference(rectify,[],[f570]) ).
fof(f570,axiom,
! [X15] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),X15))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(f12481,plain,
spl63_608,
inference(avatar_split_clause,[],[f5936,f12479]) ).
fof(f12479,plain,
( spl63_608
<=> ! [X0] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X0)),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_608])]) ).
fof(f5936,plain,
! [X0] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X0)),pls)),
inference(forward_demodulation,[],[f4017,f3861]) ).
fof(f4017,plain,
! [X0] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X0)),zero_zero(int))),
inference(cnf_transformation,[],[f1315]) ).
fof(f1315,plain,
! [X0] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X0)),zero_zero(int))),
inference(rectify,[],[f159]) ).
fof(f159,axiom,
! [X19] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X19)),zero_zero(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_int__less__0__conv) ).
fof(f12477,plain,
spl63_607,
inference(avatar_split_clause,[],[f5922,f12475]) ).
fof(f12475,plain,
( spl63_607
<=> ! [X0] : minus_minus(int,min,plus_plus(int,X0,X0)) = minus_minus(int,pls,minus_minus(int,plus_plus(int,X0,X0),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_607])]) ).
fof(f5922,plain,
! [X0] : minus_minus(int,min,plus_plus(int,X0,X0)) = minus_minus(int,pls,minus_minus(int,plus_plus(int,X0,X0),min)),
inference(forward_demodulation,[],[f5509,f5506]) ).
fof(f5506,plain,
! [X0] : minus_minus(int,plus_plus(int,minus_minus(int,min,X0),minus_minus(int,min,X0)),min) = minus_minus(int,min,plus_plus(int,X0,X0)),
inference(definition_unfolding,[],[f3998,f5445,f3968]) ).
fof(f3998,plain,
! [X0] : bit1(minus_minus(int,min,X0)) = minus_minus(int,min,bit0(X0)),
inference(cnf_transformation,[],[f1296]) ).
fof(f1296,plain,
! [X0] : bit1(minus_minus(int,min,X0)) = minus_minus(int,min,bit0(X0)),
inference(rectify,[],[f882]) ).
fof(f882,axiom,
! [X29] : bit1(minus_minus(int,min,X29)) = minus_minus(int,min,bit0(X29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_diff__bin__simps_I5_J) ).
fof(f5509,plain,
! [X0] : minus_minus(int,plus_plus(int,minus_minus(int,min,X0),minus_minus(int,min,X0)),min) = minus_minus(int,pls,minus_minus(int,plus_plus(int,X0,X0),min)),
inference(definition_unfolding,[],[f4001,f5445,f5445]) ).
fof(f4001,plain,
! [X0] : bit1(minus_minus(int,min,X0)) = minus_minus(int,pls,bit1(X0)),
inference(cnf_transformation,[],[f1299]) ).
fof(f1299,plain,
! [X0] : bit1(minus_minus(int,min,X0)) = minus_minus(int,pls,bit1(X0)),
inference(rectify,[],[f880]) ).
fof(f880,axiom,
! [X29] : minus_minus(int,pls,bit1(X29)) = bit1(minus_minus(int,min,X29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_782_diff__bin__simps_I4_J) ).
fof(f12473,plain,
( spl63_606
| spl63_343
| ~ spl63_566 ),
inference(avatar_split_clause,[],[f12317,f12159,f9149,f12470]) ).
fof(f12470,plain,
( spl63_606
<=> sP13(nat_1(pls),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_606])]) ).
fof(f12159,plain,
( spl63_566
<=> ! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP13(nat_1(pls),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_566])]) ).
fof(f12317,plain,
( sP13(nat_1(pls),min)
| spl63_343
| ~ spl63_566 ),
inference(resolution,[],[f12160,f9151]) ).
fof(f12160,plain,
( ! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP13(nat_1(pls),X1) )
| ~ spl63_566 ),
inference(avatar_component_clause,[],[f12159]) ).
fof(f12468,plain,
spl63_605,
inference(avatar_split_clause,[],[f5710,f12466]) ).
fof(f12466,plain,
( spl63_605
<=> ! [X2,X0,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X2),times_times(X0,X2,X3)))
| ~ dvd(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_605])]) ).
fof(f5710,plain,
! [X2,X3,X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X2),times_times(X0,X2,X3)))
| ~ dvd(X0) ),
inference(equality_resolution,[],[f4383]) ).
fof(f4383,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X2),X1))
| times_times(X0,X2,X3) != X1
| ~ dvd(X0) ),
inference(cnf_transformation,[],[f2545]) ).
fof(f2545,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X2),X1))
| times_times(X0,X2,X3) != X1 )
| ~ dvd(X0) ),
inference(ennf_transformation,[],[f1573]) ).
fof(f1573,plain,
! [X0] :
( dvd(X0)
=> ! [X1,X2,X3] :
( times_times(X0,X2,X3) = X1
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X2),X1)) ) ),
inference(rectify,[],[f828]) ).
fof(f828,axiom,
! [X1] :
( dvd(X1)
=> ! [X30,X39,X19] :
( times_times(X1,X39,X19) = X30
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),dvd_dvd(X1),X39),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_dvdI) ).
fof(f12464,plain,
spl63_604,
inference(avatar_split_clause,[],[f5508,f12462]) ).
fof(f12462,plain,
( spl63_604
<=> ! [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_604])]) ).
fof(f5508,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,[],[f4000,f3968,f3968]) ).
fof(f4000,plain,
! [X0] : minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)),
inference(cnf_transformation,[],[f1298]) ).
fof(f1298,plain,
! [X0] : minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)),
inference(rectify,[],[f743]) ).
fof(f743,axiom,
! [X29] : minus_minus(int,pls,bit0(X29)) = bit0(minus_minus(int,pls,X29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_diff__bin__simps_I3_J) ).
fof(f12460,plain,
spl63_603,
inference(avatar_split_clause,[],[f5364,f12458]) ).
fof(f12458,plain,
( spl63_603
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2))))
| ~ sP19(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_603])]) ).
fof(f5364,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2))))
| ~ sP19(X0,X2,X1) ),
inference(cnf_transformation,[],[f3666]) ).
fof(f3666,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2))))
| ~ sP19(X0,X2,X1) )
& ( sP19(X0,X2,X1)
| ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2)))) ) ),
inference(nnf_transformation,[],[f3233]) ).
fof(f3233,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2))))
<=> sP19(X0,X2,X1) ),
inference(definition_folding,[],[f3143,f3232]) ).
fof(f3232,plain,
! [X0,X2,X1] :
( sP19(X0,X2,X1)
<=> ( ( hBOOL(hAPP(int,bool,X0,zero_zero(int)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
& ( hBOOL(hAPP(int,bool,X0,minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f3143,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2))))
<=> ( ( hBOOL(hAPP(int,bool,X0,zero_zero(int)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
& ( hBOOL(hAPP(int,bool,X0,minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ) ) ),
inference(ennf_transformation,[],[f2193]) ).
fof(f2193,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2))))
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> hBOOL(hAPP(int,bool,X0,zero_zero(int))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
=> hBOOL(hAPP(int,bool,X0,minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X2)))) ) ) ),
inference(rectify,[],[f1001]) ).
fof(f1001,axiom,
! [X32,X4,X5] :
( hBOOL(hAPP(int,bool,X32,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X4,X5))))
<=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X5))
=> hBOOL(hAPP(int,bool,X32,zero_zero(int))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X5),X4))
=> hBOOL(hAPP(int,bool,X32,minus_minus(int,hAPP(nat,int,semiring_1_of_nat(int),X4),hAPP(nat,int,semiring_1_of_nat(int),X5)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_zdiff__int__split) ).
fof(f12456,plain,
spl63_602,
inference(avatar_split_clause,[],[f5363,f12454]) ).
fof(f12454,plain,
( spl63_602
<=> ! [X2,X0,X1] :
( sP19(X0,X2,X1)
| ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_602])]) ).
fof(f5363,plain,
! [X2,X0,X1] :
( sP19(X0,X2,X1)
| ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),minus_minus(nat,X1,X2)))) ),
inference(cnf_transformation,[],[f3666]) ).
fof(f12452,plain,
spl63_601,
inference(avatar_split_clause,[],[f5117,f12450]) ).
fof(f12450,plain,
( spl63_601
<=> ! [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_601])]) ).
fof(f5117,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,[],[f2029]) ).
fof(f2029,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,[],[f480]) ).
fof(f480,axiom,
! [X24,X25,X7] : times_times(int,plus_plus(int,X24,X25),X7) = plus_plus(int,times_times(int,X24,X7),times_times(int,X25,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_zadd__zmult__distrib) ).
fof(f12448,plain,
spl63_600,
inference(avatar_split_clause,[],[f5116,f12446]) ).
fof(f12446,plain,
( spl63_600
<=> ! [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_600])]) ).
fof(f5116,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,[],[f2028]) ).
fof(f2028,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,[],[f690]) ).
fof(f690,axiom,
! [X24,X25,X7] : times_times(int,minus_minus(int,X24,X25),X7) = minus_minus(int,times_times(int,X24,X7),times_times(int,X25,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_zdiff__zmult__distrib) ).
fof(f12444,plain,
spl63_599,
inference(avatar_split_clause,[],[f5115,f12442]) ).
fof(f12442,plain,
( spl63_599
<=> ! [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_599])]) ).
fof(f5115,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,[],[f2027]) ).
fof(f2027,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,[],[f479]) ).
fof(f479,axiom,
! [X7,X24,X25] : times_times(int,X7,plus_plus(int,X24,X25)) = plus_plus(int,times_times(int,X7,X24),times_times(int,X7,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_zadd__zmult__distrib2) ).
fof(f12440,plain,
spl63_598,
inference(avatar_split_clause,[],[f5114,f12438]) ).
fof(f12438,plain,
( spl63_598
<=> ! [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_598])]) ).
fof(f5114,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,[],[f2026]) ).
fof(f2026,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,[],[f691]) ).
fof(f691,axiom,
! [X7,X24,X25] : times_times(int,X7,minus_minus(int,X24,X25)) = minus_minus(int,times_times(int,X7,X24),times_times(int,X7,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_zdiff__zmult__distrib2) ).
fof(f12436,plain,
spl63_597,
inference(avatar_split_clause,[],[f5113,f12434]) ).
fof(f12434,plain,
( spl63_597
<=> ! [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_597])]) ).
fof(f5113,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,[],[f2025]) ).
fof(f2025,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,[],[f710]) ).
fof(f710,axiom,
! [X13,X14,X19] : times_times(nat,plus_plus(nat,X13,X14),X19) = plus_plus(nat,times_times(nat,X13,X19),times_times(nat,X14,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_add__mult__distrib) ).
fof(f12432,plain,
spl63_596,
inference(avatar_split_clause,[],[f5112,f12430]) ).
fof(f12430,plain,
( spl63_596
<=> ! [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_596])]) ).
fof(f5112,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,[],[f2024]) ).
fof(f2024,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,[],[f728]) ).
fof(f728,axiom,
! [X13,X14,X19] : times_times(nat,minus_minus(nat,X13,X14),X19) = minus_minus(nat,times_times(nat,X13,X19),times_times(nat,X14,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_diff__mult__distrib) ).
fof(f12428,plain,
( spl63_595
| spl63_343
| ~ spl63_563 ),
inference(avatar_split_clause,[],[f12312,f12146,f9149,f12425]) ).
fof(f12425,plain,
( spl63_595
<=> sP10(nat_1(pls),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_595])]) ).
fof(f12146,plain,
( spl63_563
<=> ! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP10(nat_1(pls),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_563])]) ).
fof(f12312,plain,
( sP10(nat_1(pls),min)
| spl63_343
| ~ spl63_563 ),
inference(resolution,[],[f12147,f9151]) ).
fof(f12147,plain,
( ! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP10(nat_1(pls),X1) )
| ~ spl63_563 ),
inference(avatar_component_clause,[],[f12146]) ).
fof(f12423,plain,
spl63_594,
inference(avatar_split_clause,[],[f5111,f12421]) ).
fof(f12421,plain,
( spl63_594
<=> ! [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_594])]) ).
fof(f5111,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,[],[f2023]) ).
fof(f2023,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,[],[f711]) ).
fof(f711,axiom,
! [X19,X13,X14] : times_times(nat,X19,plus_plus(nat,X13,X14)) = plus_plus(nat,times_times(nat,X19,X13),times_times(nat,X19,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_add__mult__distrib2) ).
fof(f12419,plain,
spl63_593,
inference(avatar_split_clause,[],[f5110,f12417]) ).
fof(f12417,plain,
( spl63_593
<=> ! [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_593])]) ).
fof(f5110,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,[],[f2022]) ).
fof(f2022,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,[],[f729]) ).
fof(f729,axiom,
! [X19,X13,X14] : times_times(nat,X19,minus_minus(nat,X13,X14)) = minus_minus(nat,times_times(nat,X19,X13),times_times(nat,X19,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_diff__mult__distrib2) ).
fof(f12415,plain,
spl63_592,
inference(avatar_split_clause,[],[f5109,f12413]) ).
fof(f12413,plain,
( spl63_592
<=> ! [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_592])]) ).
fof(f5109,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,[],[f2021]) ).
fof(f2021,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,[],[f738]) ).
fof(f738,axiom,
! [X24,X25,X7] : times_times(real,plus_plus(real,X24,X25),X7) = plus_plus(real,times_times(real,X24,X7),times_times(real,X25,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_real__add__mult__distrib) ).
fof(f12411,plain,
spl63_591,
inference(avatar_split_clause,[],[f4705,f12409]) ).
fof(f12409,plain,
( spl63_591
<=> ! [X0,X1] : nat_1(abs_abs(int,times_times(int,X0,X1))) = times_times(nat,nat_1(abs_abs(int,X0)),nat_1(abs_abs(int,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_591])]) ).
fof(f4705,plain,
! [X0,X1] : nat_1(abs_abs(int,times_times(int,X0,X1))) = times_times(nat,nat_1(abs_abs(int,X0)),nat_1(abs_abs(int,X1))),
inference(cnf_transformation,[],[f1807]) ).
fof(f1807,plain,
! [X0,X1] : nat_1(abs_abs(int,times_times(int,X0,X1))) = times_times(nat,nat_1(abs_abs(int,X0)),nat_1(abs_abs(int,X1))),
inference(rectify,[],[f1016]) ).
fof(f1016,axiom,
! [X7,X15] : nat_1(abs_abs(int,times_times(int,X7,X15))) = times_times(nat,nat_1(abs_abs(int,X7)),nat_1(abs_abs(int,X15))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_nat__abs__mult__distrib) ).
fof(f12407,plain,
spl63_590,
inference(avatar_split_clause,[],[f4665,f12405]) ).
fof(f12405,plain,
( spl63_590
<=> ! [X2,X0] :
( hBOOL(hAPP(int,bool,X0,sK41(X0)))
| ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_590])]) ).
fof(f4665,plain,
! [X2,X0] :
( hBOOL(hAPP(int,bool,X0,sK41(X0)))
| ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(cnf_transformation,[],[f3427]) ).
fof(f3427,plain,
! [X0] :
( ( ( hBOOL(hAPP(int,bool,X0,sK41(X0)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK41(X0))) )
| ! [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) )
& ( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),sK42(X0))))
| ! [X4] :
( ~ hBOOL(hAPP(int,bool,X0,X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f3424,f3426,f3425]) ).
fof(f3425,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
=> ( hBOOL(hAPP(int,bool,X0,sK41(X0)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK41(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3426,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
=> hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),sK42(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f3424,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ! [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) )
& ( ? [X3] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
| ! [X4] :
( ~ hBOOL(hAPP(int,bool,X0,X4))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4)) ) ) ),
inference(rectify,[],[f3423]) ).
fof(f3423,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ! [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) )
& ( ? [X2] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ! [X1] :
( ~ hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) ) ),
inference(nnf_transformation,[],[f1767]) ).
fof(f1767,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
<=> ? [X2] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(rectify,[],[f571]) ).
fof(f571,axiom,
! [X32] :
( ? [X46] :
( hBOOL(hAPP(int,bool,X32,X46))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X46)) )
<=> ? [X46] : hBOOL(hAPP(int,bool,X32,hAPP(nat,int,semiring_1_of_nat(int),X46))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_transfer__int__nat__quantifiers_I2_J) ).
fof(f12403,plain,
spl63_589,
inference(avatar_split_clause,[],[f4658,f12401]) ).
fof(f12401,plain,
( spl63_589
<=> ! [X0,X3] :
( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
| ~ hBOOL(hAPP(int,bool,X0,sK38(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_589])]) ).
fof(f4658,plain,
! [X3,X0] :
( hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
| ~ hBOOL(hAPP(int,bool,X0,sK38(X0))) ),
inference(cnf_transformation,[],[f3417]) ).
fof(f3417,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),sK37(X0)))) )
& ( ! [X3] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
| ( ~ hBOOL(hAPP(int,bool,X0,sK38(X0)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK38(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f3414,f3416,f3415]) ).
fof(f3415,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2)))
=> ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),sK37(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f3416,plain,
! [X0] :
( ? [X4] :
( ~ hBOOL(hAPP(int,bool,X0,X4))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4)) )
=> ( ~ hBOOL(hAPP(int,bool,X0,sK38(X0)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK38(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3414,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ? [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) )
& ( ! [X3] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X3)))
| ? [X4] :
( ~ hBOOL(hAPP(int,bool,X0,X4))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4)) ) ) ),
inference(rectify,[],[f3413]) ).
fof(f3413,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ? [X2] : ~ hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) )
& ( ! [X2] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2)))
| ? [X1] :
( ~ hBOOL(hAPP(int,bool,X0,X1))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) ) ),
inference(nnf_transformation,[],[f2767]) ).
fof(f2767,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(int,bool,X0,X1))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
<=> ! [X2] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(ennf_transformation,[],[f1765]) ).
fof(f1765,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
=> hBOOL(hAPP(int,bool,X0,X1)) )
<=> ! [X2] : hBOOL(hAPP(int,bool,X0,hAPP(nat,int,semiring_1_of_nat(int),X2))) ),
inference(rectify,[],[f572]) ).
fof(f572,axiom,
! [X32] :
( ! [X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X46))
=> hBOOL(hAPP(int,bool,X32,X46)) )
<=> ! [X46] : hBOOL(hAPP(int,bool,X32,hAPP(nat,int,semiring_1_of_nat(int),X46))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_transfer__int__nat__quantifiers_I1_J) ).
fof(f12399,plain,
spl63_588,
inference(avatar_split_clause,[],[f4596,f12397]) ).
fof(f12397,plain,
( spl63_588
<=> ! [X0] :
( one_one(nat) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),one_one(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_588])]) ).
fof(f4596,plain,
! [X0] :
( one_one(nat) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),one_one(nat))) ),
inference(cnf_transformation,[],[f3379]) ).
fof(f3379,plain,
! [X0] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),one_one(nat)))
| one_one(nat) != X0 )
& ( one_one(nat) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),one_one(nat))) ) ),
inference(nnf_transformation,[],[f1735]) ).
fof(f1735,plain,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),one_one(nat)))
<=> one_one(nat) = X0 ),
inference(rectify,[],[f911]) ).
fof(f911,axiom,
! [X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X27),one_one(nat)))
<=> one_one(nat) = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_nat__dvd__1__iff__1) ).
fof(f12395,plain,
spl63_587,
inference(avatar_split_clause,[],[f4523,f12393]) ).
fof(f12393,plain,
( spl63_587
<=> ! [X0,X1] :
( one_one(X0) = abs_abs(X0,hAPP(nat,X0,power_power(X0,number_number_of(X0,min)),X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_587])]) ).
fof(f4523,plain,
! [X0,X1] :
( one_one(X0) = abs_abs(X0,hAPP(nat,X0,power_power(X0,number_number_of(X0,min)),X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2719]) ).
fof(f2719,plain,
! [X0] :
( ! [X1] : one_one(X0) = abs_abs(X0,hAPP(nat,X0,power_power(X0,number_number_of(X0,min)),X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f2718]) ).
fof(f2718,plain,
! [X0] :
( ! [X1] : one_one(X0) = abs_abs(X0,hAPP(nat,X0,power_power(X0,number_number_of(X0,min)),X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1701]) ).
fof(f1701,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] : one_one(X0) = abs_abs(X0,hAPP(nat,X0,power_power(X0,number_number_of(X0,min)),X1)) ),
inference(rectify,[],[f1056]) ).
fof(f1056,axiom,
! [X1] :
( ( linordered_idom(X1)
& number_ring(X1) )
=> ! [X14] : one_one(X1) = abs_abs(X1,hAPP(nat,X1,power_power(X1,number_number_of(X1,min)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_abs__power__minus__one) ).
fof(f12391,plain,
spl63_586,
inference(avatar_split_clause,[],[f4521,f12389]) ).
fof(f12389,plain,
( spl63_586
<=> ! [X2,X0,X1] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
| ti(int,X2) != ti(int,X1)
| ~ ring_char_0(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_586])]) ).
fof(f4521,plain,
! [X2,X0,X1] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
| ti(int,X2) != ti(int,X1)
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f3340]) ).
fof(f3340,plain,
! [X0] :
( ! [X1,X2] :
( ( number_number_of(X0,X1) = number_number_of(X0,X2)
| ti(int,X2) != ti(int,X1) )
& ( ti(int,X2) = ti(int,X1)
| number_number_of(X0,X1) != number_number_of(X0,X2) ) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f2715]) ).
fof(f2715,plain,
! [X0] :
( ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> ti(int,X2) = ti(int,X1) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f2714]) ).
fof(f2714,plain,
! [X0] :
( ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> ti(int,X2) = ti(int,X1) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1699]) ).
fof(f1699,plain,
! [X0] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> ti(int,X2) = ti(int,X1) ) ),
inference(rectify,[],[f138]) ).
fof(f138,axiom,
! [X1] :
( ( ring_char_0(X1)
& number_ring(X1) )
=> ! [X4,X5] :
( number_number_of(X1,X4) = number_number_of(X1,X5)
<=> ti(int,X4) = ti(int,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_eq__number__of) ).
fof(f12387,plain,
spl63_585,
inference(avatar_split_clause,[],[f4520,f12385]) ).
fof(f12385,plain,
( spl63_585
<=> ! [X2,X0,X1] :
( ti(int,X2) = ti(int,X1)
| number_number_of(X0,X1) != number_number_of(X0,X2)
| ~ ring_char_0(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_585])]) ).
fof(f4520,plain,
! [X2,X0,X1] :
( ti(int,X2) = ti(int,X1)
| number_number_of(X0,X1) != number_number_of(X0,X2)
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f3340]) ).
fof(f12383,plain,
( spl63_584
| spl63_343
| ~ spl63_562 ),
inference(avatar_split_clause,[],[f12310,f12142,f9149,f12380]) ).
fof(f12380,plain,
( spl63_584
<=> sP9(nat_1(pls),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_584])]) ).
fof(f12142,plain,
( spl63_562
<=> ! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP9(nat_1(pls),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_562])]) ).
fof(f12310,plain,
( sP9(nat_1(pls),min)
| spl63_343
| ~ spl63_562 ),
inference(resolution,[],[f12143,f9151]) ).
fof(f12143,plain,
( ! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP9(nat_1(pls),X1) )
| ~ spl63_562 ),
inference(avatar_component_clause,[],[f12142]) ).
fof(f12378,plain,
spl63_583,
inference(avatar_split_clause,[],[f4464,f12376]) ).
fof(f12376,plain,
( spl63_583
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),times_times(X0,X1,X2)))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_583])]) ).
fof(f4464,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),times_times(X0,X1,X2)))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2653]) ).
fof(f2653,plain,
! [X0] :
( ! [X1,X2] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),times_times(X0,X1,X2)))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1648]) ).
fof(f1648,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),times_times(X0,X1,X2))) ),
inference(rectify,[],[f833]) ).
fof(f833,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30,X39] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),dvd_dvd(X1),X30),times_times(X1,X30,X39))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_dvd__triv__left) ).
fof(f12374,plain,
spl63_582,
inference(avatar_split_clause,[],[f4463,f12372]) ).
fof(f12372,plain,
( spl63_582
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),times_times(X0,X2,X1)))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_582])]) ).
fof(f4463,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),times_times(X0,X2,X1)))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2652]) ).
fof(f2652,plain,
! [X0] :
( ! [X1,X2] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),times_times(X0,X2,X1)))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1647]) ).
fof(f1647,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),times_times(X0,X2,X1))) ),
inference(rectify,[],[f832]) ).
fof(f832,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30,X39] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),dvd_dvd(X1),X30),times_times(X1,X39,X30))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_dvd__triv__right) ).
fof(f12370,plain,
spl63_581,
inference(avatar_split_clause,[],[f4462,f12368]) ).
fof(f12368,plain,
( spl63_581
<=> ! [X2,X0,X1] :
( times_times(X0,plus_plus(X0,X1,one_one(X0)),X2) = plus_plus(X0,times_times(X0,X1,X2),X2)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_581])]) ).
fof(f4462,plain,
! [X2,X0,X1] :
( times_times(X0,plus_plus(X0,X1,one_one(X0)),X2) = plus_plus(X0,times_times(X0,X1,X2),X2)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2651]) ).
fof(f2651,plain,
! [X0] :
( ! [X1,X2] : times_times(X0,plus_plus(X0,X1,one_one(X0)),X2) = plus_plus(X0,times_times(X0,X1,X2),X2)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1646]) ).
fof(f1646,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2] : times_times(X0,plus_plus(X0,X1,one_one(X0)),X2) = plus_plus(X0,times_times(X0,X1,X2),X2) ),
inference(rectify,[],[f545]) ).
fof(f545,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30,X13] : times_times(X1,plus_plus(X1,X30,one_one(X1)),X13) = plus_plus(X1,times_times(X1,X30,X13),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(f12366,plain,
spl63_580,
inference(avatar_split_clause,[],[f4461,f12364]) ).
fof(f12364,plain,
( spl63_580
<=> ! [X2,X0,X1] :
( plus_plus(X0,X1,times_times(X0,X2,X1)) = times_times(X0,plus_plus(X0,X2,one_one(X0)),X1)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_580])]) ).
fof(f4461,plain,
! [X2,X0,X1] :
( plus_plus(X0,X1,times_times(X0,X2,X1)) = times_times(X0,plus_plus(X0,X2,one_one(X0)),X1)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2650]) ).
fof(f2650,plain,
! [X0] :
( ! [X1,X2] : plus_plus(X0,X1,times_times(X0,X2,X1)) = times_times(X0,plus_plus(X0,X2,one_one(X0)),X1)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1645]) ).
fof(f1645,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2] : plus_plus(X0,X1,times_times(X0,X2,X1)) = times_times(X0,plus_plus(X0,X2,one_one(X0)),X1) ),
inference(rectify,[],[f544]) ).
fof(f544,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X13,X30] : plus_plus(X1,X13,times_times(X1,X30,X13)) = times_times(X1,plus_plus(X1,X30,one_one(X1)),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(f12362,plain,
spl63_579,
inference(avatar_split_clause,[],[f4318,f12360]) ).
fof(f12360,plain,
( spl63_579
<=> ! [X0,X3,X2,X1] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X3,X2)
| ti(X0,X1) != ti(X0,X3)
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_579])]) ).
fof(f4318,plain,
! [X2,X3,X0,X1] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X3,X2)
| ti(X0,X1) != ti(X0,X3)
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f3322]) ).
fof(f3322,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( plus_plus(X0,X1,X2) = plus_plus(X0,X3,X2)
| ti(X0,X1) != ti(X0,X3) )
& ( ti(X0,X1) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X3,X2) ) )
| ~ cancel_semigroup_add(X0) ),
inference(nnf_transformation,[],[f2473]) ).
fof(f2473,plain,
! [X0] :
( ! [X1,X2,X3] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X3,X2)
<=> ti(X0,X1) = ti(X0,X3) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f1516]) ).
fof(f1516,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X1,X2,X3] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X3,X2)
<=> ti(X0,X1) = ti(X0,X3) ) ),
inference(rectify,[],[f301]) ).
fof(f301,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X41,X6,X45] :
( plus_plus(X1,X41,X6) = plus_plus(X1,X45,X6)
<=> ti(X1,X41) = ti(X1,X45) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_add__right__cancel) ).
fof(f12358,plain,
spl63_578,
inference(avatar_split_clause,[],[f4316,f12356]) ).
fof(f12356,plain,
( spl63_578
<=> ! [X0,X3,X2,X1] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X1,X3)
| ti(X0,X2) != ti(X0,X3)
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_578])]) ).
fof(f4316,plain,
! [X2,X3,X0,X1] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X1,X3)
| ti(X0,X2) != ti(X0,X3)
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f3321]) ).
fof(f3321,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( plus_plus(X0,X1,X2) = plus_plus(X0,X1,X3)
| ti(X0,X2) != ti(X0,X3) )
& ( ti(X0,X2) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X1,X3) ) )
| ~ cancel_semigroup_add(X0) ),
inference(nnf_transformation,[],[f2472]) ).
fof(f2472,plain,
! [X0] :
( ! [X1,X2,X3] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X1,X3)
<=> ti(X0,X2) = ti(X0,X3) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f1515]) ).
fof(f1515,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X1,X2,X3] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X1,X3)
<=> ti(X0,X2) = ti(X0,X3) ) ),
inference(rectify,[],[f302]) ).
fof(f302,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X6,X41,X45] :
( plus_plus(X1,X6,X41) = plus_plus(X1,X6,X45)
<=> ti(X1,X41) = ti(X1,X45) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_add__left__cancel) ).
fof(f12354,plain,
spl63_577,
inference(avatar_split_clause,[],[f4314,f12352]) ).
fof(f12352,plain,
( spl63_577
<=> ! [X0,X3,X2,X1] :
( ti(X0,X1) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X3,X2)
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_577])]) ).
fof(f4314,plain,
! [X2,X3,X0,X1] :
( ti(X0,X1) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X3,X2)
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f2471]) ).
fof(f2471,plain,
! [X0] :
( ! [X1,X2,X3] :
( ti(X0,X1) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X3,X2) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f1514]) ).
fof(f1514,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X1,X2,X3] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X3,X2)
=> ti(X0,X1) = ti(X0,X3) ) ),
inference(rectify,[],[f297]) ).
fof(f297,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X39,X30,X40] :
( plus_plus(X1,X39,X30) = plus_plus(X1,X40,X30)
=> ti(X1,X39) = ti(X1,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_add__right__imp__eq) ).
fof(f12350,plain,
spl63_576,
inference(avatar_split_clause,[],[f4313,f12348]) ).
fof(f12348,plain,
( spl63_576
<=> ! [X0,X3,X2,X1] :
( ti(X0,X2) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X1,X3)
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_576])]) ).
fof(f4313,plain,
! [X2,X3,X0,X1] :
( ti(X0,X2) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X1,X3)
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f2470]) ).
fof(f2470,plain,
! [X0] :
( ! [X1,X2,X3] :
( ti(X0,X2) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X1,X3) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f1513]) ).
fof(f1513,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X1,X2,X3] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X1,X3)
=> ti(X0,X2) = ti(X0,X3) ) ),
inference(rectify,[],[f299]) ).
fof(f299,axiom,
! [X1] :
( cancel_semigroup_add(X1)
=> ! [X30,X39,X40] :
( plus_plus(X1,X30,X40) = plus_plus(X1,X30,X39)
=> ti(X1,X39) = ti(X1,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_add__left__imp__eq) ).
fof(f12346,plain,
spl63_575,
inference(avatar_split_clause,[],[f4259,f12344]) ).
fof(f12344,plain,
( spl63_575
<=> ! [X0,X3,X2,X1] :
( ti(X0,X2) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X1,X3)
| ~ cancel146912293up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_575])]) ).
fof(f4259,plain,
! [X2,X3,X0,X1] :
( ti(X0,X2) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X1,X3)
| ~ cancel146912293up_add(X0) ),
inference(cnf_transformation,[],[f2405]) ).
fof(f2405,plain,
! [X0] :
( ! [X1,X2,X3] :
( ti(X0,X2) = ti(X0,X3)
| plus_plus(X0,X1,X2) != plus_plus(X0,X1,X3) )
| ~ cancel146912293up_add(X0) ),
inference(ennf_transformation,[],[f1467]) ).
fof(f1467,plain,
! [X0] :
( cancel146912293up_add(X0)
=> ! [X1,X2,X3] :
( plus_plus(X0,X1,X2) = plus_plus(X0,X1,X3)
=> ti(X0,X2) = ti(X0,X3) ) ),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X1] :
( cancel146912293up_add(X1)
=> ! [X30,X39,X40] :
( plus_plus(X1,X30,X40) = plus_plus(X1,X30,X39)
=> ti(X1,X39) = ti(X1,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_add__imp__eq) ).
fof(f12342,plain,
spl63_574,
inference(avatar_split_clause,[],[f4256,f12340]) ).
fof(f12340,plain,
( spl63_574
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP(nat,X0,semiring_1_of_nat(X0),X2) != hAPP(nat,X0,semiring_1_of_nat(X0),X1)
| ~ semiring_char_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_574])]) ).
fof(f4256,plain,
! [X2,X0,X1] :
( X1 = X2
| hAPP(nat,X0,semiring_1_of_nat(X0),X2) != hAPP(nat,X0,semiring_1_of_nat(X0),X1)
| ~ semiring_char_0(X0) ),
inference(cnf_transformation,[],[f3313]) ).
fof(f3313,plain,
! [X0] :
( ! [X1,X2] :
( ( hAPP(nat,X0,semiring_1_of_nat(X0),X2) = hAPP(nat,X0,semiring_1_of_nat(X0),X1)
| X1 != X2 )
& ( X1 = X2
| hAPP(nat,X0,semiring_1_of_nat(X0),X2) != hAPP(nat,X0,semiring_1_of_nat(X0),X1) ) )
| ~ semiring_char_0(X0) ),
inference(nnf_transformation,[],[f2403]) ).
fof(f2403,plain,
! [X0] :
( ! [X1,X2] :
( hAPP(nat,X0,semiring_1_of_nat(X0),X2) = hAPP(nat,X0,semiring_1_of_nat(X0),X1)
<=> X1 = X2 )
| ~ semiring_char_0(X0) ),
inference(ennf_transformation,[],[f1465]) ).
fof(f1465,plain,
! [X0] :
( semiring_char_0(X0)
=> ! [X1,X2] :
( hAPP(nat,X0,semiring_1_of_nat(X0),X2) = hAPP(nat,X0,semiring_1_of_nat(X0),X1)
<=> X1 = X2 ) ),
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X1] :
( semiring_char_0(X1)
=> ! [X27,X16] :
( hAPP(nat,X1,semiring_1_of_nat(X1),X16) = hAPP(nat,X1,semiring_1_of_nat(X1),X27)
<=> X16 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_of__nat__eq__iff) ).
fof(f12338,plain,
( spl63_573
| ~ spl63_352
| ~ spl63_551 ),
inference(avatar_split_clause,[],[f12264,f12086,f9191,f12336]) ).
fof(f12336,plain,
( spl63_573
<=> ! [X0] : sP13(nat_1(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_573])]) ).
fof(f9191,plain,
( spl63_352
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_352])]) ).
fof(f12086,plain,
( spl63_551
<=> ! [X0,X1] :
( sP13(X1,X0)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_551])]) ).
fof(f12264,plain,
( ! [X0] : sP13(nat_1(X0),X0)
| ~ spl63_352
| ~ spl63_551 ),
inference(resolution,[],[f12087,f9192]) ).
fof(f9192,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),X0))
| ~ spl63_352 ),
inference(avatar_component_clause,[],[f9191]) ).
fof(f12087,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1))
| sP13(X1,X0) )
| ~ spl63_551 ),
inference(avatar_component_clause,[],[f12086]) ).
fof(f12334,plain,
spl63_572,
inference(avatar_split_clause,[],[f4172,f12332]) ).
fof(f12332,plain,
( spl63_572
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),abs_abs(X0,X1)))
| ~ ordere142940540dd_abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_572])]) ).
fof(f4172,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),abs_abs(X0,X1)))
| ~ ordere142940540dd_abs(X0) ),
inference(cnf_transformation,[],[f2329]) ).
fof(f2329,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),abs_abs(X0,X1)))
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f1395]) ).
fof(f1395,plain,
! [X0] :
( ordere142940540dd_abs(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),abs_abs(X0,X1))) ),
inference(rectify,[],[f1047]) ).
fof(f1047,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X30] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),abs_abs(X1,X30))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_abs__ge__zero) ).
fof(f12330,plain,
spl63_571,
inference(avatar_split_clause,[],[f4171,f12328]) ).
fof(f12328,plain,
( spl63_571
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),abs_abs(X0,X1)),zero_zero(X0)))
| ~ ordere142940540dd_abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_571])]) ).
fof(f4171,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),abs_abs(X0,X1)),zero_zero(X0)))
| ~ ordere142940540dd_abs(X0) ),
inference(cnf_transformation,[],[f2328]) ).
fof(f2328,plain,
! [X0] :
( ! [X1] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),abs_abs(X0,X1)),zero_zero(X0)))
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f1394]) ).
fof(f1394,plain,
! [X0] :
( ordere142940540dd_abs(X0)
=> ! [X1] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),abs_abs(X0,X1)),zero_zero(X0))) ),
inference(rectify,[],[f1044]) ).
fof(f1044,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X30] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),abs_abs(X1,X30)),zero_zero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_abs__not__less__zero) ).
fof(f12326,plain,
spl63_570,
inference(avatar_split_clause,[],[f4051,f12324]) ).
fof(f4051,plain,
! [X2,X0,X1] :
( zero_zero(X0) != hAPP(nat,X0,power_power(X0,X2),X1)
| zero_zero(X0) = ti(X0,X2)
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f2268]) ).
fof(f2268,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) != hAPP(nat,X0,power_power(X0,X2),X1)
| zero_zero(X0) = ti(X0,X2) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f1340]) ).
fof(f1340,plain,
! [X0] :
( ring_11004092258visors(X0)
=> ! [X1,X2] :
( zero_zero(X0) != ti(X0,X2)
=> zero_zero(X0) != hAPP(nat,X0,power_power(X0,X2),X1) ) ),
inference(rectify,[],[f263]) ).
fof(f263,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X14,X30] :
( zero_zero(X1) != ti(X1,X30)
=> zero_zero(X1) != hAPP(nat,X1,power_power(X1,X30),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_field__power__not__zero) ).
fof(f12246,plain,
( ~ spl63_147
| ~ spl63_569
| ~ spl63_156
| ~ spl63_501
| ~ spl63_540 ),
inference(avatar_split_clause,[],[f12213,f12042,f11183,f7772,f12243,f7727]) ).
fof(f7727,plain,
( spl63_147
<=> linordered_semidom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_147])]) ).
fof(f12243,plain,
( spl63_569
<=> sP8(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_569])]) ).
fof(f11183,plain,
( spl63_501
<=> ! [X0] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_501])]) ).
fof(f12042,plain,
( spl63_540
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_540])]) ).
fof(f12213,plain,
( ~ sP8(pls)
| ~ linordered_semidom(int)
| ~ spl63_156
| ~ spl63_501
| ~ spl63_540 ),
inference(forward_demodulation,[],[f12209,f7774]) ).
fof(f12209,plain,
( ~ linordered_semidom(int)
| ~ sP8(zero_zero(int))
| ~ spl63_501
| ~ spl63_540 ),
inference(resolution,[],[f12043,f11184]) ).
fof(f11184,plain,
( ! [X0] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0))
| ~ sP8(X0) )
| ~ spl63_501 ),
inference(avatar_component_clause,[],[f11183]) ).
fof(f12043,plain,
( ! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) )
| ~ spl63_540 ),
inference(avatar_component_clause,[],[f12042]) ).
fof(f12169,plain,
spl63_568,
inference(avatar_split_clause,[],[f6850,f12167]) ).
fof(f12167,plain,
( spl63_568
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| sP16(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_568])]) ).
fof(f6850,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| sP16(X0,X2,X1) ),
inference(forward_demodulation,[],[f5311,f3861]) ).
fof(f5311,plain,
! [X2,X0,X1] :
( sP16(X0,X2,X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(cnf_transformation,[],[f3628]) ).
fof(f3628,plain,
! [X0,X1,X2] :
( sP16(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(flattening,[],[f3627]) ).
fof(f3627,plain,
! [X0,X1,X2] :
( sP16(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(nnf_transformation,[],[f3227]) ).
fof(f3227,plain,
! [X0,X1,X2] :
( sP16(X0,X2,X1)
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(definition_folding,[],[f3136,f3226]) ).
fof(f3226,plain,
! [X0,X2,X1] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
<=> ( hBOOL(X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
| ~ sP16(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f3136,plain,
! [X0,X1,X2] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
<=> ( hBOOL(X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(ennf_transformation,[],[f2180]) ).
fof(f2180,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
=> ( hBOOL(X1)
<=> hBOOL(X0) ) )
=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
=> hBOOL(X1) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
=> hBOOL(X0) ) ) ),
inference(rectify,[],[f1004]) ).
fof(f1004,axiom,
! [X76,X32,X4] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4))
=> ( hBOOL(X32)
<=> hBOOL(X76) ) )
=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4))
=> hBOOL(X32) )
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4))
=> hBOOL(X76) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_imp__le__cong) ).
fof(f12165,plain,
spl63_567,
inference(avatar_split_clause,[],[f6847,f12163]) ).
fof(f6847,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X2))
| sP15(X0,X2,X1) ),
inference(forward_demodulation,[],[f5304,f3861]) ).
fof(f5304,plain,
! [X2,X0,X1] :
( sP15(X0,X2,X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ),
inference(cnf_transformation,[],[f3623]) ).
fof(f3623,plain,
! [X0,X1,X2] :
( sP15(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(flattening,[],[f3622]) ).
fof(f3622,plain,
! [X0,X1,X2] :
( sP15(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(nnf_transformation,[],[f3225]) ).
fof(f3225,plain,
! [X0,X1,X2] :
( sP15(X0,X2,X1)
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(definition_folding,[],[f3135,f3224]) ).
fof(f3224,plain,
! [X0,X2,X1] :
( ( ( hBOOL(X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
| ~ sP15(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f3135,plain,
! [X0,X1,X2] :
( ( ( hBOOL(X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(ennf_transformation,[],[f2179]) ).
fof(f2179,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
=> ( hBOOL(X1)
<=> hBOOL(X0) ) )
=> ( ( hBOOL(X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ) ),
inference(rectify,[],[f1003]) ).
fof(f1003,axiom,
! [X76,X32,X4] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4))
=> ( hBOOL(X32)
<=> hBOOL(X76) ) )
=> ( ( hBOOL(X32)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4)) )
<=> ( hBOOL(X76)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_conj__le__cong) ).
fof(f12161,plain,
spl63_566,
inference(avatar_split_clause,[],[f6651,f12159]) ).
fof(f6651,plain,
! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP13(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6650,f3861]) ).
fof(f6650,plain,
! [X1] :
( sP13(nat_1(pls),X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(forward_demodulation,[],[f5772,f5811]) ).
fof(f5772,plain,
! [X1] :
( sP13(zero_zero(nat),X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(equality_resolution,[],[f4982]) ).
fof(f4982,plain,
! [X0,X1] :
( sP13(X0,X1)
| zero_zero(nat) != X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(cnf_transformation,[],[f3532]) ).
fof(f3532,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ( zero_zero(nat) != X0
& ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X0)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) )
& ( ( ( zero_zero(nat) = X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X0)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) )
| ~ sP13(X0,X1) ) ),
inference(rectify,[],[f3531]) ).
fof(f3531,plain,
! [X1,X0] :
( ( sP13(X1,X0)
| ( zero_zero(nat) != X1
& ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
| ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X0),hAPP(nat,int,semiring_1_of_nat(int),X1)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) )
& ( ( ( zero_zero(nat) = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X0),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) )
| ~ sP13(X1,X0) ) ),
inference(flattening,[],[f3530]) ).
fof(f3530,plain,
! [X1,X0] :
( ( sP13(X1,X0)
| ( zero_zero(nat) != X1
& ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
| ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X0),hAPP(nat,int,semiring_1_of_nat(int),X1)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) )
& ( ( ( zero_zero(nat) = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X0),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) )
| ~ sP13(X1,X0) ) ),
inference(nnf_transformation,[],[f3220]) ).
fof(f3220,plain,
! [X1,X0] :
( sP13(X1,X0)
<=> ( ( zero_zero(nat) = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X0),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f12157,plain,
( ~ spl63_565
| spl63_527
| ~ spl63_180
| ~ spl63_227
| ~ spl63_277
| ~ spl63_493 ),
inference(avatar_split_clause,[],[f11563,f11150,f8528,f8119,f7894,f11641,f12154]) ).
fof(f12154,plain,
( spl63_565
<=> group_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_565])]) ).
fof(f11641,plain,
( spl63_527
<=> ! [X0] : nat_1(pls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_527])]) ).
fof(f7894,plain,
( spl63_180
<=> zero_zero(nat) = nat_1(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_180])]) ).
fof(f8119,plain,
( spl63_227
<=> ! [X0] : nat_1(pls) = minus_minus(nat,nat_1(pls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_227])]) ).
fof(f8528,plain,
( spl63_277
<=> ! [X0] : ti(nat,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_277])]) ).
fof(f11563,plain,
( ! [X0] :
( nat_1(pls) = X0
| ~ group_add(nat) )
| ~ spl63_180
| ~ spl63_227
| ~ spl63_277
| ~ spl63_493 ),
inference(forward_demodulation,[],[f11562,f8529]) ).
fof(f8529,plain,
( ! [X0] : ti(nat,X0) = X0
| ~ spl63_277 ),
inference(avatar_component_clause,[],[f8528]) ).
fof(f11562,plain,
( ! [X0] :
( ti(nat,X0) = nat_1(pls)
| ~ group_add(nat) )
| ~ spl63_180
| ~ spl63_227
| ~ spl63_277
| ~ spl63_493 ),
inference(forward_demodulation,[],[f11561,f8529]) ).
fof(f11561,plain,
( ! [X0] :
( ti(nat,X0) = ti(nat,nat_1(pls))
| ~ group_add(nat) )
| ~ spl63_180
| ~ spl63_227
| ~ spl63_493 ),
inference(trivial_inequality_removal,[],[f11560]) ).
fof(f11560,plain,
( ! [X0] :
( nat_1(pls) != nat_1(pls)
| ti(nat,X0) = ti(nat,nat_1(pls))
| ~ group_add(nat) )
| ~ spl63_180
| ~ spl63_227
| ~ spl63_493 ),
inference(forward_demodulation,[],[f11528,f7896]) ).
fof(f7896,plain,
( zero_zero(nat) = nat_1(pls)
| ~ spl63_180 ),
inference(avatar_component_clause,[],[f7894]) ).
fof(f11528,plain,
( ! [X0] :
( zero_zero(nat) != nat_1(pls)
| ti(nat,X0) = ti(nat,nat_1(pls))
| ~ group_add(nat) )
| ~ spl63_227
| ~ spl63_493 ),
inference(superposition,[],[f11151,f8120]) ).
fof(f8120,plain,
( ! [X0] : nat_1(pls) = minus_minus(nat,nat_1(pls),X0)
| ~ spl63_227 ),
inference(avatar_component_clause,[],[f8119]) ).
fof(f12152,plain,
spl63_564,
inference(avatar_split_clause,[],[f6649,f12150]) ).
fof(f12150,plain,
( spl63_564
<=> ! [X1] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),pls))
| sP13(nat_1(pls),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_564])]) ).
fof(f6649,plain,
! [X1] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),pls))
| sP13(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6648,f5821]) ).
fof(f5821,plain,
pls = hAPP(nat,int,semiring_1_of_nat(int),nat_1(pls)),
inference(forward_demodulation,[],[f5820,f3861]) ).
fof(f5820,plain,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),nat_1(pls)),
inference(forward_demodulation,[],[f3891,f5811]) ).
fof(f3891,plain,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
inference(cnf_transformation,[],[f126]) ).
fof(f126,axiom,
zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_int__0) ).
fof(f6648,plain,
! [X1] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),hAPP(nat,int,semiring_1_of_nat(int),nat_1(pls))))
| sP13(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6647,f5811]) ).
fof(f6647,plain,
! [X1] :
( sP13(nat_1(pls),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)))) ),
inference(forward_demodulation,[],[f5771,f5811]) ).
fof(f5771,plain,
! [X1] :
( sP13(zero_zero(nat),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)))) ),
inference(equality_resolution,[],[f4983]) ).
fof(f4983,plain,
! [X0,X1] :
( sP13(X0,X1)
| zero_zero(nat) != X0
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),hAPP(nat,int,semiring_1_of_nat(int),X0))) ),
inference(cnf_transformation,[],[f3532]) ).
fof(f12148,plain,
spl63_563,
inference(avatar_split_clause,[],[f6578,f12146]) ).
fof(f6578,plain,
! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP10(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6577,f3861]) ).
fof(f6577,plain,
! [X1] :
( sP10(nat_1(pls),X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(forward_demodulation,[],[f5743,f5811]) ).
fof(f5743,plain,
! [X1] :
( sP10(zero_zero(nat),X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(equality_resolution,[],[f4879]) ).
fof(f4879,plain,
! [X0,X1] :
( sP10(X0,X1)
| zero_zero(nat) != X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(cnf_transformation,[],[f3462]) ).
fof(f3462,plain,
! [X0,X1] :
( ( sP10(X0,X1)
| ( zero_zero(nat) != X0
& ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ( ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) )
& ( ( ( zero_zero(nat) = X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& ( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) )
| ~ sP10(X0,X1) ) ),
inference(rectify,[],[f3461]) ).
fof(f3461,plain,
! [X1,X0] :
( ( sP10(X1,X0)
| ( zero_zero(nat) != X1
& ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
| ( ti(int,X0) != hAPP(nat,int,semiring_1_of_nat(int),X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) )
& ( ( ( zero_zero(nat) = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
& ( ti(int,X0) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) )
| ~ sP10(X1,X0) ) ),
inference(flattening,[],[f3460]) ).
fof(f3460,plain,
! [X1,X0] :
( ( sP10(X1,X0)
| ( zero_zero(nat) != X1
& ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
| ( ti(int,X0) != hAPP(nat,int,semiring_1_of_nat(int),X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) )
& ( ( ( zero_zero(nat) = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
& ( ti(int,X0) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) )
| ~ sP10(X1,X0) ) ),
inference(nnf_transformation,[],[f3214]) ).
fof(f3214,plain,
! [X1,X0] :
( sP10(X1,X0)
<=> ( ( zero_zero(nat) = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
& ( ti(int,X0) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f12144,plain,
spl63_562,
inference(avatar_split_clause,[],[f6569,f12142]) ).
fof(f6569,plain,
! [X1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),X1))
| sP9(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6568,f3861]) ).
fof(f6568,plain,
! [X1] :
( sP9(nat_1(pls),X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(forward_demodulation,[],[f5740,f5811]) ).
fof(f5740,plain,
! [X1] :
( sP9(zero_zero(nat),X1)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(equality_resolution,[],[f4871]) ).
fof(f4871,plain,
! [X0,X1] :
( sP9(X0,X1)
| zero_zero(nat) != X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ),
inference(cnf_transformation,[],[f3458]) ).
fof(f3458,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( zero_zero(nat) != X0
& ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ( ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) )
& ( ( ( zero_zero(nat) = X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& ( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) )
| ~ sP9(X0,X1) ) ),
inference(flattening,[],[f3457]) ).
fof(f3457,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( zero_zero(nat) != X0
& ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ( ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) )
& ( ( ( zero_zero(nat) = X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& ( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) )
| ~ sP9(X0,X1) ) ),
inference(nnf_transformation,[],[f3212]) ).
fof(f3212,plain,
! [X0,X1] :
( sP9(X0,X1)
<=> ( ( zero_zero(nat) = X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& ( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f12140,plain,
spl63_561,
inference(avatar_split_clause,[],[f6457,f12138]) ).
fof(f12138,plain,
( spl63_561
<=> ! [X0,X1] :
( minus_minus(nat,X0,X1) != nat_1(pls)
| minus_minus(nat,X1,X0) != nat_1(pls)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_561])]) ).
fof(f6457,plain,
! [X0,X1] :
( minus_minus(nat,X0,X1) != nat_1(pls)
| minus_minus(nat,X1,X0) != nat_1(pls)
| X0 = X1 ),
inference(forward_demodulation,[],[f6456,f5811]) ).
fof(f6456,plain,
! [X0,X1] :
( minus_minus(nat,X1,X0) != nat_1(pls)
| X0 = X1
| zero_zero(nat) != minus_minus(nat,X0,X1) ),
inference(forward_demodulation,[],[f4762,f5811]) ).
fof(f4762,plain,
! [X0,X1] :
( X0 = X1
| zero_zero(nat) != minus_minus(nat,X1,X0)
| zero_zero(nat) != minus_minus(nat,X0,X1) ),
inference(cnf_transformation,[],[f2805]) ).
fof(f2805,plain,
! [X0,X1] :
( X0 = X1
| zero_zero(nat) != minus_minus(nat,X1,X0)
| zero_zero(nat) != minus_minus(nat,X0,X1) ),
inference(flattening,[],[f2804]) ).
fof(f2804,plain,
! [X0,X1] :
( X0 = X1
| zero_zero(nat) != minus_minus(nat,X1,X0)
| zero_zero(nat) != minus_minus(nat,X0,X1) ),
inference(ennf_transformation,[],[f1847]) ).
fof(f1847,plain,
! [X0,X1] :
( zero_zero(nat) = minus_minus(nat,X0,X1)
=> ( zero_zero(nat) = minus_minus(nat,X1,X0)
=> X0 = X1 ) ),
inference(rectify,[],[f433]) ).
fof(f433,axiom,
! [X13,X14] :
( zero_zero(nat) = minus_minus(nat,X13,X14)
=> ( zero_zero(nat) = minus_minus(nat,X14,X13)
=> X13 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_diffs0__imp__equal) ).
fof(f12134,plain,
( spl63_560
| ~ spl63_204
| ~ spl63_520
| ~ spl63_559 ),
inference(avatar_split_clause,[],[f12129,f12124,f11314,f8010,f12131]) ).
fof(f12131,plain,
( spl63_560
<=> hBOOL(hAPP(int,bool,zprime,hAPP(nat,int,semiring_1_of_nat(int),nat_1(minus_minus(int,one_one(int),min))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_560])]) ).
fof(f12124,plain,
( spl63_559
<=> 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_559])]) ).
fof(f12129,plain,
( hBOOL(hAPP(int,bool,zprime,hAPP(nat,int,semiring_1_of_nat(int),nat_1(minus_minus(int,one_one(int),min)))))
| ~ spl63_204
| ~ spl63_520
| ~ spl63_559 ),
inference(forward_demodulation,[],[f12128,f11325]) ).
fof(f12128,plain,
( hBOOL(hAPP(int,bool,zprime,hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat)))))
| ~ spl63_559 ),
inference(forward_demodulation,[],[f12126,f5836]) ).
fof(f5836,plain,
number_number_of(int,plus_plus(int,minus_minus(int,pls,min),minus_minus(int,pls,min))) = hAPP(nat,int,semiring_1_of_nat(int),plus_plus(nat,one_one(nat),one_one(nat))),
inference(forward_demodulation,[],[f5835,f5826]) ).
fof(f5835,plain,
number_number_of(int,plus_plus(int,minus_minus(int,pls,min),minus_minus(int,pls,min))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,plus_plus(int,minus_minus(int,pls,min),minus_minus(int,pls,min)))),
inference(forward_demodulation,[],[f5462,f5453]) ).
fof(f5462,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,semiring_1_of_nat(int),number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min)))),
inference(definition_unfolding,[],[f3914,f3968,f5445,f3968,f5445]) ).
fof(f3914,plain,
number_number_of(int,bit0(bit1(pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f202]) ).
fof(f202,axiom,
number_number_of(int,bit0(bit1(pls))) = hAPP(nat,int,semiring_1_of_nat(int),number_number_of(nat,bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_transfer__int__nat__numerals_I3_J) ).
fof(f12126,plain,
( hBOOL(hAPP(int,bool,zprime,number_number_of(int,plus_plus(int,minus_minus(int,pls,min),minus_minus(int,pls,min)))))
| ~ spl63_559 ),
inference(avatar_component_clause,[],[f12124]) ).
fof(f12127,plain,
spl63_559,
inference(avatar_split_clause,[],[f5824,f12124]) ).
fof(f5824,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,[],[f5458,f5453]) ).
fof(f5458,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,[],[f3893,f3968,f5445]) ).
fof(f3893,plain,
hBOOL(hAPP(int,bool,zprime,number_number_of(int,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f816]) ).
fof(f816,axiom,
hBOOL(hAPP(int,bool,zprime,number_number_of(int,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_zprime__2) ).
fof(f12119,plain,
( spl63_558
| ~ spl63_111
| ~ spl63_270
| ~ spl63_557 ),
inference(avatar_split_clause,[],[f12114,f12110,f8500,f7547,f12116]) ).
fof(f12116,plain,
( spl63_558
<=> zero_zero(real) = plus_plus(real,zero_zero(real),zero_zero(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_558])]) ).
fof(f7547,plain,
( spl63_111
<=> mult_zero(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_111])]) ).
fof(f8500,plain,
( spl63_270
<=> ! [X0,X1] :
( zero_zero(X0) = times_times(X0,X1,zero_zero(X0))
| ~ mult_zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_270])]) ).
fof(f12110,plain,
( spl63_557
<=> zero_zero(real) = plus_plus(real,times_times(real,zero_zero(real),zero_zero(real)),times_times(real,zero_zero(real),zero_zero(real))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_557])]) ).
fof(f12114,plain,
( zero_zero(real) = plus_plus(real,zero_zero(real),zero_zero(real))
| ~ spl63_111
| ~ spl63_270
| ~ spl63_557 ),
inference(forward_demodulation,[],[f12112,f8562]) ).
fof(f8562,plain,
( ! [X0] : zero_zero(real) = times_times(real,X0,zero_zero(real))
| ~ spl63_111
| ~ spl63_270 ),
inference(resolution,[],[f8501,f7549]) ).
fof(f7549,plain,
( mult_zero(real)
| ~ spl63_111 ),
inference(avatar_component_clause,[],[f7547]) ).
fof(f8501,plain,
( ! [X0,X1] :
( ~ mult_zero(X0)
| zero_zero(X0) = times_times(X0,X1,zero_zero(X0)) )
| ~ spl63_270 ),
inference(avatar_component_clause,[],[f8500]) ).
fof(f12112,plain,
( zero_zero(real) = plus_plus(real,times_times(real,zero_zero(real),zero_zero(real)),times_times(real,zero_zero(real),zero_zero(real)))
| ~ spl63_557 ),
inference(avatar_component_clause,[],[f12110]) ).
fof(f12113,plain,
spl63_557,
inference(avatar_split_clause,[],[f5762,f12110]) ).
fof(f5762,plain,
zero_zero(real) = plus_plus(real,times_times(real,zero_zero(real),zero_zero(real)),times_times(real,zero_zero(real),zero_zero(real))),
inference(equality_resolution,[],[f5761]) ).
fof(f5761,plain,
! [X0] :
( zero_zero(real) = plus_plus(real,times_times(real,X0,X0),times_times(real,zero_zero(real),zero_zero(real)))
| zero_zero(real) != X0 ),
inference(equality_resolution,[],[f4942]) ).
fof(f4942,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(cnf_transformation,[],[f3503]) ).
fof(f3503,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,[],[f3502]) ).
fof(f3502,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,[],[f1945]) ).
fof(f1945,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,[],[f758]) ).
fof(f758,axiom,
! [X4,X5] :
( zero_zero(real) = plus_plus(real,times_times(real,X4,X4),times_times(real,X5,X5))
<=> ( zero_zero(real) = X5
& zero_zero(real) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_real__two__squares__add__zero__iff) ).
fof(f12108,plain,
spl63_556,
inference(avatar_split_clause,[],[f5294,f12106]) ).
fof(f12106,plain,
( spl63_556
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_556])]) ).
fof(f5294,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3618]) ).
fof(f3618,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2,X1),X0))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) )
| ~ sP14(X0,X1,X2) ),
inference(rectify,[],[f3617]) ).
fof(f3617,plain,
! [X1,X2,X0] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
| ~ sP14(X1,X2,X0) ),
inference(nnf_transformation,[],[f3222]) ).
fof(f3222,plain,
! [X1,X2,X0] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
| ~ sP14(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f12104,plain,
spl63_555,
inference(avatar_split_clause,[],[f5168,f12102]) ).
fof(f12102,plain,
( spl63_555
<=> ! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,ti(fun(X2,bool),X0),X1)
| ~ order(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_555])]) ).
fof(f5168,plain,
! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,ti(fun(X2,bool),X0),X1)
| ~ order(X2) ),
inference(cnf_transformation,[],[f2977]) ).
fof(f2977,plain,
! [X0,X1,X2] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,ti(fun(X2,bool),X0),X1)
| ~ order(X2) ),
inference(ennf_transformation,[],[f2077]) ).
fof(f2077,plain,
! [X0,X1,X2] :
( order(X2)
=> hAPP(X2,bool,X0,X1) = hAPP(X2,bool,ti(fun(X2,bool),X0),X1) ),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
! [X0,X2,X1] :
( order(X1)
=> hAPP(X1,bool,ti(fun(X1,bool),X0),X2) = hAPP(X1,bool,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_1_arg1) ).
fof(f12100,plain,
spl63_554,
inference(avatar_split_clause,[],[f5162,f12098]) ).
fof(f12098,plain,
( spl63_554
<=> ! [X2,X0,X1] :
( hAPP(nat,X2,X0,X1) = hAPP(nat,X2,ti(fun(nat,X2),X0),X1)
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_554])]) ).
fof(f5162,plain,
! [X2,X0,X1] :
( hAPP(nat,X2,X0,X1) = hAPP(nat,X2,ti(fun(nat,X2),X0),X1)
| ~ power(X2) ),
inference(cnf_transformation,[],[f2971]) ).
fof(f2971,plain,
! [X0,X1,X2] :
( hAPP(nat,X2,X0,X1) = hAPP(nat,X2,ti(fun(nat,X2),X0),X1)
| ~ power(X2) ),
inference(ennf_transformation,[],[f2071]) ).
fof(f2071,plain,
! [X0,X1,X2] :
( power(X2)
=> hAPP(nat,X2,X0,X1) = hAPP(nat,X2,ti(fun(nat,X2),X0),X1) ),
inference(rectify,[],[f85]) ).
fof(f85,axiom,
! [X0,X2,X1] :
( power(X1)
=> hAPP(nat,X1,ti(fun(nat,X1),X0),X2) = hAPP(nat,X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_4_arg1) ).
fof(f12096,plain,
spl63_553,
inference(avatar_split_clause,[],[f5161,f12094]) ).
fof(f12094,plain,
( spl63_553
<=> ! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,ti(fun(X2,bool),X0),X1)
| ~ dvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_553])]) ).
fof(f5161,plain,
! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,ti(fun(X2,bool),X0),X1)
| ~ dvd(X2) ),
inference(cnf_transformation,[],[f2970]) ).
fof(f2970,plain,
! [X0,X1,X2] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,ti(fun(X2,bool),X0),X1)
| ~ dvd(X2) ),
inference(ennf_transformation,[],[f2070]) ).
fof(f2070,plain,
! [X0,X1,X2] :
( dvd(X2)
=> hAPP(X2,bool,X0,X1) = hAPP(X2,bool,ti(fun(X2,bool),X0),X1) ),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X0,X2,X1] :
( dvd(X1)
=> hAPP(X1,bool,ti(fun(X1,bool),X0),X2) = hAPP(X1,bool,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_3_arg1) ).
fof(f12092,plain,
spl63_552,
inference(avatar_split_clause,[],[f4985,f12090]) ).
fof(f12090,plain,
( spl63_552
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1))
| ~ sP13(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_552])]) ).
fof(f4985,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1))
| ~ sP13(X1,X0) ),
inference(cnf_transformation,[],[f3533]) ).
fof(f3533,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1))
| ~ sP13(X1,X0) )
& ( sP13(X1,X0)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1)) ) ),
inference(nnf_transformation,[],[f3221]) ).
fof(f3221,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1))
<=> sP13(X1,X0) ),
inference(definition_folding,[],[f2930,f3220]) ).
fof(f2930,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1))
<=> ( ( zero_zero(nat) = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X0),hAPP(nat,int,semiring_1_of_nat(int),X1)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) ) ),
inference(ennf_transformation,[],[f1960]) ).
fof(f1960,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1))
<=> ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0))
=> zero_zero(nat) = X1 )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X0),hAPP(nat,int,semiring_1_of_nat(int),X1))) ) ) ),
inference(rectify,[],[f933]) ).
fof(f933,axiom,
! [X28,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X28)),X27))
<=> ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X28))
=> zero_zero(nat) = X27 )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X28))
=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X28),hAPP(nat,int,semiring_1_of_nat(int),X27))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_nat__dvd__iff) ).
fof(f12088,plain,
spl63_551,
inference(avatar_split_clause,[],[f4984,f12086]) ).
fof(f4984,plain,
! [X0,X1] :
( sP13(X1,X0)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),nat_1(X0)),X1)) ),
inference(cnf_transformation,[],[f3533]) ).
fof(f12084,plain,
spl63_550,
inference(avatar_split_clause,[],[f4941,f12082]) ).
fof(f12082,plain,
( spl63_550
<=> ! [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_550])]) ).
fof(f4941,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,[],[f3503]) ).
fof(f12080,plain,
spl63_549,
inference(avatar_split_clause,[],[f4940,f12078]) ).
fof(f12078,plain,
( spl63_549
<=> ! [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_549])]) ).
fof(f4940,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,[],[f3503]) ).
fof(f12076,plain,
spl63_548,
inference(avatar_split_clause,[],[f4475,f12074]) ).
fof(f12074,plain,
( spl63_548
<=> ! [X0,X3,X2,X1] :
( times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,times_times(X0,X1,X3),X2)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_548])]) ).
fof(f4475,plain,
! [X2,X3,X0,X1] :
( times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,times_times(X0,X1,X3),X2)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2663]) ).
fof(f2663,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,times_times(X0,X1,X3),X2)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1658]) ).
fof(f1658,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2,X3] : times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,times_times(X0,X1,X3),X2) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X49,X52,X50] : times_times(X1,times_times(X1,X49,X52),X50) = times_times(X1,times_times(X1,X49,X50),X52) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(f12072,plain,
spl63_547,
inference(avatar_split_clause,[],[f4473,f12070]) ).
fof(f12070,plain,
( spl63_547
<=> ! [X0,X3,X2,X1] :
( times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,X1,times_times(X0,X2,X3))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_547])]) ).
fof(f4473,plain,
! [X2,X3,X0,X1] :
( times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,X1,times_times(X0,X2,X3))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2661]) ).
fof(f2661,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,X1,times_times(X0,X2,X3))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1656]) ).
fof(f1656,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2,X3] : times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,X1,times_times(X0,X2,X3)) ),
inference(rectify,[],[f339]) ).
fof(f339,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X49,X50,X51] : times_times(X1,X49,times_times(X1,X50,X51)) = times_times(X1,times_times(X1,X49,X50),X51) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(f12068,plain,
spl63_546,
inference(avatar_split_clause,[],[f4472,f12066]) ).
fof(f12066,plain,
( spl63_546
<=> ! [X0,X3,X2,X1] :
( times_times(X0,X1,times_times(X0,X2,X3)) = times_times(X0,X2,times_times(X0,X1,X3))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_546])]) ).
fof(f4472,plain,
! [X2,X3,X0,X1] :
( times_times(X0,X1,times_times(X0,X2,X3)) = times_times(X0,X2,times_times(X0,X1,X3))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2660]) ).
fof(f2660,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,X1,times_times(X0,X2,X3)) = times_times(X0,X2,times_times(X0,X1,X3))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1655]) ).
fof(f1655,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2,X3] : times_times(X0,X1,times_times(X0,X2,X3)) = times_times(X0,X2,times_times(X0,X1,X3)) ),
inference(rectify,[],[f338]) ).
fof(f338,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X49,X50,X51] : times_times(X1,X49,times_times(X1,X50,X51)) = times_times(X1,X50,times_times(X1,X49,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f12064,plain,
spl63_545,
inference(avatar_split_clause,[],[f4471,f12062]) ).
fof(f12062,plain,
( spl63_545
<=> ! [X0,X3,X2,X1] :
( plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,plus_plus(X0,X1,X3),X2)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_545])]) ).
fof(f4471,plain,
! [X2,X3,X0,X1] :
( plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,plus_plus(X0,X1,X3),X2)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2659]) ).
fof(f2659,plain,
! [X0] :
( ! [X1,X2,X3] : plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,plus_plus(X0,X1,X3),X2)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1654]) ).
fof(f1654,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2,X3] : plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,plus_plus(X0,X1,X3),X2) ),
inference(rectify,[],[f303]) ).
fof(f303,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30,X39,X40] : plus_plus(X1,plus_plus(X1,X30,X39),X40) = plus_plus(X1,plus_plus(X1,X30,X40),X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(f12060,plain,
spl63_544,
inference(avatar_split_clause,[],[f4469,f12058]) ).
fof(f12058,plain,
( spl63_544
<=> ! [X0,X3,X2,X1] :
( plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,X1,plus_plus(X0,X2,X3))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_544])]) ).
fof(f4469,plain,
! [X2,X3,X0,X1] :
( plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,X1,plus_plus(X0,X2,X3))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2657]) ).
fof(f2657,plain,
! [X0] :
( ! [X1,X2,X3] : plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,X1,plus_plus(X0,X2,X3))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1652]) ).
fof(f1652,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2,X3] : plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,X1,plus_plus(X0,X2,X3)) ),
inference(rectify,[],[f306]) ).
fof(f306,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30,X40,X44] : plus_plus(X1,X30,plus_plus(X1,X40,X44)) = plus_plus(X1,plus_plus(X1,X30,X40),X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f12056,plain,
spl63_543,
inference(avatar_split_clause,[],[f4468,f12054]) ).
fof(f12054,plain,
( spl63_543
<=> ! [X0,X3,X2,X1] :
( plus_plus(X0,X1,plus_plus(X0,X2,X3)) = plus_plus(X0,X2,plus_plus(X0,X1,X3))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_543])]) ).
fof(f4468,plain,
! [X2,X3,X0,X1] :
( plus_plus(X0,X1,plus_plus(X0,X2,X3)) = plus_plus(X0,X2,plus_plus(X0,X1,X3))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2656]) ).
fof(f2656,plain,
! [X0] :
( ! [X1,X2,X3] : plus_plus(X0,X1,plus_plus(X0,X2,X3)) = plus_plus(X0,X2,plus_plus(X0,X1,X3))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1651]) ).
fof(f1651,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2,X3] : plus_plus(X0,X1,plus_plus(X0,X2,X3)) = plus_plus(X0,X2,plus_plus(X0,X1,X3)) ),
inference(rectify,[],[f307]) ).
fof(f307,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30,X40,X44] : plus_plus(X1,X30,plus_plus(X1,X40,X44)) = plus_plus(X1,X40,plus_plus(X1,X30,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(f12052,plain,
spl63_542,
inference(avatar_split_clause,[],[f4403,f12050]) ).
fof(f12050,plain,
( spl63_542
<=> ! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_542])]) ).
fof(f4403,plain,
! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f2581]) ).
fof(f2581,plain,
! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f1593]) ).
fof(f1593,plain,
! [X0] :
( linordered_semidom(X0)
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0))) ),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_zero__less__one) ).
fof(f12048,plain,
spl63_541,
inference(avatar_split_clause,[],[f4402,f12046]) ).
fof(f12046,plain,
( spl63_541
<=> ! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_541])]) ).
fof(f4402,plain,
! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f2580]) ).
fof(f2580,plain,
! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f1592]) ).
fof(f1592,plain,
! [X0] :
( linordered_semidom(X0)
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),one_one(X0))) ),
inference(rectify,[],[f540]) ).
fof(f540,axiom,
! [X1] :
( linordered_semidom(X1)
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_zero__le__one) ).
fof(f12044,plain,
spl63_540,
inference(avatar_split_clause,[],[f4401,f12042]) ).
fof(f4401,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f2579]) ).
fof(f2579,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f1591]) ).
fof(f1591,plain,
! [X0] :
( linordered_semidom(X0)
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0))) ),
inference(rectify,[],[f275]) ).
fof(f275,axiom,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_not__one__less__zero) ).
fof(f12040,plain,
spl63_539,
inference(avatar_split_clause,[],[f4400,f12038]) ).
fof(f12038,plain,
( spl63_539
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_539])]) ).
fof(f4400,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f2578]) ).
fof(f2578,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f1590]) ).
fof(f1590,plain,
! [X0] :
( linordered_semidom(X0)
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),one_one(X0)),zero_zero(X0))) ),
inference(rectify,[],[f539]) ).
fof(f539,axiom,
! [X1] :
( linordered_semidom(X1)
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_not__one__le__zero) ).
fof(f12036,plain,
spl63_538,
inference(avatar_split_clause,[],[f4347,f12034]) ).
fof(f12034,plain,
( spl63_538
<=> ! [X0,X1] :
( hAPP(nat,X0,semiring_1_of_nat(X0),X1) = number_number_of(X0,hAPP(nat,int,semiring_1_of_nat(int),X1))
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_538])]) ).
fof(f4347,plain,
! [X0,X1] :
( hAPP(nat,X0,semiring_1_of_nat(X0),X1) = number_number_of(X0,hAPP(nat,int,semiring_1_of_nat(int),X1))
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f2497]) ).
fof(f2497,plain,
! [X0] :
( ! [X1] : hAPP(nat,X0,semiring_1_of_nat(X0),X1) = number_number_of(X0,hAPP(nat,int,semiring_1_of_nat(int),X1))
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f1540]) ).
fof(f1540,plain,
! [X0] :
( number_semiring(X0)
=> ! [X1] : hAPP(nat,X0,semiring_1_of_nat(X0),X1) = number_number_of(X0,hAPP(nat,int,semiring_1_of_nat(int),X1)) ),
inference(rectify,[],[f192]) ).
fof(f192,axiom,
! [X1] :
( number_semiring(X1)
=> ! [X14] : number_number_of(X1,hAPP(nat,int,semiring_1_of_nat(int),X14)) = hAPP(nat,X1,semiring_1_of_nat(X1),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_number__of__int) ).
fof(f12032,plain,
spl63_537,
inference(avatar_split_clause,[],[f4283,f12030]) ).
fof(f12030,plain,
( spl63_537
<=> ! [X0,X3,X2,X1] :
( times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,X1,times_times(X0,X2,X3))
| ~ ab_semigroup_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_537])]) ).
fof(f4283,plain,
! [X2,X3,X0,X1] :
( times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,X1,times_times(X0,X2,X3))
| ~ ab_semigroup_mult(X0) ),
inference(cnf_transformation,[],[f2431]) ).
fof(f2431,plain,
! [X0] :
( ! [X1,X2,X3] : times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,X1,times_times(X0,X2,X3))
| ~ ab_semigroup_mult(X0) ),
inference(ennf_transformation,[],[f1488]) ).
fof(f1488,plain,
! [X0] :
( ab_semigroup_mult(X0)
=> ! [X1,X2,X3] : times_times(X0,times_times(X0,X1,X2),X3) = times_times(X0,X1,times_times(X0,X2,X3)) ),
inference(rectify,[],[f340]) ).
fof(f340,axiom,
! [X1] :
( ab_semigroup_mult(X1)
=> ! [X30,X39,X40] : times_times(X1,times_times(X1,X30,X39),X40) = times_times(X1,X30,times_times(X1,X39,X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(f12028,plain,
( spl63_536
| ~ spl63_353
| ~ spl63_512 ),
inference(avatar_split_clause,[],[f11853,f11228,f9195,f12026]) ).
fof(f12026,plain,
( spl63_536
<=> ! [X0] : ~ sP14(X0,X0,ord_less_eq(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_536])]) ).
fof(f9195,plain,
( spl63_353
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_353])]) ).
fof(f11228,plain,
( spl63_512
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2,X1),X0))
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_512])]) ).
fof(f11853,plain,
( ! [X0] : ~ sP14(X0,X0,ord_less_eq(nat))
| ~ spl63_353
| ~ spl63_512 ),
inference(resolution,[],[f11229,f9196]) ).
fof(f9196,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0))
| ~ spl63_353 ),
inference(avatar_component_clause,[],[f9195]) ).
fof(f11229,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2,X1),X0))
| ~ sP14(X0,X1,X2) )
| ~ spl63_512 ),
inference(avatar_component_clause,[],[f11228]) ).
fof(f12024,plain,
spl63_535,
inference(avatar_split_clause,[],[f4282,f12022]) ).
fof(f12022,plain,
( spl63_535
<=> ! [X0,X3,X2,X1] :
( plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,X1,plus_plus(X0,X2,X3))
| ~ ab_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_535])]) ).
fof(f4282,plain,
! [X2,X3,X0,X1] :
( plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,X1,plus_plus(X0,X2,X3))
| ~ ab_semigroup_add(X0) ),
inference(cnf_transformation,[],[f2430]) ).
fof(f2430,plain,
! [X0] :
( ! [X1,X2,X3] : plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,X1,plus_plus(X0,X2,X3))
| ~ ab_semigroup_add(X0) ),
inference(ennf_transformation,[],[f1487]) ).
fof(f1487,plain,
! [X0] :
( ab_semigroup_add(X0)
=> ! [X1,X2,X3] : plus_plus(X0,plus_plus(X0,X1,X2),X3) = plus_plus(X0,X1,plus_plus(X0,X2,X3)) ),
inference(rectify,[],[f304]) ).
fof(f304,axiom,
! [X1] :
( ab_semigroup_add(X1)
=> ! [X30,X39,X40] : plus_plus(X1,plus_plus(X1,X30,X39),X40) = plus_plus(X1,X30,plus_plus(X1,X39,X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(f12020,plain,
spl63_534,
inference(avatar_split_clause,[],[f4250,f12018]) ).
fof(f12018,plain,
( spl63_534
<=> ! [X2,X0,X1] :
( number_number_of(X0,times_times(int,X1,X2)) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_534])]) ).
fof(f4250,plain,
! [X2,X0,X1] :
( number_number_of(X0,times_times(int,X1,X2)) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2397]) ).
fof(f2397,plain,
! [X0] :
( ! [X1,X2] : number_number_of(X0,times_times(int,X1,X2)) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1459]) ).
fof(f1459,plain,
! [X0] :
( number_ring(X0)
=> ! [X1,X2] : number_number_of(X0,times_times(int,X1,X2)) = times_times(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ),
inference(rectify,[],[f357]) ).
fof(f357,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8,X7] : number_number_of(X1,times_times(int,X8,X7)) = times_times(X1,number_number_of(X1,X8),number_number_of(X1,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_arith__simps_I32_J) ).
fof(f12016,plain,
spl63_533,
inference(avatar_split_clause,[],[f4248,f12014]) ).
fof(f12014,plain,
( spl63_533
<=> ! [X2,X0,X1] :
( number_number_of(X0,plus_plus(int,X1,X2)) = plus_plus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_533])]) ).
fof(f4248,plain,
! [X2,X0,X1] :
( number_number_of(X0,plus_plus(int,X1,X2)) = plus_plus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2395]) ).
fof(f2395,plain,
! [X0] :
( ! [X1,X2] : number_number_of(X0,plus_plus(int,X1,X2)) = plus_plus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1457]) ).
fof(f1457,plain,
! [X0] :
( number_ring(X0)
=> ! [X1,X2] : number_number_of(X0,plus_plus(int,X1,X2)) = plus_plus(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ),
inference(rectify,[],[f187]) ).
fof(f187,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8,X7] : number_number_of(X1,plus_plus(int,X8,X7)) = plus_plus(X1,number_number_of(X1,X8),number_number_of(X1,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_number__of__add) ).
fof(f12012,plain,
spl63_532,
inference(avatar_split_clause,[],[f4247,f12010]) ).
fof(f12010,plain,
( spl63_532
<=> ! [X2,X0,X1] :
( number_number_of(X0,minus_minus(int,X1,X2)) = minus_minus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_532])]) ).
fof(f4247,plain,
! [X2,X0,X1] :
( number_number_of(X0,minus_minus(int,X1,X2)) = minus_minus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2394]) ).
fof(f2394,plain,
! [X0] :
( ! [X1,X2] : number_number_of(X0,minus_minus(int,X1,X2)) = minus_minus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1456]) ).
fof(f1456,plain,
! [X0] :
( number_ring(X0)
=> ! [X1,X2] : number_number_of(X0,minus_minus(int,X1,X2)) = minus_minus(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ),
inference(rectify,[],[f362]) ).
fof(f362,axiom,
! [X1] :
( number_ring(X1)
=> ! [X8,X7] : number_number_of(X1,minus_minus(int,X8,X7)) = minus_minus(X1,number_number_of(X1,X8),number_number_of(X1,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_number__of__diff) ).
fof(f12008,plain,
spl63_531,
inference(avatar_split_clause,[],[f4201,f12006]) ).
fof(f12006,plain,
( spl63_531
<=> ! [X2,X0,X1] :
( abs_abs(X0,times_times(X0,X1,X2)) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X2))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_531])]) ).
fof(f4201,plain,
! [X2,X0,X1] :
( abs_abs(X0,times_times(X0,X1,X2)) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X2))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f2353]) ).
fof(f2353,plain,
! [X0] :
( ! [X1,X2] : abs_abs(X0,times_times(X0,X1,X2)) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X2))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f1419]) ).
fof(f1419,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1,X2] : abs_abs(X0,times_times(X0,X1,X2)) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X2)) ),
inference(rectify,[],[f1049]) ).
fof(f1049,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X30,X39] : abs_abs(X1,times_times(X1,X30,X39)) = times_times(X1,abs_abs(X1,X30),abs_abs(X1,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_abs__mult) ).
fof(f12004,plain,
spl63_530,
inference(avatar_split_clause,[],[f4192,f12002]) ).
fof(f12002,plain,
( spl63_530
<=> ! [X0,X1] :
( hAPP(nat,X0,semiring_1_of_nat(X0),X1) = abs_abs(X0,hAPP(nat,X0,semiring_1_of_nat(X0),X1))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_530])]) ).
fof(f4192,plain,
! [X0,X1] :
( hAPP(nat,X0,semiring_1_of_nat(X0),X1) = abs_abs(X0,hAPP(nat,X0,semiring_1_of_nat(X0),X1))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f2346]) ).
fof(f2346,plain,
! [X0] :
( ! [X1] : hAPP(nat,X0,semiring_1_of_nat(X0),X1) = abs_abs(X0,hAPP(nat,X0,semiring_1_of_nat(X0),X1))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f1412]) ).
fof(f1412,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1] : hAPP(nat,X0,semiring_1_of_nat(X0),X1) = abs_abs(X0,hAPP(nat,X0,semiring_1_of_nat(X0),X1)) ),
inference(rectify,[],[f1033]) ).
fof(f1033,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X14] : hAPP(nat,X1,semiring_1_of_nat(X1),X14) = abs_abs(X1,hAPP(nat,X1,semiring_1_of_nat(X1),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_abs__of__nat) ).
fof(f12000,plain,
spl63_529,
inference(avatar_split_clause,[],[f4170,f11998]) ).
fof(f11998,plain,
( spl63_529
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),abs_abs(X0,X1)))
| ~ ordere142940540dd_abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_529])]) ).
fof(f4170,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),abs_abs(X0,X1)))
| ~ ordere142940540dd_abs(X0) ),
inference(cnf_transformation,[],[f2327]) ).
fof(f2327,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),abs_abs(X0,X1)))
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f1393]) ).
fof(f1393,plain,
! [X0] :
( ordere142940540dd_abs(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),abs_abs(X0,X1))) ),
inference(rectify,[],[f1051]) ).
fof(f1051,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X30] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X30),abs_abs(X1,X30))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_abs__ge__self) ).
fof(f11956,plain,
( spl63_528
| ~ spl63_352
| ~ spl63_512 ),
inference(avatar_split_clause,[],[f11852,f11228,f9191,f11954]) ).
fof(f11954,plain,
( spl63_528
<=> ! [X0] : ~ sP14(X0,X0,dvd_dvd(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_528])]) ).
fof(f11852,plain,
( ! [X0] : ~ sP14(X0,X0,dvd_dvd(nat))
| ~ spl63_352
| ~ spl63_512 ),
inference(resolution,[],[f11229,f9192]) ).
fof(f11643,plain,
( ~ spl63_526
| spl63_527
| ~ spl63_180
| ~ spl63_227
| ~ spl63_277
| ~ spl63_492 ),
inference(avatar_split_clause,[],[f11514,f11146,f8528,f8119,f7894,f11641,f11637]) ).
fof(f11637,plain,
( spl63_526
<=> ab_group_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_526])]) ).
fof(f11146,plain,
( spl63_492
<=> ! [X2,X0,X1] :
( ti(X0,X2) = ti(X0,X1)
| zero_zero(X0) != minus_minus(X0,X1,X2)
| ~ ab_group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_492])]) ).
fof(f11514,plain,
( ! [X0] :
( nat_1(pls) = X0
| ~ ab_group_add(nat) )
| ~ spl63_180
| ~ spl63_227
| ~ spl63_277
| ~ spl63_492 ),
inference(forward_demodulation,[],[f11513,f8529]) ).
fof(f11513,plain,
( ! [X0] :
( ti(nat,X0) = nat_1(pls)
| ~ ab_group_add(nat) )
| ~ spl63_180
| ~ spl63_227
| ~ spl63_277
| ~ spl63_492 ),
inference(forward_demodulation,[],[f11512,f8529]) ).
fof(f11512,plain,
( ! [X0] :
( ti(nat,X0) = ti(nat,nat_1(pls))
| ~ ab_group_add(nat) )
| ~ spl63_180
| ~ spl63_227
| ~ spl63_492 ),
inference(trivial_inequality_removal,[],[f11511]) ).
fof(f11511,plain,
( ! [X0] :
( nat_1(pls) != nat_1(pls)
| ti(nat,X0) = ti(nat,nat_1(pls))
| ~ ab_group_add(nat) )
| ~ spl63_180
| ~ spl63_227
| ~ spl63_492 ),
inference(forward_demodulation,[],[f11479,f7896]) ).
fof(f11479,plain,
( ! [X0] :
( zero_zero(nat) != nat_1(pls)
| ti(nat,X0) = ti(nat,nat_1(pls))
| ~ ab_group_add(nat) )
| ~ spl63_227
| ~ spl63_492 ),
inference(superposition,[],[f11147,f8120]) ).
fof(f11147,plain,
( ! [X2,X0,X1] :
( zero_zero(X0) != minus_minus(X0,X1,X2)
| ti(X0,X2) = ti(X0,X1)
| ~ ab_group_add(X0) )
| ~ spl63_492 ),
inference(avatar_component_clause,[],[f11146]) ).
fof(f11386,plain,
spl63_525,
inference(avatar_split_clause,[],[f6868,f11384]) ).
fof(f11384,plain,
( spl63_525
<=> ! [X2,X0,X1] :
( nat_1(pls) = X1
| X0 = X2
| times_times(nat,X0,X1) != times_times(nat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_525])]) ).
fof(f6868,plain,
! [X2,X0,X1] :
( nat_1(pls) = X1
| X0 = X2
| times_times(nat,X0,X1) != times_times(nat,X2,X1) ),
inference(forward_demodulation,[],[f5335,f5811]) ).
fof(f5335,plain,
! [X2,X0,X1] :
( zero_zero(nat) = X1
| X0 = X2
| times_times(nat,X0,X1) != times_times(nat,X2,X1) ),
inference(cnf_transformation,[],[f3648]) ).
fof(f3648,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,[],[f3647]) ).
fof(f3647,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,[],[f2189]) ).
fof(f2189,plain,
! [X0,X1,X2] :
( times_times(nat,X0,X1) = times_times(nat,X2,X1)
<=> ( zero_zero(nat) = X1
| X0 = X2 ) ),
inference(rectify,[],[f696]) ).
fof(f696,axiom,
! [X27,X11,X16] :
( times_times(nat,X27,X11) = times_times(nat,X16,X11)
<=> ( zero_zero(nat) = X11
| X16 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_mult__cancel2) ).
fof(f11382,plain,
spl63_524,
inference(avatar_split_clause,[],[f6865,f11380]) ).
fof(f11380,plain,
( spl63_524
<=> ! [X2,X0,X1] :
( nat_1(pls) = X0
| X1 = X2
| times_times(nat,X0,X1) != times_times(nat,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_524])]) ).
fof(f6865,plain,
! [X2,X0,X1] :
( nat_1(pls) = X0
| X1 = X2
| times_times(nat,X0,X1) != times_times(nat,X0,X2) ),
inference(forward_demodulation,[],[f5332,f5811]) ).
fof(f5332,plain,
! [X2,X0,X1] :
( zero_zero(nat) = X0
| X1 = X2
| times_times(nat,X0,X1) != times_times(nat,X0,X2) ),
inference(cnf_transformation,[],[f3646]) ).
fof(f3646,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,[],[f3645]) ).
fof(f3645,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,[],[f2188]) ).
fof(f2188,plain,
! [X0,X1,X2] :
( times_times(nat,X0,X1) = times_times(nat,X0,X2)
<=> ( zero_zero(nat) = X0
| X1 = X2 ) ),
inference(rectify,[],[f695]) ).
fof(f695,axiom,
! [X11,X27,X16] :
( times_times(nat,X11,X27) = times_times(nat,X11,X16)
<=> ( zero_zero(nat) = X11
| X16 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_mult__cancel1) ).
fof(f11378,plain,
spl63_523,
inference(avatar_split_clause,[],[f6644,f11376]) ).
fof(f11376,plain,
( spl63_523
<=> ! [X0,X1] :
( ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0)
| nat_1(ti(int,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_523])]) ).
fof(f6644,plain,
! [X0,X1] :
( ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0)
| nat_1(ti(int,X1)) = X0 ),
inference(forward_demodulation,[],[f6643,f3970]) ).
fof(f6643,plain,
! [X0,X1] :
( nat_1(ti(int,X1)) = X0
| hAPP(nat,int,semiring_1_of_nat(int),X0) != number_number_of(int,X1) ),
inference(forward_demodulation,[],[f4937,f3970]) ).
fof(f4937,plain,
! [X0,X1] :
( nat_1(number_number_of(int,X1)) = X0
| hAPP(nat,int,semiring_1_of_nat(int),X0) != number_number_of(int,X1) ),
inference(cnf_transformation,[],[f3501]) ).
fof(f3501,plain,
! [X0,X1] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X0) = number_number_of(int,X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1)))
| nat_1(number_number_of(int,X1)) != X0 )
& ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1)))
& nat_1(number_number_of(int,X1)) = X0 )
| hAPP(nat,int,semiring_1_of_nat(int),X0) != number_number_of(int,X1) ) ),
inference(flattening,[],[f3500]) ).
fof(f3500,plain,
! [X0,X1] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X0) = number_number_of(int,X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1)))
| nat_1(number_number_of(int,X1)) != X0 )
& ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1)))
& nat_1(number_number_of(int,X1)) = X0 )
| hAPP(nat,int,semiring_1_of_nat(int),X0) != number_number_of(int,X1) ) ),
inference(nnf_transformation,[],[f1944]) ).
fof(f1944,plain,
! [X0,X1] :
( hAPP(nat,int,semiring_1_of_nat(int),X0) = number_number_of(int,X1)
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X1)))
& nat_1(number_number_of(int,X1)) = X0 ) ),
inference(rectify,[],[f496]) ).
fof(f496,axiom,
! [X27,X37] :
( hAPP(nat,int,semiring_1_of_nat(int),X27) = number_number_of(int,X37)
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),number_number_of(int,X37)))
& nat_1(number_number_of(int,X37)) = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_int__eq__iff__number__of) ).
fof(f11373,plain,
spl63_522,
inference(avatar_split_clause,[],[f5930,f11371]) ).
fof(f11371,plain,
( spl63_522
<=> ! [X0] : plus_plus(nat,X0,X0) = times_times(nat,nat_1(minus_minus(int,minus_minus(int,pls,min),min)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_522])]) ).
fof(f5930,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,nat_1(minus_minus(int,minus_minus(int,pls,min),min)),X0),
inference(forward_demodulation,[],[f5929,f5453]) ).
fof(f5929,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,nat_1(minus_minus(int,minus_minus(int,plus_plus(int,pls,pls),min),min)),X0),
inference(forward_demodulation,[],[f5928,f5453]) ).
fof(f5928,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,nat_1(minus_minus(int,minus_minus(int,plus_plus(int,plus_plus(int,pls,pls),plus_plus(int,pls,pls)),min),min)),X0),
inference(forward_demodulation,[],[f5927,f5502]) ).
fof(f5927,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,nat_1(plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min))),X0),
inference(forward_demodulation,[],[f5511,f5915]) ).
fof(f5915,plain,
! [X0] : nat_1(X0) = number_number_of(nat,X0),
inference(forward_demodulation,[],[f5914,f3973]) ).
fof(f3973,plain,
! [X0] : nat_1(ti(int,X0)) = nat_1(X0),
inference(cnf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] : nat_1(ti(int,X0)) = nat_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onat_arg1) ).
fof(f5914,plain,
! [X0] : nat_1(ti(int,X0)) = number_number_of(nat,X0),
inference(forward_demodulation,[],[f3986,f3970]) ).
fof(f3986,plain,
! [X0] : number_number_of(nat,X0) = nat_1(number_number_of(int,X0)),
inference(cnf_transformation,[],[f1285]) ).
fof(f1285,plain,
! [X0] : number_number_of(nat,X0) = nat_1(number_number_of(int,X0)),
inference(rectify,[],[f524]) ).
fof(f524,axiom,
! [X7] : number_number_of(nat,X7) = nat_1(number_number_of(int,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_nat__number__of) ).
fof(f5511,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min))),X0),
inference(definition_unfolding,[],[f4005,f3968,f5445]) ).
fof(f4005,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,number_number_of(nat,bit0(bit1(pls))),X0),
inference(cnf_transformation,[],[f1303]) ).
fof(f1303,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,number_number_of(nat,bit0(bit1(pls))),X0),
inference(rectify,[],[f789]) ).
fof(f789,axiom,
! [X15] : times_times(nat,number_number_of(nat,bit0(bit1(pls))),X15) = plus_plus(nat,X15,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_nat__mult__2) ).
fof(f11321,plain,
( spl63_521
| ~ spl63_128
| ~ spl63_322 ),
inference(avatar_split_clause,[],[f8809,f8801,f7632,f11318]) ).
fof(f11318,plain,
( spl63_521
<=> one_one(nat) = number_number_of(nat,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_521])]) ).
fof(f7632,plain,
( spl63_128
<=> number_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_128])]) ).
fof(f8801,plain,
( spl63_322
<=> ! [X0] :
( one_one(X0) = number_number_of(X0,one_one(int))
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_322])]) ).
fof(f8809,plain,
( one_one(nat) = number_number_of(nat,one_one(int))
| ~ spl63_128
| ~ spl63_322 ),
inference(resolution,[],[f8802,f7634]) ).
fof(f7634,plain,
( number_semiring(nat)
| ~ spl63_128 ),
inference(avatar_component_clause,[],[f7632]) ).
fof(f8802,plain,
( ! [X0] :
( ~ number_semiring(X0)
| one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ spl63_322 ),
inference(avatar_component_clause,[],[f8801]) ).
fof(f11316,plain,
( spl63_520
| ~ spl63_488
| ~ spl63_519 ),
inference(avatar_split_clause,[],[f11312,f11309,f11025,f11314]) ).
fof(f11309,plain,
( spl63_519
<=> ! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(minus_minus(int,minus_minus(int,pls,min),min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_519])]) ).
fof(f11312,plain,
( ! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(minus_minus(int,one_one(int),min)))
| ~ spl63_488
| ~ spl63_519 ),
inference(forward_demodulation,[],[f11310,f11027]) ).
fof(f11310,plain,
( ! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(minus_minus(int,minus_minus(int,pls,min),min)))
| ~ spl63_519 ),
inference(avatar_component_clause,[],[f11309]) ).
fof(f11311,plain,
spl63_519,
inference(avatar_split_clause,[],[f5926,f11309]) ).
fof(f5926,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(minus_minus(int,minus_minus(int,pls,min),min))),
inference(forward_demodulation,[],[f5925,f5453]) ).
fof(f5925,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(minus_minus(int,minus_minus(int,plus_plus(int,pls,pls),min),min))),
inference(forward_demodulation,[],[f5924,f5453]) ).
fof(f5924,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(minus_minus(int,minus_minus(int,plus_plus(int,plus_plus(int,pls,pls),plus_plus(int,pls,pls)),min),min))),
inference(forward_demodulation,[],[f5923,f5502]) ).
fof(f5923,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,nat_1(plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min)))),
inference(forward_demodulation,[],[f5510,f5915]) ).
fof(f5510,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min)))),
inference(definition_unfolding,[],[f4004,f3968,f5445]) ).
fof(f4004,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1302]) ).
fof(f1302,plain,
! [X0] : plus_plus(nat,X0,X0) = times_times(nat,X0,number_number_of(nat,bit0(bit1(pls)))),
inference(rectify,[],[f790]) ).
fof(f790,axiom,
! [X15] : plus_plus(nat,X15,X15) = times_times(nat,X15,number_number_of(nat,bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_nat__mult__2__right) ).
fof(f11307,plain,
spl63_518,
inference(avatar_split_clause,[],[f5661,f11305]) ).
fof(f11305,plain,
( spl63_518
<=> ! [X0,X1] :
( ti(int,X0) = ti(int,X1)
| plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_518])]) ).
fof(f5661,plain,
! [X0,X1] :
( ti(int,X0) = ti(int,X1)
| plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ),
inference(definition_unfolding,[],[f4883,f3968,f3968]) ).
fof(f4883,plain,
! [X0,X1] :
( ti(int,X0) = ti(int,X1)
| bit0(X0) != bit0(X1) ),
inference(cnf_transformation,[],[f3464]) ).
fof(f3464,plain,
! [X0,X1] :
( ( bit0(X0) = bit0(X1)
| ti(int,X0) != ti(int,X1) )
& ( ti(int,X0) = ti(int,X1)
| bit0(X0) != bit0(X1) ) ),
inference(nnf_transformation,[],[f1927]) ).
fof(f1927,plain,
! [X0,X1] :
( bit0(X0) = bit0(X1)
<=> ti(int,X0) = ti(int,X1) ),
inference(rectify,[],[f141]) ).
fof(f141,axiom,
! [X11,X12] :
( bit0(X11) = bit0(X12)
<=> ti(int,X11) = ti(int,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_rel__simps_I48_J) ).
fof(f11303,plain,
spl63_517,
inference(avatar_split_clause,[],[f5660,f11301]) ).
fof(f11301,plain,
( spl63_517
<=> ! [X0,X1] :
( plus_plus(int,X0,X0) = plus_plus(int,X1,X1)
| ti(int,X0) != ti(int,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_517])]) ).
fof(f5660,plain,
! [X0,X1] :
( plus_plus(int,X0,X0) = plus_plus(int,X1,X1)
| ti(int,X0) != ti(int,X1) ),
inference(definition_unfolding,[],[f4884,f3968,f3968]) ).
fof(f4884,plain,
! [X0,X1] :
( bit0(X0) = bit0(X1)
| ti(int,X0) != ti(int,X1) ),
inference(cnf_transformation,[],[f3464]) ).
fof(f11299,plain,
spl63_516,
inference(avatar_split_clause,[],[f5547,f11297]) ).
fof(f11297,plain,
( spl63_516
<=> ! [X0,X1] :
( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,minus_minus(int,X1,min))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_516])]) ).
fof(f5547,plain,
! [X0,X1] :
( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,minus_minus(int,X1,min))
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f4236,f3966]) ).
fof(f4236,plain,
! [X0,X1] :
( number_number_of(X0,succ(X1)) = plus_plus(X0,one_one(X0),number_number_of(X0,X1))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2384]) ).
fof(f2384,plain,
! [X0] :
( ! [X1] : number_number_of(X0,succ(X1)) = plus_plus(X0,one_one(X0),number_number_of(X0,X1))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1446]) ).
fof(f1446,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : number_number_of(X0,succ(X1)) = plus_plus(X0,one_one(X0),number_number_of(X0,X1)) ),
inference(rectify,[],[f630]) ).
fof(f630,axiom,
! [X1] :
( number_ring(X1)
=> ! [X19] : number_number_of(X1,succ(X19)) = plus_plus(X1,one_one(X1),number_number_of(X1,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_number__of__succ) ).
fof(f11243,plain,
( spl63_515
| ~ spl63_247
| ~ spl63_279
| ~ spl63_514 ),
inference(avatar_split_clause,[],[f11239,f11236,f8536,f8226,f11241]) ).
fof(f11241,plain,
( spl63_515
<=> ! [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_515])]) ).
fof(f11236,plain,
( spl63_514
<=> ! [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_514])]) ).
fof(f11239,plain,
( ! [X0] : minus_minus(int,plus_plus(int,X0,X0),min) = plus_plus(int,minus_minus(int,X0,min),X0)
| ~ spl63_247
| ~ spl63_279
| ~ spl63_514 ),
inference(forward_demodulation,[],[f11237,f8600]) ).
fof(f11237,plain,
( ! [X0] : plus_plus(int,plus_plus(int,one_one(int),X0),X0) = minus_minus(int,plus_plus(int,X0,X0),min)
| ~ spl63_514 ),
inference(avatar_component_clause,[],[f11236]) ).
fof(f11238,plain,
spl63_514,
inference(avatar_split_clause,[],[f5505,f11236]) ).
fof(f5505,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,[],[f3997,f5445]) ).
fof(f3997,plain,
! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(cnf_transformation,[],[f1295]) ).
fof(f1295,plain,
! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(rectify,[],[f190]) ).
fof(f190,axiom,
! [X19] : bit1(X19) = plus_plus(int,plus_plus(int,one_one(int),X19),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
fof(f11234,plain,
spl63_513,
inference(avatar_split_clause,[],[f5323,f11232]) ).
fof(f11232,plain,
( spl63_513
<=> ! [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_513])]) ).
fof(f5323,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),X2))
| ~ hBOOL(hAPP(int,bool,zcong(X1,X0),X2)) ),
inference(cnf_transformation,[],[f3637]) ).
fof(f3637,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,[],[f2183]) ).
fof(f2183,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),X2))
<=> hBOOL(hAPP(int,bool,zcong(X1,X0),X2)) ),
inference(rectify,[],[f981]) ).
fof(f981,axiom,
! [X6,X41,X27] :
( hBOOL(hAPP(int,bool,zcong(X6,X41),X27))
<=> hBOOL(hAPP(int,bool,zcong(X41,X6),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_zcong__sym) ).
fof(f11230,plain,
spl63_512,
inference(avatar_split_clause,[],[f5295,f11228]) ).
fof(f5295,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2,X1),X0))
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3618]) ).
fof(f11226,plain,
( spl63_511
| ~ spl63_42
| ~ spl63_320 ),
inference(avatar_split_clause,[],[f8794,f8790,f7202,f11223]) ).
fof(f11223,plain,
( spl63_511
<=> one_one(int) = number_number_of(int,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_511])]) ).
fof(f7202,plain,
( spl63_42
<=> number_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_42])]) ).
fof(f8790,plain,
( spl63_320
<=> ! [X0] :
( one_one(X0) = number_number_of(X0,one_one(int))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_320])]) ).
fof(f8794,plain,
( one_one(int) = number_number_of(int,one_one(int))
| ~ spl63_42
| ~ spl63_320 ),
inference(resolution,[],[f8791,f7204]) ).
fof(f7204,plain,
( number_ring(int)
| ~ spl63_42 ),
inference(avatar_component_clause,[],[f7202]) ).
fof(f8791,plain,
( ! [X0] :
( ~ number_ring(X0)
| one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ spl63_320 ),
inference(avatar_component_clause,[],[f8790]) ).
fof(f11221,plain,
spl63_510,
inference(avatar_split_clause,[],[f5188,f11219]) ).
fof(f11219,plain,
( spl63_510
<=> ! [X2,X0,X1] :
( ti(int,X0) = plus_plus(int,X2,X1)
| ti(int,X2) != minus_minus(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_510])]) ).
fof(f5188,plain,
! [X2,X0,X1] :
( ti(int,X0) = plus_plus(int,X2,X1)
| ti(int,X2) != minus_minus(int,X0,X1) ),
inference(cnf_transformation,[],[f3002]) ).
fof(f3002,plain,
! [X0,X1,X2] :
( ti(int,X0) = plus_plus(int,X2,X1)
| ti(int,X2) != minus_minus(int,X0,X1) ),
inference(ennf_transformation,[],[f2093]) ).
fof(f2093,plain,
! [X0,X1,X2] :
( ti(int,X2) = minus_minus(int,X0,X1)
=> ti(int,X0) = plus_plus(int,X2,X1) ),
inference(rectify,[],[f817]) ).
fof(f817,axiom,
! [X30,X39,X40] :
( minus_minus(int,X30,X39) = ti(int,X40)
=> ti(int,X30) = plus_plus(int,X40,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_Int2_Oaux1) ).
fof(f11217,plain,
spl63_509,
inference(avatar_split_clause,[],[f5177,f11215]) ).
fof(f11215,plain,
( spl63_509
<=> ! [X2,X0,X1] :
( X0 = X1
| times_times(real,X2,X0) != times_times(real,X2,X1)
| zero_zero(real) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_509])]) ).
fof(f5177,plain,
! [X2,X0,X1] :
( X0 = X1
| times_times(real,X2,X0) != times_times(real,X2,X1)
| zero_zero(real) = X2 ),
inference(cnf_transformation,[],[f3595]) ).
fof(f3595,plain,
! [X0,X1,X2] :
( ( ( times_times(real,X2,X0) = times_times(real,X2,X1)
| X0 != X1 )
& ( X0 = X1
| times_times(real,X2,X0) != times_times(real,X2,X1) ) )
| zero_zero(real) = X2 ),
inference(nnf_transformation,[],[f2986]) ).
fof(f2986,plain,
! [X0,X1,X2] :
( ( times_times(real,X2,X0) = times_times(real,X2,X1)
<=> X0 = X1 )
| zero_zero(real) = X2 ),
inference(ennf_transformation,[],[f2084]) ).
fof(f2084,plain,
! [X0,X1,X2] :
( zero_zero(real) != X2
=> ( times_times(real,X2,X0) = times_times(real,X2,X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f701]) ).
fof(f701,axiom,
! [X6,X41,X45] :
( zero_zero(real) != X45
=> ( times_times(real,X45,X6) = times_times(real,X45,X41)
<=> X6 = X41 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_real__mult__left__cancel) ).
fof(f11213,plain,
spl63_508,
inference(avatar_split_clause,[],[f5175,f11211]) ).
fof(f11211,plain,
( spl63_508
<=> ! [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_508])]) ).
fof(f5175,plain,
! [X2,X0,X1] :
( X0 = X1
| times_times(real,X1,X2) != times_times(real,X0,X2)
| zero_zero(real) = X2 ),
inference(cnf_transformation,[],[f3594]) ).
fof(f3594,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,[],[f2985]) ).
fof(f2985,plain,
! [X0,X1,X2] :
( ( times_times(real,X1,X2) = times_times(real,X0,X2)
<=> X0 = X1 )
| zero_zero(real) = X2 ),
inference(ennf_transformation,[],[f2083]) ).
fof(f2083,plain,
! [X0,X1,X2] :
( zero_zero(real) != X2
=> ( times_times(real,X1,X2) = times_times(real,X0,X2)
<=> X0 = X1 ) ),
inference(rectify,[],[f702]) ).
fof(f702,axiom,
! [X6,X41,X45] :
( zero_zero(real) != X45
=> ( times_times(real,X6,X45) = times_times(real,X41,X45)
<=> X6 = X41 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_real__mult__right__cancel) ).
fof(f11209,plain,
spl63_507,
inference(avatar_split_clause,[],[f4943,f11207]) ).
fof(f11207,plain,
( spl63_507
<=> ! [X0,X1] :
( X0 = X1
| hAPP(nat,int,semiring_1_of_nat(int),X0) != hAPP(nat,int,semiring_1_of_nat(int),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_507])]) ).
fof(f4943,plain,
! [X0,X1] :
( X0 = X1
| hAPP(nat,int,semiring_1_of_nat(int),X0) != hAPP(nat,int,semiring_1_of_nat(int),X1) ),
inference(cnf_transformation,[],[f3504]) ).
fof(f3504,plain,
! [X0,X1] :
( ( hAPP(nat,int,semiring_1_of_nat(int),X0) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(nat,int,semiring_1_of_nat(int),X0) != hAPP(nat,int,semiring_1_of_nat(int),X1) ) ),
inference(nnf_transformation,[],[f1946]) ).
fof(f1946,plain,
! [X0,X1] :
( hAPP(nat,int,semiring_1_of_nat(int),X0) = hAPP(nat,int,semiring_1_of_nat(int),X1)
<=> X0 = X1 ),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X27,X16] :
( hAPP(nat,int,semiring_1_of_nat(int),X16) = hAPP(nat,int,semiring_1_of_nat(int),X27)
<=> X16 = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_int__int__eq) ).
fof(f11205,plain,
spl63_506,
inference(avatar_split_clause,[],[f4704,f11203]) ).
fof(f11203,plain,
( spl63_506
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),minus_minus(nat,X0,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_506])]) ).
fof(f4704,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),minus_minus(nat,X0,X1)),X0)),
inference(cnf_transformation,[],[f1806]) ).
fof(f1806,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),minus_minus(nat,X0,X1)),X0)),
inference(rectify,[],[f737]) ).
fof(f737,axiom,
! [X13,X14] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),minus_minus(nat,X13,X14)),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_Nat_Odiff__le__self) ).
fof(f11201,plain,
spl63_505,
inference(avatar_split_clause,[],[f4703,f11199]) ).
fof(f11199,plain,
( spl63_505
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),plus_plus(nat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_505])]) ).
fof(f4703,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),plus_plus(nat,X1,X0))),
inference(cnf_transformation,[],[f1805]) ).
fof(f1805,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),plus_plus(nat,X1,X0))),
inference(rectify,[],[f722]) ).
fof(f722,axiom,
! [X14,X13] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),plus_plus(nat,X13,X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_le__add2) ).
fof(f11197,plain,
spl63_504,
inference(avatar_split_clause,[],[f4702,f11195]) ).
fof(f11195,plain,
( spl63_504
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),plus_plus(nat,X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_504])]) ).
fof(f4702,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),plus_plus(nat,X0,X1))),
inference(cnf_transformation,[],[f1804]) ).
fof(f1804,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),plus_plus(nat,X0,X1))),
inference(rectify,[],[f721]) ).
fof(f721,axiom,
! [X14,X13] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),plus_plus(nat,X14,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_le__add1) ).
fof(f11193,plain,
spl63_503,
inference(avatar_split_clause,[],[f4701,f11191]) ).
fof(f11191,plain,
( spl63_503
<=> ! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X0,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_503])]) ).
fof(f4701,plain,
! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X0,X1)),X1)),
inference(cnf_transformation,[],[f1803]) ).
fof(f1803,plain,
! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X0,X1)),X1)),
inference(rectify,[],[f217]) ).
fof(f217,axiom,
! [X21,X20] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X21,X20)),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_not__add__less2) ).
fof(f11189,plain,
spl63_502,
inference(avatar_split_clause,[],[f4700,f11187]) ).
fof(f11187,plain,
( spl63_502
<=> ! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X0,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_502])]) ).
fof(f4700,plain,
! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X0,X1)),X0)),
inference(cnf_transformation,[],[f1802]) ).
fof(f1802,plain,
! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X0,X1)),X0)),
inference(rectify,[],[f216]) ).
fof(f216,axiom,
! [X20,X21] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),plus_plus(nat,X20,X21)),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_not__add__less1) ).
fof(f11185,plain,
spl63_501,
inference(avatar_split_clause,[],[f4586,f11183]) ).
fof(f4586,plain,
! [X0] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f3376]) ).
fof(f3376,plain,
! [X0] :
( ( sP8(X0)
| ( ti(int,X0) != ti(int,sK34(X0))
& one_one(int) != ti(int,sK34(X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),sK34(X0)),X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK34(X0))) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) )
& ( ( ! [X2] :
( ti(int,X0) = ti(int,X2)
| ti(int,X2) = one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X2),X0))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) )
| ~ sP8(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f3374,f3375]) ).
fof(f3375,plain,
! [X0] :
( ? [X1] :
( ti(int,X0) != ti(int,X1)
& one_one(int) != ti(int,X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
=> ( ti(int,X0) != ti(int,sK34(X0))
& one_one(int) != ti(int,sK34(X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),sK34(X0)),X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK34(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3374,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ti(int,X0) != ti(int,X1)
& one_one(int) != ti(int,X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) )
& ( ( ! [X2] :
( ti(int,X0) = ti(int,X2)
| ti(int,X2) = one_one(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X2),X0))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) )
| ~ sP8(X0) ) ),
inference(rectify,[],[f3373]) ).
fof(f3373,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ti(int,X0) != ti(int,X1)
& one_one(int) != ti(int,X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) )
& ( ( ! [X1] :
( ti(int,X0) = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) )
| ~ sP8(X0) ) ),
inference(flattening,[],[f3372]) ).
fof(f3372,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ti(int,X0) != ti(int,X1)
& one_one(int) != ti(int,X1)
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) )
& ( ( ! [X1] :
( ti(int,X0) = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) )
| ~ sP8(X0) ) ),
inference(nnf_transformation,[],[f3210]) ).
fof(f3210,plain,
! [X0] :
( sP8(X0)
<=> ( ! [X1] :
( ti(int,X0) = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f11181,plain,
( spl63_500
| ~ spl63_41
| ~ spl63_320 ),
inference(avatar_split_clause,[],[f8793,f8790,f7197,f11178]) ).
fof(f11178,plain,
( spl63_500
<=> one_one(real) = number_number_of(real,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_500])]) ).
fof(f7197,plain,
( spl63_41
<=> number_ring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_41])]) ).
fof(f8793,plain,
( one_one(real) = number_number_of(real,one_one(int))
| ~ spl63_41
| ~ spl63_320 ),
inference(resolution,[],[f8791,f7199]) ).
fof(f7199,plain,
( number_ring(real)
| ~ spl63_41 ),
inference(avatar_component_clause,[],[f7197]) ).
fof(f11176,plain,
spl63_499,
inference(avatar_split_clause,[],[f4456,f11174]) ).
fof(f11174,plain,
( spl63_499
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),one_one(X0)),X1))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_499])]) ).
fof(f4456,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),one_one(X0)),X1))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2645]) ).
fof(f2645,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),one_one(X0)),X1))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1640]) ).
fof(f1640,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),one_one(X0)),X1)) ),
inference(rectify,[],[f871]) ).
fof(f871,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),dvd_dvd(X1),one_one(X1)),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_one__dvd) ).
fof(f11172,plain,
spl63_498,
inference(avatar_split_clause,[],[f4455,f11170]) ).
fof(f11170,plain,
( spl63_498
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),zero_zero(X0)))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_498])]) ).
fof(f4455,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),zero_zero(X0)))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2644]) ).
fof(f2644,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),zero_zero(X0)))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1639]) ).
fof(f1639,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),zero_zero(X0))) ),
inference(rectify,[],[f821]) ).
fof(f821,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),dvd_dvd(X1),X30),zero_zero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_dvd__0__right) ).
fof(f11168,plain,
spl63_497,
inference(avatar_split_clause,[],[f4454,f11166]) ).
fof(f11166,plain,
( spl63_497
<=> ! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),X1)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_497])]) ).
fof(f4454,plain,
! [X0,X1] :
( plus_plus(X0,X1,X1) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),X1)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2643]) ).
fof(f2643,plain,
! [X0] :
( ! [X1] : plus_plus(X0,X1,X1) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),X1)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1638]) ).
fof(f1638,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : plus_plus(X0,X1,X1) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),X1) ),
inference(rectify,[],[f543]) ).
fof(f543,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X13] : plus_plus(X1,X13,X13) = times_times(X1,plus_plus(X1,one_one(X1),one_one(X1)),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(f11164,plain,
spl63_496,
inference(avatar_split_clause,[],[f4281,f11162]) ).
fof(f11162,plain,
( spl63_496
<=> ! [X2,X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,X2)
| zero_zero(X0) != ti(X0,X2)
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_496])]) ).
fof(f4281,plain,
! [X2,X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,X2)
| zero_zero(X0) != ti(X0,X2)
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f3316]) ).
fof(f3316,plain,
! [X0] :
( ! [X1,X2] :
( ( ti(X0,X1) = plus_plus(X0,X1,X2)
| zero_zero(X0) != ti(X0,X2) )
& ( zero_zero(X0) = ti(X0,X2)
| ti(X0,X1) != plus_plus(X0,X1,X2) ) )
| ~ semiri456707255roduct(X0) ),
inference(nnf_transformation,[],[f2429]) ).
fof(f2429,plain,
! [X0] :
( ! [X1,X2] :
( ti(X0,X1) = plus_plus(X0,X1,X2)
<=> zero_zero(X0) = ti(X0,X2) )
| ~ semiri456707255roduct(X0) ),
inference(ennf_transformation,[],[f1486]) ).
fof(f1486,plain,
! [X0] :
( semiri456707255roduct(X0)
=> ! [X1,X2] :
( ti(X0,X1) = plus_plus(X0,X1,X2)
<=> zero_zero(X0) = ti(X0,X2) ) ),
inference(rectify,[],[f310]) ).
fof(f310,axiom,
! [X1] :
( semiri456707255roduct(X1)
=> ! [X41,X6] :
( plus_plus(X1,X41,X6) = ti(X1,X41)
<=> zero_zero(X1) = ti(X1,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_add__0__iff) ).
fof(f11160,plain,
spl63_495,
inference(avatar_split_clause,[],[f4280,f11158]) ).
fof(f11158,plain,
( spl63_495
<=> ! [X2,X0,X1] :
( zero_zero(X0) = ti(X0,X2)
| ti(X0,X1) != plus_plus(X0,X1,X2)
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_495])]) ).
fof(f4280,plain,
! [X2,X0,X1] :
( zero_zero(X0) = ti(X0,X2)
| ti(X0,X1) != plus_plus(X0,X1,X2)
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f3316]) ).
fof(f11156,plain,
spl63_494,
inference(avatar_split_clause,[],[f4101,f11154]) ).
fof(f11154,plain,
( spl63_494
<=> ! [X2,X0,X1] :
( zero_zero(X0) = minus_minus(X0,X1,X2)
| ti(X0,X2) != ti(X0,X1)
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_494])]) ).
fof(f4101,plain,
! [X2,X0,X1] :
( zero_zero(X0) = minus_minus(X0,X1,X2)
| ti(X0,X2) != ti(X0,X1)
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f3269]) ).
fof(f3269,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = minus_minus(X0,X1,X2)
| ti(X0,X2) != ti(X0,X1) )
& ( ti(X0,X2) = ti(X0,X1)
| zero_zero(X0) != minus_minus(X0,X1,X2) ) )
| ~ group_add(X0) ),
inference(nnf_transformation,[],[f2299]) ).
fof(f2299,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) = minus_minus(X0,X1,X2)
<=> ti(X0,X2) = ti(X0,X1) )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f1370]) ).
fof(f1370,plain,
! [X0] :
( group_add(X0)
=> ! [X1,X2] :
( zero_zero(X0) = minus_minus(X0,X1,X2)
<=> ti(X0,X2) = ti(X0,X1) ) ),
inference(rectify,[],[f418]) ).
fof(f418,axiom,
! [X1] :
( group_add(X1)
=> ! [X6,X41] :
( zero_zero(X1) = minus_minus(X1,X6,X41)
<=> ti(X1,X6) = ti(X1,X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_right__minus__eq) ).
fof(f11152,plain,
spl63_493,
inference(avatar_split_clause,[],[f4100,f11150]) ).
fof(f4100,plain,
! [X2,X0,X1] :
( ti(X0,X2) = ti(X0,X1)
| zero_zero(X0) != minus_minus(X0,X1,X2)
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f3269]) ).
fof(f11148,plain,
spl63_492,
inference(avatar_split_clause,[],[f4060,f11146]) ).
fof(f4060,plain,
! [X2,X0,X1] :
( ti(X0,X2) = ti(X0,X1)
| zero_zero(X0) != minus_minus(X0,X1,X2)
| ~ ab_group_add(X0) ),
inference(cnf_transformation,[],[f3255]) ).
fof(f3255,plain,
! [X0] :
( ! [X1,X2] :
( ( ti(X0,X2) = ti(X0,X1)
| zero_zero(X0) != minus_minus(X0,X1,X2) )
& ( zero_zero(X0) = minus_minus(X0,X1,X2)
| ti(X0,X2) != ti(X0,X1) ) )
| ~ ab_group_add(X0) ),
inference(nnf_transformation,[],[f2272]) ).
fof(f2272,plain,
! [X0] :
( ! [X1,X2] :
( ti(X0,X2) = ti(X0,X1)
<=> zero_zero(X0) = minus_minus(X0,X1,X2) )
| ~ ab_group_add(X0) ),
inference(ennf_transformation,[],[f1344]) ).
fof(f1344,plain,
! [X0] :
( ab_group_add(X0)
=> ! [X1,X2] :
( ti(X0,X2) = ti(X0,X1)
<=> zero_zero(X0) = minus_minus(X0,X1,X2) ) ),
inference(rectify,[],[f419]) ).
fof(f419,axiom,
! [X1] :
( ab_group_add(X1)
=> ! [X6,X41] :
( ti(X1,X6) = ti(X1,X41)
<=> zero_zero(X1) = minus_minus(X1,X6,X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_eq__iff__diff__eq__0) ).
fof(f11144,plain,
spl63_491,
inference(avatar_split_clause,[],[f4059,f11142]) ).
fof(f11142,plain,
( spl63_491
<=> ! [X2,X0,X1] :
( zero_zero(X0) = minus_minus(X0,X1,X2)
| ti(X0,X2) != ti(X0,X1)
| ~ ab_group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_491])]) ).
fof(f4059,plain,
! [X2,X0,X1] :
( zero_zero(X0) = minus_minus(X0,X1,X2)
| ti(X0,X2) != ti(X0,X1)
| ~ ab_group_add(X0) ),
inference(cnf_transformation,[],[f3255]) ).
fof(f11140,plain,
spl63_490,
inference(avatar_split_clause,[],[f4016,f11138]) ).
fof(f11138,plain,
( spl63_490
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),times_times(nat,X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_490])]) ).
fof(f4016,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),times_times(nat,X0,X0))),
inference(cnf_transformation,[],[f1314]) ).
fof(f1314,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),times_times(nat,X0,X0))),
inference(rectify,[],[f671]) ).
fof(f671,axiom,
! [X13] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X13),times_times(nat,X13,X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_le__square) ).
fof(f11136,plain,
( ~ spl63_489
| ~ spl63_69
| ~ spl63_217
| ~ spl63_240
| ~ spl63_280 ),
inference(avatar_split_clause,[],[f8617,f8540,f8198,f8079,f7337,f11133]) ).
fof(f11133,plain,
( spl63_489
<=> pls = plus_plus(int,one_one(int),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_489])]) ).
fof(f7337,plain,
( spl63_69
<=> one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_69])]) ).
fof(f8079,plain,
( spl63_217
<=> ! [X0] : ti(int,X0) = plus_plus(int,X0,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_217])]) ).
fof(f8198,plain,
( spl63_240
<=> ! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_240])]) ).
fof(f8540,plain,
( spl63_280
<=> ! [X0] : pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_280])]) ).
fof(f8617,plain,
( pls != plus_plus(int,one_one(int),pls)
| ~ spl63_69
| ~ spl63_217
| ~ spl63_240
| ~ spl63_280 ),
inference(forward_demodulation,[],[f8609,f8322]) ).
fof(f8322,plain,
( one_one(int) = ti(int,one_one(int))
| ~ spl63_69
| ~ spl63_240 ),
inference(resolution,[],[f8199,f7339]) ).
fof(f7339,plain,
( one(int)
| ~ spl63_69 ),
inference(avatar_component_clause,[],[f7337]) ).
fof(f8199,plain,
( ! [X0] :
( ~ one(X0)
| one_one(X0) = ti(X0,one_one(X0)) )
| ~ spl63_240 ),
inference(avatar_component_clause,[],[f8198]) ).
fof(f8609,plain,
( pls != plus_plus(int,ti(int,one_one(int)),pls)
| ~ spl63_217
| ~ spl63_280 ),
inference(superposition,[],[f8541,f8080]) ).
fof(f8080,plain,
( ! [X0] : ti(int,X0) = plus_plus(int,X0,pls)
| ~ spl63_217 ),
inference(avatar_component_clause,[],[f8079]) ).
fof(f8541,plain,
( ! [X0] : pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0)
| ~ spl63_280 ),
inference(avatar_component_clause,[],[f8540]) ).
fof(f11028,plain,
( spl63_488
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279 ),
inference(avatar_split_clause,[],[f8607,f8536,f8198,f8075,f7337,f11025]) ).
fof(f8075,plain,
( spl63_216
<=> ! [X0] : ti(int,X0) = plus_plus(int,pls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_216])]) ).
fof(f8607,plain,
( one_one(int) = minus_minus(int,pls,min)
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279 ),
inference(forward_demodulation,[],[f8599,f8322]) ).
fof(f8599,plain,
( minus_minus(int,pls,min) = ti(int,one_one(int))
| ~ spl63_216
| ~ spl63_279 ),
inference(superposition,[],[f8537,f8076]) ).
fof(f8076,plain,
( ! [X0] : ti(int,X0) = plus_plus(int,pls,X0)
| ~ spl63_216 ),
inference(avatar_component_clause,[],[f8075]) ).
fof(f10622,plain,
( ~ spl63_487
| ~ spl63_191
| ~ spl63_279 ),
inference(avatar_split_clause,[],[f8603,f8536,f7946,f10619]) ).
fof(f10619,plain,
( spl63_487
<=> min = minus_minus(int,one_one(int),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_487])]) ).
fof(f7946,plain,
( spl63_191
<=> ! [X0] : min != plus_plus(int,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_191])]) ).
fof(f8603,plain,
( min != minus_minus(int,one_one(int),min)
| ~ spl63_191
| ~ spl63_279 ),
inference(superposition,[],[f7947,f8537]) ).
fof(f7947,plain,
( ! [X0] : min != plus_plus(int,X0,X0)
| ~ spl63_191 ),
inference(avatar_component_clause,[],[f7946]) ).
fof(f10354,plain,
( spl63_486
| ~ spl63_202
| ~ spl63_248 ),
inference(avatar_split_clause,[],[f8370,f8230,f8002,f10352]) ).
fof(f10352,plain,
( spl63_486
<=> ! [X0] : times_times(real,X0,one_one(real)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_486])]) ).
fof(f8002,plain,
( spl63_202
<=> ! [X0] : times_times(real,one_one(real),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_202])]) ).
fof(f8230,plain,
( spl63_248
<=> ! [X0,X1] : times_times(real,X0,X1) = times_times(real,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_248])]) ).
fof(f8370,plain,
( ! [X0] : times_times(real,X0,one_one(real)) = X0
| ~ spl63_202
| ~ spl63_248 ),
inference(superposition,[],[f8231,f8003]) ).
fof(f8003,plain,
( ! [X0] : times_times(real,one_one(real),X0) = X0
| ~ spl63_202 ),
inference(avatar_component_clause,[],[f8002]) ).
fof(f8231,plain,
( ! [X0,X1] : times_times(real,X0,X1) = times_times(real,X1,X0)
| ~ spl63_248 ),
inference(avatar_component_clause,[],[f8230]) ).
fof(f10344,plain,
spl63_485,
inference(avatar_split_clause,[],[f6754,f10342]) ).
fof(f10342,plain,
( spl63_485
<=> ! [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_485])]) ).
fof(f6754,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,[],[f5101,f5100]) ).
fof(f5100,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,[],[f2012]) ).
fof(f2012,plain,
! [X0,X1,X2] : minus_minus(nat,minus_minus(nat,X0,X1),X2) = minus_minus(nat,X0,plus_plus(nat,X1,X2)),
inference(rectify,[],[f465]) ).
fof(f465,axiom,
! [X20,X21,X19] : minus_minus(nat,minus_minus(nat,X20,X21),X19) = minus_minus(nat,X20,plus_plus(nat,X21,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_diff__diff__left) ).
fof(f5101,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,[],[f2013]) ).
fof(f2013,plain,
! [X0,X1,X2] : minus_minus(nat,minus_minus(nat,X0,X1),X2) = minus_minus(nat,minus_minus(nat,X0,X2),X1),
inference(rectify,[],[f365]) ).
fof(f365,axiom,
! [X20,X21,X19] : minus_minus(nat,minus_minus(nat,X20,X21),X19) = minus_minus(nat,minus_minus(nat,X20,X19),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_diff__commute) ).
fof(f10340,plain,
spl63_484,
inference(avatar_split_clause,[],[f6704,f10337]) ).
fof(f10337,plain,
( spl63_484
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),one_one(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_484])]) ).
fof(f6704,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),one_one(nat))),
inference(forward_demodulation,[],[f6703,f6423]) ).
fof(f6423,plain,
! [X0] : one_one(nat) = hAPP(nat,nat,power_power(nat,X0),nat_1(pls)),
inference(forward_demodulation,[],[f5721,f5811]) ).
fof(f5721,plain,
! [X0] : one_one(nat) = hAPP(nat,nat,power_power(nat,X0),zero_zero(nat)),
inference(equality_resolution,[],[f4724]) ).
fof(f4724,plain,
! [X0,X1] :
( one_one(nat) = hAPP(nat,nat,power_power(nat,X0),X1)
| zero_zero(nat) != X1 ),
inference(cnf_transformation,[],[f2770]) ).
fof(f2770,plain,
! [X0,X1] :
( ( hAPP(nat,nat,power_power(nat,X0),X1) = times_times(nat,X0,hAPP(nat,nat,power_power(nat,X0),minus_minus(nat,X1,one_one(nat))))
| zero_zero(nat) = X1 )
& ( one_one(nat) = hAPP(nat,nat,power_power(nat,X0),X1)
| zero_zero(nat) != X1 ) ),
inference(ennf_transformation,[],[f1825]) ).
fof(f1825,plain,
! [X0,X1] :
( ( zero_zero(nat) != X1
=> hAPP(nat,nat,power_power(nat,X0),X1) = times_times(nat,X0,hAPP(nat,nat,power_power(nat,X0),minus_minus(nat,X1,one_one(nat)))) )
& ( zero_zero(nat) = X1
=> one_one(nat) = hAPP(nat,nat,power_power(nat,X0),X1) ) ),
inference(rectify,[],[f787]) ).
fof(f787,axiom,
! [X64,X13] :
( ( zero_zero(nat) != X13
=> hAPP(nat,nat,power_power(nat,X64),X13) = times_times(nat,X64,hAPP(nat,nat,power_power(nat,X64),minus_minus(nat,X13,one_one(nat)))) )
& ( zero_zero(nat) = X13
=> one_one(nat) = hAPP(nat,nat,power_power(nat,X64),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_power__eq__if) ).
fof(f6703,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),hAPP(nat,nat,power_power(nat,X0),nat_1(pls)))),
inference(forward_demodulation,[],[f5773,f5811]) ).
fof(f5773,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X0),zero_zero(nat)))),
inference(equality_resolution,[],[f5058]) ).
fof(f5058,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X0),X1)))
| zero_zero(nat) != X1 ),
inference(cnf_transformation,[],[f3573]) ).
fof(f3573,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X0),X1)))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
& zero_zero(nat) != X1 ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
| zero_zero(nat) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X0),X1))) ) ),
inference(flattening,[],[f3572]) ).
fof(f3572,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X0),X1)))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
& zero_zero(nat) != X1 ) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
| zero_zero(nat) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X0),X1))) ) ),
inference(nnf_transformation,[],[f1993]) ).
fof(f1993,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X0),X1)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
| zero_zero(nat) = X1 ) ),
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X4,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,power_power(nat,X4),X16)))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X4))
| zero_zero(nat) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_zero__less__power__nat__eq) ).
fof(f10335,plain,
spl63_483,
inference(avatar_split_clause,[],[f6630,f10333]) ).
fof(f10333,plain,
( spl63_483
<=> ! [X1] :
( nat_1(pls) = X1
| nat_1(pls) = hAPP(nat,nat,power_power(nat,nat_1(pls)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_483])]) ).
fof(f6630,plain,
! [X1] :
( nat_1(pls) = X1
| nat_1(pls) = hAPP(nat,nat,power_power(nat,nat_1(pls)),X1) ),
inference(forward_demodulation,[],[f6629,f5811]) ).
fof(f6629,plain,
! [X1] :
( nat_1(pls) = hAPP(nat,nat,power_power(nat,nat_1(pls)),X1)
| zero_zero(nat) = X1 ),
inference(forward_demodulation,[],[f5757,f5811]) ).
fof(f5757,plain,
! [X1] :
( zero_zero(nat) = hAPP(nat,nat,power_power(nat,zero_zero(nat)),X1)
| zero_zero(nat) = X1 ),
inference(equality_resolution,[],[f4933]) ).
fof(f4933,plain,
! [X0,X1] :
( zero_zero(nat) = hAPP(nat,nat,power_power(nat,X0),X1)
| zero_zero(nat) != X0
| zero_zero(nat) = X1 ),
inference(cnf_transformation,[],[f3497]) ).
fof(f3497,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,[],[f3496]) ).
fof(f3496,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,[],[f1942]) ).
fof(f1942,plain,
! [X0,X1] :
( zero_zero(nat) = hAPP(nat,nat,power_power(nat,X0),X1)
<=> ( zero_zero(nat) = X0
& zero_zero(nat) != X1 ) ),
inference(rectify,[],[f326]) ).
fof(f326,axiom,
! [X27,X16] :
( zero_zero(nat) = hAPP(nat,nat,power_power(nat,X27),X16)
<=> ( zero_zero(nat) = X27
& zero_zero(nat) != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_nat__power__eq__0__iff) ).
fof(f10331,plain,
spl63_482,
inference(avatar_split_clause,[],[f6622,f10329]) ).
fof(f10329,plain,
( spl63_482
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(int,bool,zcong(X0,X1),pls))
| ti(int,X0) = ti(int,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_482])]) ).
fof(f6622,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(int,bool,zcong(X0,X1),pls))
| ti(int,X0) = ti(int,X1) ),
inference(forward_demodulation,[],[f4922,f3861]) ).
fof(f4922,plain,
! [X0,X1] :
( ti(int,X0) = ti(int,X1)
| ~ hBOOL(hAPP(int,bool,zcong(X0,X1),zero_zero(int))) ),
inference(cnf_transformation,[],[f3491]) ).
fof(f3491,plain,
! [X0,X1] :
( ( hBOOL(hAPP(int,bool,zcong(X0,X1),zero_zero(int)))
| ti(int,X0) != ti(int,X1) )
& ( ti(int,X0) = ti(int,X1)
| ~ hBOOL(hAPP(int,bool,zcong(X0,X1),zero_zero(int))) ) ),
inference(nnf_transformation,[],[f1938]) ).
fof(f1938,plain,
! [X0,X1] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),zero_zero(int)))
<=> ti(int,X0) = ti(int,X1) ),
inference(rectify,[],[f983]) ).
fof(f983,axiom,
! [X6,X41] :
( hBOOL(hAPP(int,bool,zcong(X6,X41),zero_zero(int)))
<=> ti(int,X6) = ti(int,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_IntPrimes_Ozcong__zero) ).
fof(f10327,plain,
spl63_481,
inference(avatar_split_clause,[],[f6621,f10325]) ).
fof(f10325,plain,
( spl63_481
<=> ! [X0,X1] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),pls))
| ti(int,X0) != ti(int,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_481])]) ).
fof(f6621,plain,
! [X0,X1] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),pls))
| ti(int,X0) != ti(int,X1) ),
inference(forward_demodulation,[],[f4923,f3861]) ).
fof(f4923,plain,
! [X0,X1] :
( hBOOL(hAPP(int,bool,zcong(X0,X1),zero_zero(int)))
| ti(int,X0) != ti(int,X1) ),
inference(cnf_transformation,[],[f3491]) ).
fof(f10323,plain,
spl63_480,
inference(avatar_split_clause,[],[f6606,f10321]) ).
fof(f10321,plain,
( spl63_480
<=> ! [X0,X1] :
( times_times(nat,X0,X1) != nat_1(pls)
| nat_1(pls) = X0
| nat_1(pls) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_480])]) ).
fof(f6606,plain,
! [X0,X1] :
( times_times(nat,X0,X1) != nat_1(pls)
| nat_1(pls) = X0
| nat_1(pls) = X1 ),
inference(forward_demodulation,[],[f6605,f5811]) ).
fof(f6605,plain,
! [X0,X1] :
( nat_1(pls) = X0
| nat_1(pls) = X1
| zero_zero(nat) != times_times(nat,X0,X1) ),
inference(forward_demodulation,[],[f6604,f5811]) ).
fof(f6604,plain,
! [X0,X1] :
( nat_1(pls) = X1
| zero_zero(nat) = X0
| zero_zero(nat) != times_times(nat,X0,X1) ),
inference(forward_demodulation,[],[f4909,f5811]) ).
fof(f4909,plain,
! [X0,X1] :
( zero_zero(nat) = X1
| zero_zero(nat) = X0
| zero_zero(nat) != times_times(nat,X0,X1) ),
inference(cnf_transformation,[],[f3480]) ).
fof(f3480,plain,
! [X0,X1] :
( ( zero_zero(nat) = times_times(nat,X0,X1)
| ( zero_zero(nat) != X1
& zero_zero(nat) != X0 ) )
& ( zero_zero(nat) = X1
| zero_zero(nat) = X0
| zero_zero(nat) != times_times(nat,X0,X1) ) ),
inference(flattening,[],[f3479]) ).
fof(f3479,plain,
! [X0,X1] :
( ( zero_zero(nat) = times_times(nat,X0,X1)
| ( zero_zero(nat) != X1
& zero_zero(nat) != X0 ) )
& ( zero_zero(nat) = X1
| zero_zero(nat) = X0
| zero_zero(nat) != times_times(nat,X0,X1) ) ),
inference(nnf_transformation,[],[f1935]) ).
fof(f1935,plain,
! [X0,X1] :
( zero_zero(nat) = times_times(nat,X0,X1)
<=> ( zero_zero(nat) = X1
| zero_zero(nat) = X0 ) ),
inference(rectify,[],[f694]) ).
fof(f694,axiom,
! [X27,X16] :
( zero_zero(nat) = times_times(nat,X27,X16)
<=> ( zero_zero(nat) = X16
| zero_zero(nat) = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_mult__is__0) ).
fof(f10284,plain,
( spl63_479
| ~ spl63_94
| ~ spl63_369
| ~ spl63_478 ),
inference(avatar_split_clause,[],[f10280,f10277,f9259,f7462,f10282]) ).
fof(f10282,plain,
( spl63_479
<=> ! [X0,X1] : times_times(int,X0,X1) = times_times(int,ti(int,X0),ti(int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_479])]) ).
fof(f7462,plain,
( spl63_94
<=> ab_semigroup_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_94])]) ).
fof(f9259,plain,
( spl63_369
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ ab_semigroup_mult(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_369])]) ).
fof(f10277,plain,
( spl63_478
<=> ! [X0,X1] : ti(int,times_times(int,X0,X1)) = times_times(int,ti(int,X0),ti(int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_478])]) ).
fof(f10280,plain,
( ! [X0,X1] : times_times(int,X0,X1) = times_times(int,ti(int,X0),ti(int,X1))
| ~ spl63_94
| ~ spl63_369
| ~ spl63_478 ),
inference(forward_demodulation,[],[f10278,f9565]) ).
fof(f9565,plain,
( ! [X0,X1] : times_times(int,X0,X1) = ti(int,times_times(int,X0,X1))
| ~ spl63_94
| ~ spl63_369 ),
inference(resolution,[],[f9260,f7464]) ).
fof(f7464,plain,
( ab_semigroup_mult(int)
| ~ spl63_94 ),
inference(avatar_component_clause,[],[f7462]) ).
fof(f9260,plain,
( ! [X2,X0,X1] :
( ~ ab_semigroup_mult(X2)
| times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) )
| ~ spl63_369 ),
inference(avatar_component_clause,[],[f9259]) ).
fof(f10278,plain,
( ! [X0,X1] : ti(int,times_times(int,X0,X1)) = times_times(int,ti(int,X0),ti(int,X1))
| ~ spl63_478 ),
inference(avatar_component_clause,[],[f10277]) ).
fof(f10279,plain,
spl63_478,
inference(avatar_split_clause,[],[f6378,f10277]) ).
fof(f6378,plain,
! [X0,X1] : ti(int,times_times(int,X0,X1)) = times_times(int,ti(int,X0),ti(int,X1)),
inference(forward_demodulation,[],[f6377,f3970]) ).
fof(f6377,plain,
! [X0,X1] : ti(int,times_times(int,X0,X1)) = times_times(int,number_number_of(int,X0),ti(int,X1)),
inference(forward_demodulation,[],[f6376,f3970]) ).
fof(f6376,plain,
! [X0,X1] : times_times(int,number_number_of(int,X0),number_number_of(int,X1)) = ti(int,times_times(int,X0,X1)),
inference(forward_demodulation,[],[f4699,f3970]) ).
fof(f4699,plain,
! [X0,X1] : times_times(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,times_times(int,X0,X1)),
inference(cnf_transformation,[],[f1801]) ).
fof(f1801,plain,
! [X0,X1] : times_times(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,times_times(int,X0,X1)),
inference(rectify,[],[f482]) ).
fof(f482,axiom,
! [X8,X7] : times_times(int,number_number_of(int,X8),number_number_of(int,X7)) = number_number_of(int,times_times(int,X8,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_times__numeral__code_I5_J) ).
fof(f10275,plain,
( spl63_477
| ~ spl63_69
| ~ spl63_240 ),
inference(avatar_split_clause,[],[f8322,f8198,f7337,f10272]) ).
fof(f10272,plain,
( spl63_477
<=> one_one(int) = ti(int,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_477])]) ).
fof(f10233,plain,
( spl63_476
| ~ spl63_95
| ~ spl63_367
| ~ spl63_475 ),
inference(avatar_split_clause,[],[f10229,f10226,f9251,f7467,f10231]) ).
fof(f10231,plain,
( spl63_476
<=> ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,ti(int,X0),ti(int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_476])]) ).
fof(f10226,plain,
( spl63_475
<=> ! [X0,X1] : ti(int,plus_plus(int,X0,X1)) = plus_plus(int,ti(int,X0),ti(int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_475])]) ).
fof(f10229,plain,
( ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,ti(int,X0),ti(int,X1))
| ~ spl63_95
| ~ spl63_367
| ~ spl63_475 ),
inference(forward_demodulation,[],[f10227,f9559]) ).
fof(f10227,plain,
( ! [X0,X1] : ti(int,plus_plus(int,X0,X1)) = plus_plus(int,ti(int,X0),ti(int,X1))
| ~ spl63_475 ),
inference(avatar_component_clause,[],[f10226]) ).
fof(f10228,plain,
spl63_475,
inference(avatar_split_clause,[],[f6375,f10226]) ).
fof(f6375,plain,
! [X0,X1] : ti(int,plus_plus(int,X0,X1)) = plus_plus(int,ti(int,X0),ti(int,X1)),
inference(forward_demodulation,[],[f6374,f3970]) ).
fof(f6374,plain,
! [X0,X1] : ti(int,plus_plus(int,X0,X1)) = plus_plus(int,number_number_of(int,X0),ti(int,X1)),
inference(forward_demodulation,[],[f6373,f3970]) ).
fof(f6373,plain,
! [X0,X1] : plus_plus(int,number_number_of(int,X0),number_number_of(int,X1)) = ti(int,plus_plus(int,X0,X1)),
inference(forward_demodulation,[],[f4698,f3970]) ).
fof(f4698,plain,
! [X0,X1] : plus_plus(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,plus_plus(int,X0,X1)),
inference(cnf_transformation,[],[f1800]) ).
fof(f1800,plain,
! [X0,X1] : plus_plus(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,plus_plus(int,X0,X1)),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X8,X7] : plus_plus(int,number_number_of(int,X8),number_number_of(int,X7)) = number_number_of(int,plus_plus(int,X8,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_plus__numeral__code_I9_J) ).
fof(f10218,plain,
( spl63_474
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279
| ~ spl63_473 ),
inference(avatar_split_clause,[],[f10214,f10211,f8536,f8198,f8075,f7337,f10216]) ).
fof(f10216,plain,
( spl63_474
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,number_number_of(X0,one_one(int)),X1)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_474])]) ).
fof(f10211,plain,
( spl63_473
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,number_number_of(X0,minus_minus(int,pls,min)),X1)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_473])]) ).
fof(f10214,plain,
( ! [X0,X1] :
( ti(X0,X1) = times_times(X0,number_number_of(X0,one_one(int)),X1)
| ~ number_ring(X0) )
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279
| ~ spl63_473 ),
inference(forward_demodulation,[],[f10212,f8607]) ).
fof(f10212,plain,
( ! [X0,X1] :
( ti(X0,X1) = times_times(X0,number_number_of(X0,minus_minus(int,pls,min)),X1)
| ~ number_ring(X0) )
| ~ spl63_473 ),
inference(avatar_component_clause,[],[f10211]) ).
fof(f10213,plain,
spl63_473,
inference(avatar_split_clause,[],[f6077,f10211]) ).
fof(f6077,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,number_number_of(X0,minus_minus(int,pls,min)),X1)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f5546,f5453]) ).
fof(f5546,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,number_number_of(X0,minus_minus(int,plus_plus(int,pls,pls),min)),X1)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f4235,f5445]) ).
fof(f4235,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,number_number_of(X0,bit1(pls)),X1)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2383]) ).
fof(f2383,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = times_times(X0,number_number_of(X0,bit1(pls)),X1)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1445]) ).
fof(f1445,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : ti(X0,X1) = times_times(X0,number_number_of(X0,bit1(pls)),X1) ),
inference(rectify,[],[f596]) ).
fof(f596,axiom,
! [X1] :
( number_ring(X1)
=> ! [X30] : ti(X1,X30) = times_times(X1,number_number_of(X1,bit1(pls)),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_mult__numeral__1) ).
fof(f10203,plain,
( spl63_472
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279
| ~ spl63_471 ),
inference(avatar_split_clause,[],[f10199,f10196,f8536,f8198,f8075,f7337,f10201]) ).
fof(f10201,plain,
( spl63_472
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,number_number_of(X0,one_one(int)))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_472])]) ).
fof(f10196,plain,
( spl63_471
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,number_number_of(X0,minus_minus(int,pls,min)))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_471])]) ).
fof(f10199,plain,
( ! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,number_number_of(X0,one_one(int)))
| ~ number_ring(X0) )
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279
| ~ spl63_471 ),
inference(forward_demodulation,[],[f10197,f8607]) ).
fof(f10197,plain,
( ! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,number_number_of(X0,minus_minus(int,pls,min)))
| ~ number_ring(X0) )
| ~ spl63_471 ),
inference(avatar_component_clause,[],[f10196]) ).
fof(f10198,plain,
spl63_471,
inference(avatar_split_clause,[],[f6076,f10196]) ).
fof(f6076,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,number_number_of(X0,minus_minus(int,pls,min)))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f5545,f5453]) ).
fof(f5545,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,number_number_of(X0,minus_minus(int,plus_plus(int,pls,pls),min)))
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f4234,f5445]) ).
fof(f4234,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,number_number_of(X0,bit1(pls)))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2382]) ).
fof(f2382,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = times_times(X0,X1,number_number_of(X0,bit1(pls)))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1444]) ).
fof(f1444,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : ti(X0,X1) = times_times(X0,X1,number_number_of(X0,bit1(pls))) ),
inference(rectify,[],[f595]) ).
fof(f595,axiom,
! [X1] :
( number_ring(X1)
=> ! [X30] : ti(X1,X30) = times_times(X1,X30,number_number_of(X1,bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_mult__numeral__1__right) ).
fof(f10194,plain,
spl63_470,
inference(avatar_split_clause,[],[f5167,f10192]) ).
fof(f10192,plain,
( spl63_470
<=> ! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,X0,ti(X2,X1))
| ~ order(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_470])]) ).
fof(f5167,plain,
! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,X0,ti(X2,X1))
| ~ order(X2) ),
inference(cnf_transformation,[],[f2976]) ).
fof(f2976,plain,
! [X0,X1,X2] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,X0,ti(X2,X1))
| ~ order(X2) ),
inference(ennf_transformation,[],[f2076]) ).
fof(f2076,plain,
! [X0,X1,X2] :
( order(X2)
=> hAPP(X2,bool,X0,X1) = hAPP(X2,bool,X0,ti(X2,X1)) ),
inference(rectify,[],[f77]) ).
fof(f77,axiom,
! [X0,X2,X1] :
( order(X1)
=> hAPP(X1,bool,X0,X2) = hAPP(X1,bool,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_1_arg2) ).
fof(f10190,plain,
( spl63_469
| ~ spl63_40
| ~ spl63_239 ),
inference(avatar_split_clause,[],[f8319,f8194,f7192,f10187]) ).
fof(f10187,plain,
( spl63_469
<=> one_one(int) = abs_abs(int,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_469])]) ).
fof(f7192,plain,
( spl63_40
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_40])]) ).
fof(f8194,plain,
( spl63_239
<=> ! [X0] :
( one_one(X0) = abs_abs(X0,one_one(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_239])]) ).
fof(f8319,plain,
( one_one(int) = abs_abs(int,one_one(int))
| ~ spl63_40
| ~ spl63_239 ),
inference(resolution,[],[f8195,f7194]) ).
fof(f7194,plain,
( linordered_idom(int)
| ~ spl63_40 ),
inference(avatar_component_clause,[],[f7192]) ).
fof(f8195,plain,
( ! [X0] :
( ~ linordered_idom(X0)
| one_one(X0) = abs_abs(X0,one_one(X0)) )
| ~ spl63_239 ),
inference(avatar_component_clause,[],[f8194]) ).
fof(f10185,plain,
spl63_468,
inference(avatar_split_clause,[],[f5166,f10183]) ).
fof(f10183,plain,
( spl63_468
<=> ! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = ti(bool,hAPP(X2,bool,X0,X1))
| ~ order(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_468])]) ).
fof(f5166,plain,
! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = ti(bool,hAPP(X2,bool,X0,X1))
| ~ order(X2) ),
inference(cnf_transformation,[],[f2975]) ).
fof(f2975,plain,
! [X0,X1,X2] :
( hAPP(X2,bool,X0,X1) = ti(bool,hAPP(X2,bool,X0,X1))
| ~ order(X2) ),
inference(ennf_transformation,[],[f2075]) ).
fof(f2075,plain,
! [X0,X1,X2] :
( order(X2)
=> hAPP(X2,bool,X0,X1) = ti(bool,hAPP(X2,bool,X0,X1)) ),
inference(rectify,[],[f78]) ).
fof(f78,axiom,
! [X0,X2,X1] :
( order(X1)
=> hAPP(X1,bool,X0,X2) = ti(bool,hAPP(X1,bool,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_1_res) ).
fof(f10181,plain,
spl63_467,
inference(avatar_split_clause,[],[f5160,f10179]) ).
fof(f5160,plain,
! [X2,X0,X1] :
( hAPP(nat,X2,X0,X1) = ti(X2,hAPP(nat,X2,X0,X1))
| ~ power(X2) ),
inference(cnf_transformation,[],[f2969]) ).
fof(f2969,plain,
! [X0,X1,X2] :
( hAPP(nat,X2,X0,X1) = ti(X2,hAPP(nat,X2,X0,X1))
| ~ power(X2) ),
inference(ennf_transformation,[],[f2069]) ).
fof(f2069,plain,
! [X0,X1,X2] :
( power(X2)
=> hAPP(nat,X2,X0,X1) = ti(X2,hAPP(nat,X2,X0,X1)) ),
inference(rectify,[],[f87]) ).
fof(f87,axiom,
! [X0,X2,X1] :
( power(X1)
=> hAPP(nat,X1,X0,X2) = ti(X1,hAPP(nat,X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_4_res) ).
fof(f10177,plain,
spl63_466,
inference(avatar_split_clause,[],[f5159,f10175]) ).
fof(f10175,plain,
( spl63_466
<=> ! [X2,X0,X1] :
( hAPP(nat,X2,X0,X1) = hAPP(nat,X2,X0,ti(nat,X1))
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_466])]) ).
fof(f5159,plain,
! [X2,X0,X1] :
( hAPP(nat,X2,X0,X1) = hAPP(nat,X2,X0,ti(nat,X1))
| ~ power(X2) ),
inference(cnf_transformation,[],[f2968]) ).
fof(f2968,plain,
! [X0,X1,X2] :
( hAPP(nat,X2,X0,X1) = hAPP(nat,X2,X0,ti(nat,X1))
| ~ power(X2) ),
inference(ennf_transformation,[],[f2068]) ).
fof(f2068,plain,
! [X0,X1,X2] :
( power(X2)
=> hAPP(nat,X2,X0,X1) = hAPP(nat,X2,X0,ti(nat,X1)) ),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X0,X2,X1] :
( power(X1)
=> hAPP(nat,X1,X0,X2) = hAPP(nat,X1,X0,ti(nat,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_4_arg2) ).
fof(f10173,plain,
spl63_465,
inference(avatar_split_clause,[],[f5158,f10171]) ).
fof(f10171,plain,
( spl63_465
<=> ! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,X0,ti(X2,X1))
| ~ dvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_465])]) ).
fof(f5158,plain,
! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,X0,ti(X2,X1))
| ~ dvd(X2) ),
inference(cnf_transformation,[],[f2967]) ).
fof(f2967,plain,
! [X0,X1,X2] :
( hAPP(X2,bool,X0,X1) = hAPP(X2,bool,X0,ti(X2,X1))
| ~ dvd(X2) ),
inference(ennf_transformation,[],[f2067]) ).
fof(f2067,plain,
! [X0,X1,X2] :
( dvd(X2)
=> hAPP(X2,bool,X0,X1) = hAPP(X2,bool,X0,ti(X2,X1)) ),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X0,X2,X1] :
( dvd(X1)
=> hAPP(X1,bool,X0,X2) = hAPP(X1,bool,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_3_arg2) ).
fof(f10169,plain,
spl63_464,
inference(avatar_split_clause,[],[f5157,f10167]) ).
fof(f10167,plain,
( spl63_464
<=> ! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = ti(bool,hAPP(X2,bool,X0,X1))
| ~ dvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_464])]) ).
fof(f5157,plain,
! [X2,X0,X1] :
( hAPP(X2,bool,X0,X1) = ti(bool,hAPP(X2,bool,X0,X1))
| ~ dvd(X2) ),
inference(cnf_transformation,[],[f2966]) ).
fof(f2966,plain,
! [X0,X1,X2] :
( hAPP(X2,bool,X0,X1) = ti(bool,hAPP(X2,bool,X0,X1))
| ~ dvd(X2) ),
inference(ennf_transformation,[],[f2066]) ).
fof(f2066,plain,
! [X0,X1,X2] :
( dvd(X2)
=> hAPP(X2,bool,X0,X1) = ti(bool,hAPP(X2,bool,X0,X1)) ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X0,X2,X1] :
( dvd(X1)
=> hAPP(X1,bool,X0,X2) = ti(bool,hAPP(X1,bool,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_3_res) ).
fof(f10165,plain,
spl63_463,
inference(avatar_split_clause,[],[f5108,f10163]) ).
fof(f10163,plain,
( spl63_463
<=> ! [X2,X0,X1] : times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_463])]) ).
fof(f5108,plain,
! [X2,X0,X1] : times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)),
inference(cnf_transformation,[],[f2020]) ).
fof(f2020,plain,
! [X0,X1,X2] : times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)),
inference(rectify,[],[f352]) ).
fof(f352,axiom,
! [X24,X25,X26] : times_times(int,times_times(int,X24,X25),X26) = times_times(int,X24,times_times(int,X25,X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_zmult__assoc) ).
fof(f10161,plain,
spl63_462,
inference(avatar_split_clause,[],[f5107,f10159]) ).
fof(f10159,plain,
( spl63_462
<=> ! [X2,X0,X1] : times_times(nat,times_times(nat,X0,X1),X2) = times_times(nat,X0,times_times(nat,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_462])]) ).
fof(f5107,plain,
! [X2,X0,X1] : times_times(nat,times_times(nat,X0,X1),X2) = times_times(nat,X0,times_times(nat,X1,X2)),
inference(cnf_transformation,[],[f2019]) ).
fof(f2019,plain,
! [X0,X1,X2] : times_times(nat,times_times(nat,X0,X1),X2) = times_times(nat,X0,times_times(nat,X1,X2)),
inference(rectify,[],[f675]) ).
fof(f675,axiom,
! [X13,X14,X19] : times_times(nat,times_times(nat,X13,X14),X19) = times_times(nat,X13,times_times(nat,X14,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_nat__mult__assoc) ).
fof(f10157,plain,
spl63_461,
inference(avatar_split_clause,[],[f5106,f10155]) ).
fof(f10155,plain,
( spl63_461
<=> ! [X2,X0,X1] : times_times(real,times_times(real,X0,X1),X2) = times_times(real,X0,times_times(real,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_461])]) ).
fof(f5106,plain,
! [X2,X0,X1] : times_times(real,times_times(real,X0,X1),X2) = times_times(real,X0,times_times(real,X1,X2)),
inference(cnf_transformation,[],[f2018]) ).
fof(f2018,plain,
! [X0,X1,X2] : times_times(real,times_times(real,X0,X1),X2) = times_times(real,X0,times_times(real,X1,X2)),
inference(rectify,[],[f813]) ).
fof(f813,axiom,
! [X24,X25,X26] : times_times(real,times_times(real,X24,X25),X26) = times_times(real,X24,times_times(real,X25,X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_real__mult__assoc) ).
fof(f10153,plain,
spl63_460,
inference(avatar_split_clause,[],[f5105,f10151]) ).
fof(f10151,plain,
( spl63_460
<=> ! [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_460])]) ).
fof(f5105,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,[],[f2017]) ).
fof(f2017,plain,
! [X0,X1,X2] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,plus_plus(int,X0,X1),X2),
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X24,X25,X26] : plus_plus(int,plus_plus(int,X24,X25),X26) = plus_plus(int,X24,plus_plus(int,X25,X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_zadd__assoc) ).
fof(f10149,plain,
spl63_459,
inference(avatar_split_clause,[],[f5104,f10147]) ).
fof(f10147,plain,
( spl63_459
<=> ! [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_459])]) ).
fof(f5104,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,[],[f2016]) ).
fof(f2016,plain,
! [X0,X1,X2] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X9,X10,X15] : plus_plus(int,X9,plus_plus(int,X10,X15)) = plus_plus(int,X10,plus_plus(int,X9,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_zadd__left__commute) ).
fof(f10145,plain,
( spl63_458
| ~ spl63_39
| ~ spl63_239 ),
inference(avatar_split_clause,[],[f8318,f8194,f7187,f10142]) ).
fof(f10142,plain,
( spl63_458
<=> one_one(real) = abs_abs(real,one_one(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_458])]) ).
fof(f7187,plain,
( spl63_39
<=> linordered_idom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_39])]) ).
fof(f8318,plain,
( one_one(real) = abs_abs(real,one_one(real))
| ~ spl63_39
| ~ spl63_239 ),
inference(resolution,[],[f8195,f7189]) ).
fof(f7189,plain,
( linordered_idom(real)
| ~ spl63_39 ),
inference(avatar_component_clause,[],[f7187]) ).
fof(f10140,plain,
spl63_457,
inference(avatar_split_clause,[],[f5103,f10138]) ).
fof(f10138,plain,
( spl63_457
<=> ! [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_457])]) ).
fof(f5103,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,[],[f2015]) ).
fof(f2015,plain,
! [X0,X1,X2] : plus_plus(nat,X0,plus_plus(nat,X1,X2)) = plus_plus(nat,plus_plus(nat,X0,X1),X2),
inference(rectify,[],[f222]) ).
fof(f222,axiom,
! [X13,X14,X19] : plus_plus(nat,plus_plus(nat,X13,X14),X19) = plus_plus(nat,X13,plus_plus(nat,X14,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_nat__add__assoc) ).
fof(f10136,plain,
spl63_456,
inference(avatar_split_clause,[],[f5102,f10134]) ).
fof(f10134,plain,
( spl63_456
<=> ! [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_456])]) ).
fof(f5102,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,[],[f2014]) ).
fof(f2014,plain,
! [X0,X1,X2] : plus_plus(nat,X0,plus_plus(nat,X1,X2)) = plus_plus(nat,X1,plus_plus(nat,X0,X2)),
inference(rectify,[],[f221]) ).
fof(f221,axiom,
! [X9,X10,X15] : plus_plus(nat,X9,plus_plus(nat,X10,X15)) = plus_plus(nat,X10,plus_plus(nat,X9,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_nat__add__left__commute) ).
fof(f10132,plain,
spl63_455,
inference(avatar_split_clause,[],[f5100,f10130]) ).
fof(f10130,plain,
( spl63_455
<=> ! [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_455])]) ).
fof(f10128,plain,
spl63_454,
inference(avatar_split_clause,[],[f5099,f10126]) ).
fof(f10126,plain,
( spl63_454
<=> ! [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_454])]) ).
fof(f5099,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,[],[f2011]) ).
fof(f2011,plain,
! [X0,X1,X2] : minus_minus(nat,X0,X2) = minus_minus(nat,plus_plus(nat,X0,X1),plus_plus(nat,X2,X1)),
inference(rectify,[],[f467]) ).
fof(f467,axiom,
! [X13,X19,X14] : minus_minus(nat,X13,X14) = minus_minus(nat,plus_plus(nat,X13,X19),plus_plus(nat,X14,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_diff__cancel2) ).
fof(f10124,plain,
spl63_453,
inference(avatar_split_clause,[],[f5098,f10122]) ).
fof(f10122,plain,
( spl63_453
<=> ! [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_453])]) ).
fof(f5098,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,[],[f2010]) ).
fof(f2010,plain,
! [X0,X1,X2] : minus_minus(nat,X1,X2) = minus_minus(nat,plus_plus(nat,X0,X1),plus_plus(nat,X0,X2)),
inference(rectify,[],[f466]) ).
fof(f466,axiom,
! [X19,X13,X14] : minus_minus(nat,X13,X14) = minus_minus(nat,plus_plus(nat,X19,X13),plus_plus(nat,X19,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_Nat_Odiff__cancel) ).
fof(f10120,plain,
spl63_452,
inference(avatar_split_clause,[],[f4900,f10118]) ).
fof(f10118,plain,
( spl63_452
<=> ! [X0,X1] :
( sP11(X0,X1)
| ti(int,X0) != one_one(int)
| one_one(int) != ti(int,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_452])]) ).
fof(f4900,plain,
! [X0,X1] :
( sP11(X0,X1)
| ti(int,X0) != one_one(int)
| one_one(int) != ti(int,X1) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f3474,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ( ti(int,X0) != number_number_of(int,min)
| number_number_of(int,min) != ti(int,X1) )
& ( ti(int,X0) != one_one(int)
| one_one(int) != ti(int,X1) ) ) )
& ( ( ti(int,X0) = number_number_of(int,min)
& number_number_of(int,min) = ti(int,X1) )
| ( ti(int,X0) = one_one(int)
& one_one(int) = ti(int,X1) )
| ~ sP11(X0,X1) ) ),
inference(rectify,[],[f3473]) ).
fof(f3473,plain,
! [X1,X0] :
( ( sP11(X1,X0)
| ( ( number_number_of(int,min) != ti(int,X1)
| ti(int,X0) != number_number_of(int,min) )
& ( one_one(int) != ti(int,X1)
| ti(int,X0) != one_one(int) ) ) )
& ( ( number_number_of(int,min) = ti(int,X1)
& ti(int,X0) = number_number_of(int,min) )
| ( one_one(int) = ti(int,X1)
& ti(int,X0) = one_one(int) )
| ~ sP11(X1,X0) ) ),
inference(flattening,[],[f3472]) ).
fof(f3472,plain,
! [X1,X0] :
( ( sP11(X1,X0)
| ( ( number_number_of(int,min) != ti(int,X1)
| ti(int,X0) != number_number_of(int,min) )
& ( one_one(int) != ti(int,X1)
| ti(int,X0) != one_one(int) ) ) )
& ( ( number_number_of(int,min) = ti(int,X1)
& ti(int,X0) = number_number_of(int,min) )
| ( one_one(int) = ti(int,X1)
& ti(int,X0) = one_one(int) )
| ~ sP11(X1,X0) ) ),
inference(nnf_transformation,[],[f3216]) ).
fof(f3216,plain,
! [X1,X0] :
( sP11(X1,X0)
<=> ( ( number_number_of(int,min) = ti(int,X1)
& ti(int,X0) = number_number_of(int,min) )
| ( one_one(int) = ti(int,X1)
& ti(int,X0) = one_one(int) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f10116,plain,
spl63_451,
inference(avatar_split_clause,[],[f4763,f10114]) ).
fof(f10114,plain,
( spl63_451
<=> ! [X0,X1] :
( one_one(int) = abs_abs(int,X0)
| one_one(int) != abs_abs(int,times_times(int,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_451])]) ).
fof(f4763,plain,
! [X0,X1] :
( one_one(int) = abs_abs(int,X0)
| one_one(int) != abs_abs(int,times_times(int,X0,X1)) ),
inference(cnf_transformation,[],[f2806]) ).
fof(f2806,plain,
! [X0,X1] :
( one_one(int) = abs_abs(int,X0)
| one_one(int) != abs_abs(int,times_times(int,X0,X1)) ),
inference(ennf_transformation,[],[f1848]) ).
fof(f1848,plain,
! [X0,X1] :
( one_one(int) = abs_abs(int,times_times(int,X0,X1))
=> one_one(int) = abs_abs(int,X0) ),
inference(rectify,[],[f1036]) ).
fof(f1036,axiom,
! [X13,X14] :
( one_one(int) = abs_abs(int,times_times(int,X13,X14))
=> one_one(int) = abs_abs(int,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_abs__zmult__eq__1) ).
fof(f10112,plain,
spl63_450,
inference(avatar_split_clause,[],[f4453,f10110]) ).
fof(f10110,plain,
( spl63_450
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),X1))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_450])]) ).
fof(f4453,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),X1))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2642]) ).
fof(f2642,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),X1))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1637]) ).
fof(f1637,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),dvd_dvd(X0),X1),X1)) ),
inference(rectify,[],[f861]) ).
fof(f861,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),dvd_dvd(X1),X30),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_dvd__refl) ).
fof(f10108,plain,
spl63_449,
inference(avatar_split_clause,[],[f4191,f10106]) ).
fof(f10106,plain,
( spl63_449
<=> ! [X0,X1] :
( times_times(X0,X1,X1) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X1))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_449])]) ).
fof(f4191,plain,
! [X0,X1] :
( times_times(X0,X1,X1) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X1))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f2345]) ).
fof(f2345,plain,
! [X0] :
( ! [X1] : times_times(X0,X1,X1) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X1))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f1411]) ).
fof(f1411,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1] : times_times(X0,X1,X1) = times_times(X0,abs_abs(X0,X1),abs_abs(X0,X1)) ),
inference(rectify,[],[f1050]) ).
fof(f1050,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X30] : times_times(X1,X30,X30) = times_times(X1,abs_abs(X1,X30),abs_abs(X1,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_abs__mult__self) ).
fof(f10104,plain,
spl63_448,
inference(avatar_split_clause,[],[f4181,f10102]) ).
fof(f10102,plain,
( spl63_448
<=> ! [X2,X0,X1] :
( abs_abs(X0,minus_minus(X0,X1,X2)) = abs_abs(X0,minus_minus(X0,X2,X1))
| ~ ordere142940540dd_abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_448])]) ).
fof(f4181,plain,
! [X2,X0,X1] :
( abs_abs(X0,minus_minus(X0,X1,X2)) = abs_abs(X0,minus_minus(X0,X2,X1))
| ~ ordere142940540dd_abs(X0) ),
inference(cnf_transformation,[],[f2335]) ).
fof(f2335,plain,
! [X0] :
( ! [X1,X2] : abs_abs(X0,minus_minus(X0,X1,X2)) = abs_abs(X0,minus_minus(X0,X2,X1))
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f1401]) ).
fof(f1401,plain,
! [X0] :
( ordere142940540dd_abs(X0)
=> ! [X1,X2] : abs_abs(X0,minus_minus(X0,X1,X2)) = abs_abs(X0,minus_minus(X0,X2,X1)) ),
inference(rectify,[],[f1048]) ).
fof(f1048,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X30,X39] : abs_abs(X1,minus_minus(X1,X30,X39)) = abs_abs(X1,minus_minus(X1,X39,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_abs__minus__commute) ).
fof(f10097,plain,
spl63_447,
inference(avatar_split_clause,[],[f4082,f10095]) ).
fof(f10095,plain,
( spl63_447
<=> ! [X0,X1] :
( zero_zero(X0) = plus_plus(X0,X1,X1)
| zero_zero(X0) != ti(X0,X1)
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_447])]) ).
fof(f4082,plain,
! [X0,X1] :
( zero_zero(X0) = plus_plus(X0,X1,X1)
| zero_zero(X0) != ti(X0,X1)
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f3263]) ).
fof(f3263,plain,
! [X0] :
( ! [X1] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1)
| zero_zero(X0) != ti(X0,X1) )
& ( zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != plus_plus(X0,X1,X1) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f2286]) ).
fof(f2286,plain,
! [X0] :
( ! [X1] :
( zero_zero(X0) = plus_plus(X0,X1,X1)
<=> zero_zero(X0) = ti(X0,X1) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f1358]) ).
fof(f1358,plain,
! [X0] :
( linord219039673up_add(X0)
=> ! [X1] :
( zero_zero(X0) = plus_plus(X0,X1,X1)
<=> zero_zero(X0) = ti(X0,X1) ) ),
inference(rectify,[],[f314]) ).
fof(f314,axiom,
! [X1] :
( linord219039673up_add(X1)
=> ! [X6] :
( zero_zero(X1) = plus_plus(X1,X6,X6)
<=> zero_zero(X1) = ti(X1,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_double__zero__sym) ).
fof(f10093,plain,
spl63_446,
inference(avatar_split_clause,[],[f4081,f10091]) ).
fof(f10091,plain,
( spl63_446
<=> ! [X0,X1] :
( zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != plus_plus(X0,X1,X1)
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_446])]) ).
fof(f4081,plain,
! [X0,X1] :
( zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != plus_plus(X0,X1,X1)
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f3263]) ).
fof(f10089,plain,
spl63_445,
inference(avatar_split_clause,[],[f4044,f10087]) ).
fof(f10087,plain,
( spl63_445
<=> ! [X2,X0,X1] :
( zero_zero(X0) = times_times(X0,X1,X2)
| zero_zero(X0) != ti(X0,X2)
| ~ ring_n68954251visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_445])]) ).
fof(f4044,plain,
! [X2,X0,X1] :
( zero_zero(X0) = times_times(X0,X1,X2)
| zero_zero(X0) != ti(X0,X2)
| ~ ring_n68954251visors(X0) ),
inference(cnf_transformation,[],[f3249]) ).
fof(f3249,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = times_times(X0,X1,X2)
| ( zero_zero(X0) != ti(X0,X2)
& zero_zero(X0) != ti(X0,X1) ) )
& ( zero_zero(X0) = ti(X0,X2)
| zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != times_times(X0,X1,X2) ) )
| ~ ring_n68954251visors(X0) ),
inference(flattening,[],[f3248]) ).
fof(f3248,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = times_times(X0,X1,X2)
| ( zero_zero(X0) != ti(X0,X2)
& zero_zero(X0) != ti(X0,X1) ) )
& ( zero_zero(X0) = ti(X0,X2)
| zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != times_times(X0,X1,X2) ) )
| ~ ring_n68954251visors(X0) ),
inference(nnf_transformation,[],[f2259]) ).
fof(f2259,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) = times_times(X0,X1,X2)
<=> ( zero_zero(X0) = ti(X0,X2)
| zero_zero(X0) = ti(X0,X1) ) )
| ~ ring_n68954251visors(X0) ),
inference(ennf_transformation,[],[f1334]) ).
fof(f1334,plain,
! [X0] :
( ring_n68954251visors(X0)
=> ! [X1,X2] :
( zero_zero(X0) = times_times(X0,X1,X2)
<=> ( zero_zero(X0) = ti(X0,X2)
| zero_zero(X0) = ti(X0,X1) ) ) ),
inference(rectify,[],[f428]) ).
fof(f428,axiom,
! [X1] :
( ring_n68954251visors(X1)
=> ! [X6,X41] :
( zero_zero(X1) = times_times(X1,X6,X41)
<=> ( zero_zero(X1) = ti(X1,X41)
| zero_zero(X1) = ti(X1,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_mult__eq__0__iff) ).
fof(f10085,plain,
spl63_444,
inference(avatar_split_clause,[],[f4043,f10083]) ).
fof(f10083,plain,
( spl63_444
<=> ! [X2,X0,X1] :
( zero_zero(X0) = times_times(X0,X1,X2)
| zero_zero(X0) != ti(X0,X1)
| ~ ring_n68954251visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_444])]) ).
fof(f4043,plain,
! [X2,X0,X1] :
( zero_zero(X0) = times_times(X0,X1,X2)
| zero_zero(X0) != ti(X0,X1)
| ~ ring_n68954251visors(X0) ),
inference(cnf_transformation,[],[f3249]) ).
fof(f10081,plain,
spl63_443,
inference(avatar_split_clause,[],[f4015,f10079]) ).
fof(f10079,plain,
( spl63_443
<=> ! [X0] : hAPP(nat,int,semiring_1_of_nat(int),X0) = abs_abs(int,hAPP(nat,int,semiring_1_of_nat(int),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_443])]) ).
fof(f4015,plain,
! [X0] : hAPP(nat,int,semiring_1_of_nat(int),X0) = abs_abs(int,hAPP(nat,int,semiring_1_of_nat(int),X0)),
inference(cnf_transformation,[],[f1313]) ).
fof(f1313,plain,
! [X0] : hAPP(nat,int,semiring_1_of_nat(int),X0) = abs_abs(int,hAPP(nat,int,semiring_1_of_nat(int),X0)),
inference(rectify,[],[f1034]) ).
fof(f1034,axiom,
! [X13] : hAPP(nat,int,semiring_1_of_nat(int),X13) = abs_abs(int,hAPP(nat,int,semiring_1_of_nat(int),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_abs__int__eq) ).
fof(f10075,plain,
( spl63_442
| ~ spl63_255
| ~ spl63_411 ),
inference(avatar_split_clause,[],[f9760,f9471,f8258,f10073]) ).
fof(f10073,plain,
( spl63_442
<=> ! [X0] : pls = legendre(X0,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_442])]) ).
fof(f8258,plain,
( spl63_255
<=> ! [X0,X1] : hBOOL(hAPP(int,bool,zcong(X0,X1),one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_255])]) ).
fof(f9471,plain,
( spl63_411
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(int,bool,zcong(X0,pls),X1))
| pls = legendre(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_411])]) ).
fof(f9760,plain,
( ! [X0] : pls = legendre(X0,one_one(int))
| ~ spl63_255
| ~ spl63_411 ),
inference(resolution,[],[f9472,f8259]) ).
fof(f8259,plain,
( ! [X0,X1] : hBOOL(hAPP(int,bool,zcong(X0,X1),one_one(int)))
| ~ spl63_255 ),
inference(avatar_component_clause,[],[f8258]) ).
fof(f9472,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(int,bool,zcong(X0,pls),X1))
| pls = legendre(X0,X1) )
| ~ spl63_411 ),
inference(avatar_component_clause,[],[f9471]) ).
fof(f9902,plain,
spl63_441,
inference(avatar_split_clause,[],[f6632,f9900]) ).
fof(f9900,plain,
( spl63_441
<=> ! [X0,X1] :
( hAPP(nat,nat,power_power(nat,X0),X1) != nat_1(pls)
| nat_1(pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_441])]) ).
fof(f6632,plain,
! [X0,X1] :
( hAPP(nat,nat,power_power(nat,X0),X1) != nat_1(pls)
| nat_1(pls) = X0 ),
inference(forward_demodulation,[],[f6631,f5811]) ).
fof(f6631,plain,
! [X0,X1] :
( nat_1(pls) = X0
| zero_zero(nat) != hAPP(nat,nat,power_power(nat,X0),X1) ),
inference(forward_demodulation,[],[f4932,f5811]) ).
fof(f4932,plain,
! [X0,X1] :
( zero_zero(nat) = X0
| zero_zero(nat) != hAPP(nat,nat,power_power(nat,X0),X1) ),
inference(cnf_transformation,[],[f3497]) ).
fof(f9895,plain,
spl63_440,
inference(avatar_split_clause,[],[f6594,f9893]) ).
fof(f9893,plain,
( spl63_440
<=> ! [X0,X1] :
( min = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_440])]) ).
fof(f6594,plain,
! [X0,X1] :
( min = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f6593,f3874]) ).
fof(f6593,plain,
! [X0,X1] :
( ti(int,min) = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f4896,f3970]) ).
fof(f4896,plain,
! [X0,X1] :
( number_number_of(int,min) = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f9891,plain,
spl63_439,
inference(avatar_split_clause,[],[f6592,f9889]) ).
fof(f9889,plain,
( spl63_439
<=> ! [X0,X1] :
( min = ti(int,X1)
| ti(int,X0) = one_one(int)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_439])]) ).
fof(f6592,plain,
! [X0,X1] :
( min = ti(int,X1)
| ti(int,X0) = one_one(int)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f6591,f3874]) ).
fof(f6591,plain,
! [X0,X1] :
( ti(int,min) = ti(int,X1)
| ti(int,X0) = one_one(int)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f4897,f3970]) ).
fof(f4897,plain,
! [X0,X1] :
( number_number_of(int,min) = ti(int,X1)
| ti(int,X0) = one_one(int)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f9887,plain,
spl63_438,
inference(avatar_split_clause,[],[f6590,f9885]) ).
fof(f9885,plain,
( spl63_438
<=> ! [X0,X1] :
( ti(int,X0) = min
| one_one(int) = ti(int,X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_438])]) ).
fof(f6590,plain,
! [X0,X1] :
( ti(int,X0) = min
| one_one(int) = ti(int,X1)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f6589,f3874]) ).
fof(f6589,plain,
! [X0,X1] :
( ti(int,X0) = ti(int,min)
| one_one(int) = ti(int,X1)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f4898,f3970]) ).
fof(f4898,plain,
! [X0,X1] :
( ti(int,X0) = number_number_of(int,min)
| one_one(int) = ti(int,X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f9883,plain,
spl63_437,
inference(avatar_split_clause,[],[f6588,f9881]) ).
fof(f9881,plain,
( spl63_437
<=> ! [X0,X1] :
( ti(int,X0) = min
| ti(int,X0) = one_one(int)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_437])]) ).
fof(f6588,plain,
! [X0,X1] :
( ti(int,X0) = min
| ti(int,X0) = one_one(int)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f6587,f3874]) ).
fof(f6587,plain,
! [X0,X1] :
( ti(int,X0) = ti(int,min)
| ti(int,X0) = one_one(int)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f4899,f3970]) ).
fof(f4899,plain,
! [X0,X1] :
( ti(int,X0) = number_number_of(int,min)
| ti(int,X0) = one_one(int)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f9879,plain,
spl63_436,
inference(avatar_split_clause,[],[f6447,f9877]) ).
fof(f9877,plain,
( spl63_436
<=> ! [X0,X1] :
( nat_1(pls) = X0
| one_one(nat) = X1
| times_times(nat,X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_436])]) ).
fof(f6447,plain,
! [X0,X1] :
( nat_1(pls) = X0
| one_one(nat) = X1
| times_times(nat,X0,X1) != X0 ),
inference(forward_demodulation,[],[f4753,f5811]) ).
fof(f4753,plain,
! [X0,X1] :
( zero_zero(nat) = X0
| one_one(nat) = X1
| times_times(nat,X0,X1) != X0 ),
inference(cnf_transformation,[],[f2791]) ).
fof(f2791,plain,
! [X0,X1] :
( zero_zero(nat) = X0
| one_one(nat) = X1
| times_times(nat,X0,X1) != X0 ),
inference(flattening,[],[f2790]) ).
fof(f2790,plain,
! [X0,X1] :
( zero_zero(nat) = X0
| one_one(nat) = X1
| times_times(nat,X0,X1) != X0 ),
inference(ennf_transformation,[],[f1840]) ).
fof(f1840,plain,
! [X0,X1] :
( times_times(nat,X0,X1) = X0
=> ( zero_zero(nat) = X0
| one_one(nat) = X1 ) ),
inference(rectify,[],[f755]) ).
fof(f755,axiom,
! [X13,X14] :
( times_times(nat,X13,X14) = X13
=> ( zero_zero(nat) = X13
| one_one(nat) = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_mult__eq__self__implies__10) ).
fof(f9875,plain,
spl63_435,
inference(avatar_split_clause,[],[f5934,f9873]) ).
fof(f9873,plain,
( spl63_435
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),nat_1(pls)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_435])]) ).
fof(f5934,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),nat_1(pls)),X0)),
inference(forward_demodulation,[],[f4013,f5811]) ).
fof(f4013,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X0)),
inference(cnf_transformation,[],[f1311]) ).
fof(f1311,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X0)),
inference(rectify,[],[f661]) ).
fof(f661,axiom,
! [X14] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_le0) ).
fof(f9871,plain,
spl63_434,
inference(avatar_split_clause,[],[f5931,f9869]) ).
fof(f9869,plain,
( spl63_434
<=> ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),nat_1(pls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_434])]) ).
fof(f5931,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),nat_1(pls))),
inference(forward_demodulation,[],[f4010,f5811]) ).
fof(f4010,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f1308]) ).
fof(f1308,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),zero_zero(nat))),
inference(rectify,[],[f240]) ).
fof(f240,axiom,
! [X14] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),zero_zero(nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_less__nat__zero__code) ).
fof(f9867,plain,
spl63_433,
inference(avatar_split_clause,[],[f5834,f9864]) ).
fof(f9864,plain,
( spl63_433
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_433])]) ).
fof(f5834,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),one_one(int))),
inference(forward_demodulation,[],[f3913,f3861]) ).
fof(f3913,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
inference(cnf_transformation,[],[f157]) ).
fof(f157,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_int__0__less__1) ).
fof(f9862,plain,
spl63_432,
inference(avatar_split_clause,[],[f5832,f9859]) ).
fof(f9859,plain,
( spl63_432
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_432])]) ).
fof(f5832,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),one_one(int))),
inference(forward_demodulation,[],[f3911,f3861]) ).
fof(f3911,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
inference(cnf_transformation,[],[f566]) ).
fof(f566,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f9857,plain,
spl63_431,
inference(avatar_split_clause,[],[f5830,f9854]) ).
fof(f9854,plain,
( spl63_431
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_431])]) ).
fof(f5830,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),n)),
inference(forward_demodulation,[],[f3907,f5811]) ).
fof(f3907,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)),
inference(cnf_transformation,[],[f112]) ).
fof(f112,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),n)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_n0) ).
fof(f9852,plain,
( spl63_430
| ~ spl63_230
| ~ spl63_411 ),
inference(avatar_split_clause,[],[f9759,f9471,f8131,f9850]) ).
fof(f9850,plain,
( spl63_430
<=> ! [X0] : pls = legendre(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_430])]) ).
fof(f8131,plain,
( spl63_230
<=> ! [X0] : hBOOL(hAPP(int,bool,zcong(X0,pls),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_230])]) ).
fof(f9759,plain,
( ! [X0] : pls = legendre(X0,X0)
| ~ spl63_230
| ~ spl63_411 ),
inference(resolution,[],[f9472,f8132]) ).
fof(f8132,plain,
( ! [X0] : hBOOL(hAPP(int,bool,zcong(X0,pls),X0))
| ~ spl63_230 ),
inference(avatar_component_clause,[],[f8131]) ).
fof(f9848,plain,
spl63_429,
inference(avatar_split_clause,[],[f5829,f9845]) ).
fof(f9845,plain,
( spl63_429
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),tn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_429])]) ).
fof(f5829,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),nat_1(pls)),tn)),
inference(forward_demodulation,[],[f3906,f5811]) ).
fof(f3906,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)),
inference(cnf_transformation,[],[f212]) ).
fof(f212,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),tn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_tn0) ).
fof(f9843,plain,
spl63_428,
inference(avatar_split_clause,[],[f5596,f9841]) ).
fof(f9841,plain,
( spl63_428
<=> ! [X0] :
( ti(int,X0) = min
| min != minus_minus(int,plus_plus(int,X0,X0),min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_428])]) ).
fof(f5596,plain,
! [X0] :
( ti(int,X0) = min
| min != minus_minus(int,plus_plus(int,X0,X0),min) ),
inference(definition_unfolding,[],[f4567,f5445]) ).
fof(f4567,plain,
! [X0] :
( ti(int,X0) = min
| bit1(X0) != min ),
inference(cnf_transformation,[],[f3362]) ).
fof(f3362,plain,
! [X0] :
( ( bit1(X0) = min
| ti(int,X0) != min )
& ( ti(int,X0) = min
| bit1(X0) != min ) ),
inference(nnf_transformation,[],[f1725]) ).
fof(f1725,plain,
! [X0] :
( bit1(X0) = min
<=> ti(int,X0) = min ),
inference(rectify,[],[f869]) ).
fof(f869,axiom,
! [X11] :
( min = bit1(X11)
<=> min = ti(int,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_771_rel__simps_I47_J) ).
fof(f9839,plain,
spl63_427,
inference(avatar_split_clause,[],[f5595,f9837]) ).
fof(f9837,plain,
( spl63_427
<=> ! [X0] :
( min = minus_minus(int,plus_plus(int,X0,X0),min)
| ti(int,X0) != min ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_427])]) ).
fof(f5595,plain,
! [X0] :
( min = minus_minus(int,plus_plus(int,X0,X0),min)
| ti(int,X0) != min ),
inference(definition_unfolding,[],[f4568,f5445]) ).
fof(f4568,plain,
! [X0] :
( bit1(X0) = min
| ti(int,X0) != min ),
inference(cnf_transformation,[],[f3362]) ).
fof(f9835,plain,
spl63_426,
inference(avatar_split_clause,[],[f5097,f9833]) ).
fof(f9833,plain,
( spl63_426
<=> ! [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_426])]) ).
fof(f5097,plain,
! [X2,X0,X1] : hBOOL(hAPP(int,bool,zcong(times_times(int,X0,X1),times_times(int,X2,X1)),X1)),
inference(cnf_transformation,[],[f2009]) ).
fof(f2009,plain,
! [X0,X1,X2] : hBOOL(hAPP(int,bool,zcong(times_times(int,X0,X1),times_times(int,X2,X1)),X1)),
inference(rectify,[],[f985]) ).
fof(f985,axiom,
! [X30,X13,X39] : hBOOL(hAPP(int,bool,zcong(times_times(int,X30,X13),times_times(int,X39,X13)),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_zcong__zmult__self) ).
fof(f9831,plain,
spl63_425,
inference(avatar_split_clause,[],[f4934,f9829]) ).
fof(f9829,plain,
( spl63_425
<=> ! [X0,X1] :
( nat_1(X1) = X0
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_425])]) ).
fof(f4934,plain,
! [X0,X1] :
( nat_1(X1) = X0
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0) ),
inference(cnf_transformation,[],[f3499]) ).
fof(f3499,plain,
! [X0,X1] :
( ( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| nat_1(X1) != X0 )
& ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
& nat_1(X1) = X0 )
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0) ) ),
inference(flattening,[],[f3498]) ).
fof(f3498,plain,
! [X0,X1] :
( ( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
| nat_1(X1) != X0 )
& ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
& nat_1(X1) = X0 )
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0) ) ),
inference(nnf_transformation,[],[f1943]) ).
fof(f1943,plain,
! [X0,X1] :
( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0)
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
& nat_1(X1) = X0 ) ),
inference(rectify,[],[f416]) ).
fof(f416,axiom,
! [X27,X28] :
( hAPP(nat,int,semiring_1_of_nat(int),X27) = ti(int,X28)
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X28))
& nat_1(X28) = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_int__eq__iff) ).
fof(f9827,plain,
spl63_424,
inference(avatar_split_clause,[],[f4661,f9825]) ).
fof(f9825,plain,
( spl63_424
<=> ! [X4,X0] :
( hBOOL(hAPP(nat,bool,X0,nat_1(sK40(X0))))
| ~ hBOOL(hAPP(nat,bool,X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_424])]) ).
fof(f4661,plain,
! [X0,X4] :
( hBOOL(hAPP(nat,bool,X0,nat_1(sK40(X0))))
| ~ hBOOL(hAPP(nat,bool,X0,X4)) ),
inference(cnf_transformation,[],[f3422]) ).
fof(f3422,plain,
! [X0] :
( ( hBOOL(hAPP(nat,bool,X0,sK39(X0)))
| ! [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
& ( ( hBOOL(hAPP(nat,bool,X0,nat_1(sK40(X0))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK40(X0))) )
| ! [X4] : ~ hBOOL(hAPP(nat,bool,X0,X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f3419,f3421,f3420]) ).
fof(f3420,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP(nat,bool,X0,X1))
=> hBOOL(hAPP(nat,bool,X0,sK39(X0))) ),
introduced(choice_axiom,[]) ).
fof(f3421,plain,
! [X0] :
( ? [X3] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X3)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) )
=> ( hBOOL(hAPP(nat,bool,X0,nat_1(sK40(X0))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK40(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3419,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP(nat,bool,X0,X1))
| ! [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
& ( ? [X3] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X3)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) )
| ! [X4] : ~ hBOOL(hAPP(nat,bool,X0,X4)) ) ),
inference(rectify,[],[f3418]) ).
fof(f3418,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP(nat,bool,X0,X1))
| ! [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
& ( ? [X2] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
| ! [X1] : ~ hBOOL(hAPP(nat,bool,X0,X1)) ) ),
inference(nnf_transformation,[],[f1766]) ).
fof(f1766,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP(nat,bool,X0,X1))
<=> ? [X2] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(rectify,[],[f391]) ).
fof(f391,axiom,
! [X32] :
( ? [X57] : hBOOL(hAPP(nat,bool,X32,X57))
<=> ? [X46] :
( hBOOL(hAPP(nat,bool,X32,nat_1(X46)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_ex__nat) ).
fof(f9823,plain,
spl63_423,
inference(avatar_split_clause,[],[f4656,f9821]) ).
fof(f9821,plain,
( spl63_423
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X1))
| ~ hBOOL(hAPP(nat,bool,X0,nat_1(sK35(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_423])]) ).
fof(f4656,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X1))
| ~ hBOOL(hAPP(nat,bool,X0,nat_1(sK35(X0)))) ),
inference(cnf_transformation,[],[f3412]) ).
fof(f3412,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP(nat,bool,X0,X1))
| ( ~ hBOOL(hAPP(nat,bool,X0,nat_1(sK35(X0))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK35(X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) )
| ~ hBOOL(hAPP(nat,bool,X0,sK36(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f3409,f3411,f3410]) ).
fof(f3410,plain,
! [X0] :
( ? [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
=> ( ~ hBOOL(hAPP(nat,bool,X0,nat_1(sK35(X0))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK35(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f3411,plain,
! [X0] :
( ? [X4] : ~ hBOOL(hAPP(nat,bool,X0,X4))
=> ~ hBOOL(hAPP(nat,bool,X0,sK36(X0))) ),
introduced(choice_axiom,[]) ).
fof(f3409,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP(nat,bool,X0,X1))
| ? [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
& ( ! [X3] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X3)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X3)) )
| ? [X4] : ~ hBOOL(hAPP(nat,bool,X0,X4)) ) ),
inference(rectify,[],[f3408]) ).
fof(f3408,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP(nat,bool,X0,X1))
| ? [X2] :
( ~ hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) )
& ( ! [X2] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) )
| ? [X1] : ~ hBOOL(hAPP(nat,bool,X0,X1)) ) ),
inference(nnf_transformation,[],[f2766]) ).
fof(f2766,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(nat,bool,X0,X1))
<=> ! [X2] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X2)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2)) ) ),
inference(ennf_transformation,[],[f1764]) ).
fof(f1764,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(nat,bool,X0,X1))
<=> ! [X2] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X2))
=> hBOOL(hAPP(nat,bool,X0,nat_1(X2))) ) ),
inference(rectify,[],[f390]) ).
fof(f390,axiom,
! [X32] :
( ! [X57] : hBOOL(hAPP(nat,bool,X32,X57))
<=> ! [X46] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X46))
=> hBOOL(hAPP(nat,bool,X32,nat_1(X46))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_all__nat) ).
fof(f9819,plain,
spl63_422,
inference(avatar_split_clause,[],[f4452,f9817]) ).
fof(f9817,plain,
( spl63_422
<=> ! [X0,X1] :
( ti(X0,X1) = hAPP(nat,X0,power_power(X0,X1),one_one(nat))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_422])]) ).
fof(f4452,plain,
! [X0,X1] :
( ti(X0,X1) = hAPP(nat,X0,power_power(X0,X1),one_one(nat))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2641]) ).
fof(f2641,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = hAPP(nat,X0,power_power(X0,X1),one_one(nat))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1636]) ).
fof(f1636,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : ti(X0,X1) = hAPP(nat,X0,power_power(X0,X1),one_one(nat)) ),
inference(rectify,[],[f325]) ).
fof(f325,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X9] : ti(X1,X9) = hAPP(nat,X1,power_power(X1,X9),one_one(nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(f9815,plain,
spl63_421,
inference(avatar_split_clause,[],[f4356,f9813]) ).
fof(f9813,plain,
( spl63_421
<=> ! [X0,X1] :
( ti(X0,X1) = hAPP(nat,X0,power_power(X0,X1),one_one(nat))
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_421])]) ).
fof(f4356,plain,
! [X0,X1] :
( ti(X0,X1) = hAPP(nat,X0,power_power(X0,X1),one_one(nat))
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f2508]) ).
fof(f2508,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = hAPP(nat,X0,power_power(X0,X1),one_one(nat))
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f1549]) ).
fof(f1549,plain,
! [X0] :
( monoid_mult(X0)
=> ! [X1] : ti(X0,X1) = hAPP(nat,X0,power_power(X0,X1),one_one(nat)) ),
inference(rectify,[],[f255]) ).
fof(f255,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X30] : ti(X1,X30) = hAPP(nat,X1,power_power(X1,X30),one_one(nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_power__one__right) ).
fof(f9811,plain,
spl63_420,
inference(avatar_split_clause,[],[f4176,f9809]) ).
fof(f9809,plain,
( spl63_420
<=> ! [X0,X1] :
( zero_zero(X0) = abs_abs(X0,X1)
| zero_zero(X0) != ti(X0,X1)
| ~ ordere142940540dd_abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_420])]) ).
fof(f4176,plain,
! [X0,X1] :
( zero_zero(X0) = abs_abs(X0,X1)
| zero_zero(X0) != ti(X0,X1)
| ~ ordere142940540dd_abs(X0) ),
inference(cnf_transformation,[],[f3300]) ).
fof(f3300,plain,
! [X0] :
( ! [X1] :
( ( zero_zero(X0) = abs_abs(X0,X1)
| zero_zero(X0) != ti(X0,X1) )
& ( zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != abs_abs(X0,X1) ) )
| ~ ordere142940540dd_abs(X0) ),
inference(nnf_transformation,[],[f2332]) ).
fof(f2332,plain,
! [X0] :
( ! [X1] :
( zero_zero(X0) = abs_abs(X0,X1)
<=> zero_zero(X0) = ti(X0,X1) )
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f1398]) ).
fof(f1398,plain,
! [X0] :
( ordere142940540dd_abs(X0)
=> ! [X1] :
( zero_zero(X0) = abs_abs(X0,X1)
<=> zero_zero(X0) = ti(X0,X1) ) ),
inference(rectify,[],[f1029]) ).
fof(f1029,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X6] :
( zero_zero(X1) = abs_abs(X1,X6)
<=> zero_zero(X1) = ti(X1,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_abs__eq__0) ).
fof(f9807,plain,
( spl63_419
| ~ spl63_222
| ~ spl63_411 ),
inference(avatar_split_clause,[],[f9758,f9471,f8099,f9805]) ).
fof(f9805,plain,
( spl63_419
<=> ! [X0] : pls = legendre(pls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_419])]) ).
fof(f8099,plain,
( spl63_222
<=> ! [X0,X1] : hBOOL(hAPP(int,bool,zcong(X0,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_222])]) ).
fof(f9758,plain,
( ! [X0] : pls = legendre(pls,X0)
| ~ spl63_222
| ~ spl63_411 ),
inference(resolution,[],[f9472,f8100]) ).
fof(f8100,plain,
( ! [X0,X1] : hBOOL(hAPP(int,bool,zcong(X0,X0),X1))
| ~ spl63_222 ),
inference(avatar_component_clause,[],[f8099]) ).
fof(f9803,plain,
spl63_418,
inference(avatar_split_clause,[],[f4175,f9801]) ).
fof(f9801,plain,
( spl63_418
<=> ! [X0,X1] :
( zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != abs_abs(X0,X1)
| ~ ordere142940540dd_abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_418])]) ).
fof(f4175,plain,
! [X0,X1] :
( zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != abs_abs(X0,X1)
| ~ ordere142940540dd_abs(X0) ),
inference(cnf_transformation,[],[f3300]) ).
fof(f9799,plain,
spl63_417,
inference(avatar_split_clause,[],[f3910,f9796]) ).
fof(f9796,plain,
( spl63_417
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_417])]) ).
fof(f3910,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
inference(cnf_transformation,[],[f99]) ).
fof(f99,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_t1) ).
fof(f9794,plain,
spl63_416,
inference(avatar_split_clause,[],[f3909,f9791]) ).
fof(f9791,plain,
( spl63_416
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_416])]) ).
fof(f3909,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
inference(cnf_transformation,[],[f329]) ).
fof(f329,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_tpos) ).
fof(f9749,plain,
( spl63_415
| ~ spl63_37
| ~ spl63_238 ),
inference(avatar_split_clause,[],[f8315,f8190,f7177,f9746]) ).
fof(f9746,plain,
( spl63_415
<=> zero_zero(real) = abs_abs(real,zero_zero(real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_415])]) ).
fof(f7177,plain,
( spl63_37
<=> ordere142940540dd_abs(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_37])]) ).
fof(f8190,plain,
( spl63_238
<=> ! [X0] :
( zero_zero(X0) = abs_abs(X0,zero_zero(X0))
| ~ ordere142940540dd_abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_238])]) ).
fof(f8315,plain,
( zero_zero(real) = abs_abs(real,zero_zero(real))
| ~ spl63_37
| ~ spl63_238 ),
inference(resolution,[],[f8191,f7179]) ).
fof(f7179,plain,
( ordere142940540dd_abs(real)
| ~ spl63_37 ),
inference(avatar_component_clause,[],[f7177]) ).
fof(f8191,plain,
( ! [X0] :
( ~ ordere142940540dd_abs(X0)
| zero_zero(X0) = abs_abs(X0,zero_zero(X0)) )
| ~ spl63_238 ),
inference(avatar_component_clause,[],[f8190]) ).
fof(f9651,plain,
( spl63_414
| ~ spl63_31
| ~ spl63_237 ),
inference(avatar_split_clause,[],[f8312,f8186,f7147,f9649]) ).
fof(f9649,plain,
( spl63_414
<=> ! [X0] : zero_zero(real) = minus_minus(real,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_414])]) ).
fof(f7147,plain,
( spl63_31
<=> group_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_31])]) ).
fof(f8186,plain,
( spl63_237
<=> ! [X0,X1] :
( zero_zero(X0) = minus_minus(X0,X1,X1)
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_237])]) ).
fof(f8312,plain,
( ! [X0] : zero_zero(real) = minus_minus(real,X0,X0)
| ~ spl63_31
| ~ spl63_237 ),
inference(resolution,[],[f8187,f7149]) ).
fof(f7149,plain,
( group_add(real)
| ~ spl63_31 ),
inference(avatar_component_clause,[],[f7147]) ).
fof(f8187,plain,
( ! [X0,X1] :
( ~ group_add(X0)
| zero_zero(X0) = minus_minus(X0,X1,X1) )
| ~ spl63_237 ),
inference(avatar_component_clause,[],[f8186]) ).
fof(f9482,plain,
spl63_413,
inference(avatar_split_clause,[],[f6995,f9479]) ).
fof(f9479,plain,
( spl63_413
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),sK62)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_413])]) ).
fof(f6995,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),sK62)),
inference(forward_demodulation,[],[f5441,f3861]) ).
fof(f5441,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK62)),
inference(cnf_transformation,[],[f3694]) ).
fof(f3694,plain,
( ! [X1] :
( ti(int,X1) = ti(int,sK62)
| ~ 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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK62)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f3197,f3693]) ).
fof(f3693,plain,
( ? [X0] :
( ! [X1] :
( ti(int,X0) = ti(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
=> ( ! [X1] :
( ti(int,X1) = ti(int,sK62)
| ~ 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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK62)) ) ),
introduced(choice_axiom,[]) ).
fof(f3197,plain,
? [X0] :
( ! [X1] :
( ti(int,X0) = ti(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ),
inference(flattening,[],[f3196]) ).
fof(f3196,plain,
? [X0] :
( ! [X1] :
( ti(int,X0) = ti(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ),
inference(ennf_transformation,[],[f2244]) ).
fof(f2244,plain,
? [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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
=> ti(int,X0) = ti(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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ),
inference(rectify,[],[f939]) ).
fof(f939,axiom,
? [X46] :
( ! [X47] :
( ( hBOOL(hAPP(int,bool,zcong(s1,X47),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X47),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X47)) )
=> ti(int,X47) = ti(int,X46) )
& hBOOL(hAPP(int,bool,zcong(s1,X46),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X46),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_841__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) ).
fof(f9477,plain,
spl63_412,
inference(avatar_split_clause,[],[f6586,f9475]) ).
fof(f9475,plain,
( spl63_412
<=> ! [X0,X1] :
( min != ti(int,X1)
| ti(int,X0) != min
| sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_412])]) ).
fof(f6586,plain,
! [X0,X1] :
( min != ti(int,X1)
| ti(int,X0) != min
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f6585,f3874]) ).
fof(f6585,plain,
! [X0,X1] :
( ti(int,min) != ti(int,X1)
| ti(int,X0) != min
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f6584,f3970]) ).
fof(f6584,plain,
! [X0,X1] :
( ti(int,X0) != min
| sP11(X0,X1)
| number_number_of(int,min) != ti(int,X1) ),
inference(forward_demodulation,[],[f6583,f3874]) ).
fof(f6583,plain,
! [X0,X1] :
( ti(int,X0) != ti(int,min)
| sP11(X0,X1)
| number_number_of(int,min) != ti(int,X1) ),
inference(forward_demodulation,[],[f4901,f3970]) ).
fof(f4901,plain,
! [X0,X1] :
( sP11(X0,X1)
| ti(int,X0) != number_number_of(int,min)
| number_number_of(int,min) != ti(int,X1) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f9473,plain,
spl63_411,
inference(avatar_split_clause,[],[f6429,f9471]) ).
fof(f6429,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(int,bool,zcong(X0,pls),X1))
| pls = legendre(X0,X1) ),
inference(forward_demodulation,[],[f6428,f3861]) ).
fof(f6428,plain,
! [X0,X1] :
( pls = legendre(X0,X1)
| ~ hBOOL(hAPP(int,bool,zcong(X0,zero_zero(int)),X1)) ),
inference(forward_demodulation,[],[f4726,f3861]) ).
fof(f4726,plain,
! [X0,X1] :
( zero_zero(int) = legendre(X0,X1)
| ~ hBOOL(hAPP(int,bool,zcong(X0,zero_zero(int)),X1)) ),
inference(cnf_transformation,[],[f2771]) ).
fof(f2771,plain,
! [X0,X1] :
( ( ( ( number_number_of(int,min) = legendre(X0,X1)
| 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,[],[f1826]) ).
fof(f1826,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(int,bool,zcong(X0,zero_zero(int)),X1))
=> ( ( ~ hBOOL(hAPP(int,bool,quadRes(X1),X0))
=> number_number_of(int,min) = legendre(X0,X1) )
& ( 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,[],[f975]) ).
fof(f975,axiom,
! [X30,X64] :
( ( ~ hBOOL(hAPP(int,bool,zcong(X30,zero_zero(int)),X64))
=> ( ( ~ hBOOL(hAPP(int,bool,quadRes(X64),X30))
=> number_number_of(int,min) = legendre(X30,X64) )
& ( hBOOL(hAPP(int,bool,quadRes(X64),X30))
=> one_one(int) = legendre(X30,X64) ) ) )
& ( hBOOL(hAPP(int,bool,zcong(X30,zero_zero(int)),X64))
=> zero_zero(int) = legendre(X30,X64) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_Legendre__def) ).
fof(f9469,plain,
spl63_410,
inference(avatar_split_clause,[],[f6162,f9467]) ).
fof(f9467,plain,
( spl63_410
<=> ! [X0,X1] :
( one_one(X0) = hAPP(nat,X0,power_power(X0,X1),nat_1(pls))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_410])]) ).
fof(f6162,plain,
! [X0,X1] :
( one_one(X0) = hAPP(nat,X0,power_power(X0,X1),nat_1(pls))
| ~ comm_semiring_1(X0) ),
inference(forward_demodulation,[],[f4451,f5811]) ).
fof(f4451,plain,
! [X0,X1] :
( one_one(X0) = hAPP(nat,X0,power_power(X0,X1),zero_zero(nat))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2640]) ).
fof(f2640,plain,
! [X0] :
( ! [X1] : one_one(X0) = hAPP(nat,X0,power_power(X0,X1),zero_zero(nat))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1635]) ).
fof(f1635,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : one_one(X0) = hAPP(nat,X0,power_power(X0,X1),zero_zero(nat)) ),
inference(rectify,[],[f291]) ).
fof(f291,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X9] : one_one(X1) = hAPP(nat,X1,power_power(X1,X9),zero_zero(nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(f9465,plain,
spl63_409,
inference(avatar_split_clause,[],[f6142,f9463]) ).
fof(f9463,plain,
( spl63_409
<=> ! [X0,X1] :
( one_one(X0) = hAPP(nat,X0,power_power(X0,X1),nat_1(pls))
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_409])]) ).
fof(f6142,plain,
! [X0,X1] :
( one_one(X0) = hAPP(nat,X0,power_power(X0,X1),nat_1(pls))
| ~ power(X0) ),
inference(forward_demodulation,[],[f4380,f5811]) ).
fof(f4380,plain,
! [X0,X1] :
( one_one(X0) = hAPP(nat,X0,power_power(X0,X1),zero_zero(nat))
| ~ power(X0) ),
inference(cnf_transformation,[],[f2543]) ).
fof(f2543,plain,
! [X0] :
( ! [X1] : one_one(X0) = hAPP(nat,X0,power_power(X0,X1),zero_zero(nat))
| ~ power(X0) ),
inference(ennf_transformation,[],[f1571]) ).
fof(f1571,plain,
! [X0] :
( power(X0)
=> ! [X1] : one_one(X0) = hAPP(nat,X0,power_power(X0,X1),zero_zero(nat)) ),
inference(rectify,[],[f285]) ).
fof(f285,axiom,
! [X1] :
( power(X1)
=> ! [X30] : one_one(X1) = hAPP(nat,X1,power_power(X1,X30),zero_zero(nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_power__0) ).
fof(f9461,plain,
spl63_408,
inference(avatar_split_clause,[],[f5900,f9458]) ).
fof(f9458,plain,
( spl63_408
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_408])]) ).
fof(f5900,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),sK24)),
inference(forward_demodulation,[],[f3949,f3861]) ).
fof(f3949,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK24)),
inference(cnf_transformation,[],[f3241]) ).
fof(f3241,plain,
( hBOOL(hAPP(int,bool,zcong(s1,sK24),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK24),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK24)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f2250,f3240]) ).
fof(f3240,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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
=> ( hBOOL(hAPP(int,bool,zcong(s1,sK24),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),sK24),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),sK24)) ) ),
introduced(choice_axiom,[]) ).
fof(f2250,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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ),
inference(ennf_transformation,[],[f1257]) ).
fof(f1257,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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ),
inference(rectify,[],[f941]) ).
fof(f941,axiom,
~ ! [X74] :
~ ( hBOOL(hAPP(int,bool,zcong(s1,X74),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X74),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843__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(f9456,plain,
spl63_407,
inference(avatar_split_clause,[],[f5880,f9453]) ).
fof(f9453,plain,
( spl63_407
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),s)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_407])]) ).
fof(f5880,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),s)),
inference(forward_demodulation,[],[f3938,f3861]) ).
fof(f3938,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),s)),
inference(cnf_transformation,[],[f894]) ).
fof(f894,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(int,fun(int,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(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),s)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_s0p) ).
fof(f9451,plain,
spl63_406,
inference(avatar_split_clause,[],[f5802,f9449]) ).
fof(f9449,plain,
( spl63_406
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(nat,bool,X0,X4))
| ~ sP18(X0,plus_plus(nat,X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_406])]) ).
fof(f5802,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(nat,bool,X0,X4))
| ~ sP18(X0,plus_plus(nat,X2,X4),X2) ),
inference(equality_resolution,[],[f5350]) ).
fof(f5350,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(nat,bool,X0,X4))
| plus_plus(nat,X2,X4) != X1
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f3661]) ).
fof(f3661,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(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f3659,f3660]) ).
fof(f3660,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(f3659,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(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(rectify,[],[f3658]) ).
fof(f3658,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(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(flattening,[],[f3657]) ).
fof(f3657,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(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3230]) ).
fof(f3230,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f9447,plain,
spl63_405,
inference(avatar_split_clause,[],[f5801,f9445]) ).
fof(f9445,plain,
( spl63_405
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(nat,bool,X0,X4))
| ~ sP17(X0,plus_plus(nat,X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_405])]) ).
fof(f5801,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(nat,bool,X0,X4))
| ~ sP17(X0,plus_plus(nat,X2,X4),X2) ),
inference(equality_resolution,[],[f5342]) ).
fof(f5342,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(nat,bool,X0,X4))
| plus_plus(nat,X2,X4) != X1
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f3655]) ).
fof(f3655,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(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f3653,f3654]) ).
fof(f3654,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(f3653,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(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(rectify,[],[f3652]) ).
fof(f3652,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(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(flattening,[],[f3651]) ).
fof(f3651,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(nat,fun(nat,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3228]) ).
fof(f3228,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f9443,plain,
spl63_404,
inference(avatar_split_clause,[],[f5766,f9441]) ).
fof(f9441,plain,
( spl63_404
<=> ! [X1] : ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_404])]) ).
fof(f5766,plain,
! [X1] : ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X1),X1)),
inference(equality_resolution,[],[f4953]) ).
fof(f4953,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X0),X1)) ),
inference(cnf_transformation,[],[f3510]) ).
fof(f3510,plain,
! [X0,X1] :
( ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X0),X1))
| X0 = X1
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X0),X1)) )
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X0),X1)) ) ),
inference(flattening,[],[f3509]) ).
fof(f3509,plain,
! [X0,X1] :
( ( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X0),X1))
| X0 = X1
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X0),X1)) )
| ~ hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X0),X1)) ) ),
inference(nnf_transformation,[],[f1950]) ).
fof(f1950,plain,
! [X0,X1] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X0),X1))
<=> ( X0 != X1
& hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X0),X1)) ) ),
inference(rectify,[],[f708]) ).
fof(f708,axiom,
! [X4,X5] :
( hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X4),X5))
<=> ( X4 != X5
& hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X4),X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_real__less__def) ).
fof(f9419,plain,
spl63_403,
inference(avatar_split_clause,[],[f5396,f9417]) ).
fof(f9417,plain,
( spl63_403
<=> ! [X0,X3,X2,X1] : if(X0,X1,X2,X3) = if(X0,ti(bool,X1),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_403])]) ).
fof(f5396,plain,
! [X2,X3,X0,X1] : if(X0,X1,X2,X3) = if(X0,ti(bool,X1),X2,X3),
inference(cnf_transformation,[],[f2208]) ).
fof(f2208,plain,
! [X0,X1,X2,X3] : if(X0,X1,X2,X3) = if(X0,ti(bool,X1),X2,X3),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X1,X0,X2,X3] : if(X1,ti(bool,X0),X2,X3) = if(X1,X0,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_If_arg1) ).
fof(f9415,plain,
spl63_402,
inference(avatar_split_clause,[],[f5395,f9413]) ).
fof(f9413,plain,
( spl63_402
<=> ! [X0,X3,X2,X1] : if(X0,X1,X2,X3) = if(X0,X1,ti(X0,X2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_402])]) ).
fof(f5395,plain,
! [X2,X3,X0,X1] : if(X0,X1,X2,X3) = if(X0,X1,ti(X0,X2),X3),
inference(cnf_transformation,[],[f2207]) ).
fof(f2207,plain,
! [X0,X1,X2,X3] : if(X0,X1,X2,X3) = if(X0,X1,ti(X0,X2),X3),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X1,X0,X2,X3] : if(X1,X0,X2,X3) = if(X1,X0,ti(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_If_arg2) ).
fof(f9411,plain,
spl63_401,
inference(avatar_split_clause,[],[f5394,f9409]) ).
fof(f9409,plain,
( spl63_401
<=> ! [X0,X3,X2,X1] : if(X0,X1,X2,X3) = if(X0,X1,X2,ti(X0,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_401])]) ).
fof(f5394,plain,
! [X2,X3,X0,X1] : if(X0,X1,X2,X3) = if(X0,X1,X2,ti(X0,X3)),
inference(cnf_transformation,[],[f2206]) ).
fof(f2206,plain,
! [X0,X1,X2,X3] : if(X0,X1,X2,X3) = if(X0,X1,X2,ti(X0,X3)),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X1,X0,X2,X3] : if(X1,X0,X2,X3) = if(X1,X0,X2,ti(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_If_arg3) ).
fof(f9407,plain,
spl63_400,
inference(avatar_split_clause,[],[f5393,f9405]) ).
fof(f9405,plain,
( spl63_400
<=> ! [X0,X3,X2,X1] : if(X0,X1,X2,X3) = ti(X0,if(X0,X1,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_400])]) ).
fof(f5393,plain,
! [X2,X3,X0,X1] : if(X0,X1,X2,X3) = ti(X0,if(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f2205]) ).
fof(f2205,plain,
! [X0,X1,X2,X3] : if(X0,X1,X2,X3) = ti(X0,if(X0,X1,X2,X3)),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X1,X0,X2,X3] : if(X1,X0,X2,X3) = ti(X1,if(X1,X0,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_If_res) ).
fof(f9403,plain,
spl63_399,
inference(avatar_split_clause,[],[f5356,f9401]) ).
fof(f9401,plain,
( spl63_399
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2)))
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_399])]) ).
fof(f5356,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2)))
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f3662]) ).
fof(f3662,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,[],[f3231]) ).
fof(f3231,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2)))
<=> sP18(X0,X1,X2) ),
inference(definition_folding,[],[f3142,f3230]) ).
fof(f3142,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ) ),
inference(ennf_transformation,[],[f2192]) ).
fof(f2192,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ) ),
inference(rectify,[],[f597]) ).
fof(f597,axiom,
! [X32,X6,X41] :
( hBOOL(hAPP(nat,bool,X32,minus_minus(nat,X6,X41)))
<=> ~ ( ? [X66] :
( ~ hBOOL(hAPP(nat,bool,X32,X66))
& plus_plus(nat,X41,X66) = X6 )
| ( ~ hBOOL(hAPP(nat,bool,X32,zero_zero(nat)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6),X41)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_nat__diff__split__asm) ).
fof(f9399,plain,
spl63_398,
inference(avatar_split_clause,[],[f5355,f9397]) ).
fof(f9397,plain,
( spl63_398
<=> ! [X2,X0,X1] :
( sP18(X0,X1,X2)
| ~ hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_398])]) ).
fof(f5355,plain,
! [X2,X0,X1] :
( sP18(X0,X1,X2)
| ~ hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2))) ),
inference(cnf_transformation,[],[f3662]) ).
fof(f9395,plain,
spl63_397,
inference(avatar_split_clause,[],[f5348,f9393]) ).
fof(f9393,plain,
( spl63_397
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2)))
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_397])]) ).
fof(f5348,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2)))
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f3656]) ).
fof(f3656,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,[],[f3229]) ).
fof(f3229,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2)))
<=> sP17(X0,X1,X2) ),
inference(definition_folding,[],[f3141,f3228]) ).
fof(f3141,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(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ) ),
inference(ennf_transformation,[],[f2191]) ).
fof(f2191,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(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,X0,zero_zero(nat))) ) ) ),
inference(rectify,[],[f598]) ).
fof(f598,axiom,
! [X32,X6,X41] :
( hBOOL(hAPP(nat,bool,X32,minus_minus(nat,X6,X41)))
<=> ( ! [X66] :
( plus_plus(nat,X41,X66) = X6
=> hBOOL(hAPP(nat,bool,X32,X66)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X6),X41))
=> hBOOL(hAPP(nat,bool,X32,zero_zero(nat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_nat__diff__split) ).
fof(f9391,plain,
spl63_396,
inference(avatar_split_clause,[],[f5347,f9389]) ).
fof(f9389,plain,
( spl63_396
<=> ! [X2,X0,X1] :
( sP17(X0,X1,X2)
| ~ hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_396])]) ).
fof(f5347,plain,
! [X2,X0,X1] :
( sP17(X0,X1,X2)
| ~ hBOOL(hAPP(nat,bool,X0,minus_minus(nat,X1,X2))) ),
inference(cnf_transformation,[],[f3656]) ).
fof(f9387,plain,
spl63_395,
inference(avatar_split_clause,[],[f5156,f9385]) ).
fof(f9385,plain,
( spl63_395
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_395])]) ).
fof(f5156,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ power(X2) ),
inference(cnf_transformation,[],[f2965]) ).
fof(f2965,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ power(X2) ),
inference(ennf_transformation,[],[f2065]) ).
fof(f2065,plain,
! [X0,X1,X2] :
( power(X2)
=> times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X2,X1] :
( power(X1)
=> times_times(X1,ti(X1,X0),X2) = times_times(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg1) ).
fof(f9383,plain,
spl63_394,
inference(avatar_split_clause,[],[f5155,f9381]) ).
fof(f9381,plain,
( spl63_394
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ dvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_394])]) ).
fof(f5155,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ dvd(X2) ),
inference(cnf_transformation,[],[f2964]) ).
fof(f2964,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ dvd(X2) ),
inference(ennf_transformation,[],[f2064]) ).
fof(f2064,plain,
! [X0,X1,X2] :
( dvd(X2)
=> times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X0,X2,X1] :
( dvd(X1)
=> times_times(X1,ti(X1,X0),X2) = times_times(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg1) ).
fof(f9359,plain,
spl63_393,
inference(avatar_split_clause,[],[f5154,f9357]) ).
fof(f9357,plain,
( spl63_393
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_393])]) ).
fof(f5154,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ power(X2) ),
inference(cnf_transformation,[],[f2963]) ).
fof(f2963,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ power(X2) ),
inference(ennf_transformation,[],[f2063]) ).
fof(f2063,plain,
! [X0,X1,X2] :
( power(X2)
=> times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X0,X2,X1] :
( power(X1)
=> times_times(X1,X0,X2) = times_times(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg2) ).
fof(f9355,plain,
spl63_392,
inference(avatar_split_clause,[],[f5153,f9353]) ).
fof(f9353,plain,
( spl63_392
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ dvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_392])]) ).
fof(f5153,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ dvd(X2) ),
inference(cnf_transformation,[],[f2962]) ).
fof(f2962,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ dvd(X2) ),
inference(ennf_transformation,[],[f2062]) ).
fof(f2062,plain,
! [X0,X1,X2] :
( dvd(X2)
=> times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X0,X2,X1] :
( dvd(X1)
=> times_times(X1,X0,X2) = times_times(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg2) ).
fof(f9351,plain,
spl63_391,
inference(avatar_split_clause,[],[f5152,f9349]) ).
fof(f9349,plain,
( spl63_391
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ dvd(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_391])]) ).
fof(f5152,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ dvd(X2) ),
inference(cnf_transformation,[],[f2961]) ).
fof(f2961,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ dvd(X2) ),
inference(ennf_transformation,[],[f2061]) ).
fof(f2061,plain,
! [X0,X1,X2] :
( dvd(X2)
=> times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X2,X1] :
( dvd(X1)
=> times_times(X1,X0,X2) = ti(X1,times_times(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).
fof(f9347,plain,
spl63_390,
inference(avatar_split_clause,[],[f5151,f9345]) ).
fof(f9345,plain,
( spl63_390
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_390])]) ).
fof(f5151,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ power(X2) ),
inference(cnf_transformation,[],[f2960]) ).
fof(f2960,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ power(X2) ),
inference(ennf_transformation,[],[f2060]) ).
fof(f2060,plain,
! [X0,X1,X2] :
( power(X2)
=> times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X0,X2,X1] :
( power(X1)
=> times_times(X1,X0,X2) = ti(X1,times_times(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).
fof(f9343,plain,
spl63_389,
inference(avatar_split_clause,[],[f5150,f9341]) ).
fof(f9341,plain,
( spl63_389
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ no_zero_divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_389])]) ).
fof(f5150,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ no_zero_divisors(X2) ),
inference(cnf_transformation,[],[f2959]) ).
fof(f2959,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ no_zero_divisors(X2) ),
inference(ennf_transformation,[],[f2059]) ).
fof(f2059,plain,
! [X0,X1,X2] :
( no_zero_divisors(X2)
=> times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X0,X2,X1] :
( no_zero_divisors(X1)
=> times_times(X1,ti(X1,X0),X2) = times_times(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_arg1) ).
fof(f9339,plain,
spl63_388,
inference(avatar_split_clause,[],[f5149,f9337]) ).
fof(f9337,plain,
( spl63_388
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ mult_zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_388])]) ).
fof(f5149,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ mult_zero(X2) ),
inference(cnf_transformation,[],[f2958]) ).
fof(f2958,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ mult_zero(X2) ),
inference(ennf_transformation,[],[f2058]) ).
fof(f2058,plain,
! [X0,X1,X2] :
( mult_zero(X2)
=> times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X0,X2,X1] :
( mult_zero(X1)
=> times_times(X1,ti(X1,X0),X2) = times_times(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_arg1) ).
fof(f9335,plain,
spl63_387,
inference(avatar_split_clause,[],[f5148,f9333]) ).
fof(f9333,plain,
( spl63_387
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ cancel_semigroup_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_387])]) ).
fof(f5148,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ cancel_semigroup_add(X2) ),
inference(cnf_transformation,[],[f2957]) ).
fof(f2957,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ cancel_semigroup_add(X2) ),
inference(ennf_transformation,[],[f2057]) ).
fof(f2057,plain,
! [X0,X1,X2] :
( cancel_semigroup_add(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X0,X2,X1] :
( cancel_semigroup_add(X1)
=> plus_plus(X1,ti(X1,X0),X2) = plus_plus(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_arg1) ).
fof(f9331,plain,
spl63_386,
inference(avatar_split_clause,[],[f5147,f9329]) ).
fof(f9329,plain,
( spl63_386
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ no_zero_divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_386])]) ).
fof(f5147,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ no_zero_divisors(X2) ),
inference(cnf_transformation,[],[f2956]) ).
fof(f2956,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ no_zero_divisors(X2) ),
inference(ennf_transformation,[],[f2056]) ).
fof(f2056,plain,
! [X0,X1,X2] :
( no_zero_divisors(X2)
=> times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X0,X2,X1] :
( no_zero_divisors(X1)
=> times_times(X1,X0,X2) = times_times(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_arg2) ).
fof(f9327,plain,
spl63_385,
inference(avatar_split_clause,[],[f5146,f9325]) ).
fof(f9325,plain,
( spl63_385
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ mult_zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_385])]) ).
fof(f5146,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ mult_zero(X2) ),
inference(cnf_transformation,[],[f2955]) ).
fof(f2955,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ mult_zero(X2) ),
inference(ennf_transformation,[],[f2055]) ).
fof(f2055,plain,
! [X0,X1,X2] :
( mult_zero(X2)
=> times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X0,X2,X1] :
( mult_zero(X1)
=> times_times(X1,X0,X2) = times_times(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_arg2) ).
fof(f9323,plain,
spl63_384,
inference(avatar_split_clause,[],[f5145,f9321]) ).
fof(f9321,plain,
( spl63_384
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ mult_zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_384])]) ).
fof(f5145,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ mult_zero(X2) ),
inference(cnf_transformation,[],[f2954]) ).
fof(f2954,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ mult_zero(X2) ),
inference(ennf_transformation,[],[f2054]) ).
fof(f2054,plain,
! [X0,X1,X2] :
( mult_zero(X2)
=> times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X0,X2,X1] :
( mult_zero(X1)
=> times_times(X1,X0,X2) = ti(X1,times_times(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_res) ).
fof(f9319,plain,
( ~ spl63_383
| ~ spl63_69
| ~ spl63_217
| ~ spl63_240
| ~ spl63_280 ),
inference(avatar_split_clause,[],[f8621,f8540,f8198,f8079,f7337,f9316]) ).
fof(f9316,plain,
( spl63_383
<=> pls = ti(int,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_383])]) ).
fof(f8621,plain,
( pls != ti(int,one_one(int))
| ~ spl63_69
| ~ spl63_217
| ~ spl63_240
| ~ spl63_280 ),
inference(forward_demodulation,[],[f8620,f8322]) ).
fof(f8620,plain,
( pls != ti(int,ti(int,one_one(int)))
| ~ spl63_217
| ~ spl63_280 ),
inference(forward_demodulation,[],[f8613,f8080]) ).
fof(f8613,plain,
( pls != ti(int,plus_plus(int,one_one(int),pls))
| ~ spl63_217
| ~ spl63_280 ),
inference(superposition,[],[f8541,f8080]) ).
fof(f9314,plain,
spl63_382,
inference(avatar_split_clause,[],[f5144,f9312]) ).
fof(f9312,plain,
( spl63_382
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ no_zero_divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_382])]) ).
fof(f5144,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ no_zero_divisors(X2) ),
inference(cnf_transformation,[],[f2953]) ).
fof(f2953,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ no_zero_divisors(X2) ),
inference(ennf_transformation,[],[f2053]) ).
fof(f2053,plain,
! [X0,X1,X2] :
( no_zero_divisors(X2)
=> times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X0,X2,X1] :
( no_zero_divisors(X1)
=> times_times(X1,X0,X2) = ti(X1,times_times(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_3_res) ).
fof(f9310,plain,
spl63_381,
inference(avatar_split_clause,[],[f5143,f9308]) ).
fof(f9308,plain,
( spl63_381
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ cancel_semigroup_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_381])]) ).
fof(f5143,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ cancel_semigroup_add(X2) ),
inference(cnf_transformation,[],[f2952]) ).
fof(f2952,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ cancel_semigroup_add(X2) ),
inference(ennf_transformation,[],[f2052]) ).
fof(f2052,plain,
! [X0,X1,X2] :
( cancel_semigroup_add(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X2,X1] :
( cancel_semigroup_add(X1)
=> plus_plus(X1,X0,X2) = plus_plus(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_arg2) ).
fof(f9306,plain,
spl63_380,
inference(avatar_split_clause,[],[f5142,f9304]) ).
fof(f9304,plain,
( spl63_380
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ cancel_semigroup_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_380])]) ).
fof(f5142,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ cancel_semigroup_add(X2) ),
inference(cnf_transformation,[],[f2951]) ).
fof(f2951,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ cancel_semigroup_add(X2) ),
inference(ennf_transformation,[],[f2051]) ).
fof(f2051,plain,
! [X0,X1,X2] :
( cancel_semigroup_add(X2)
=> plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1)) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X0,X2,X1] :
( cancel_semigroup_add(X1)
=> plus_plus(X1,X0,X2) = ti(X1,plus_plus(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).
fof(f9302,plain,
spl63_379,
inference(avatar_split_clause,[],[f5141,f9300]) ).
fof(f9300,plain,
( spl63_379
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_379])]) ).
fof(f5141,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ semiring(X2) ),
inference(cnf_transformation,[],[f2950]) ).
fof(f2950,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ semiring(X2) ),
inference(ennf_transformation,[],[f2050]) ).
fof(f2050,plain,
! [X0,X1,X2] :
( semiring(X2)
=> times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X2,X1] :
( semiring(X1)
=> times_times(X1,ti(X1,X0),X2) = times_times(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_arg1) ).
fof(f9298,plain,
spl63_378,
inference(avatar_split_clause,[],[f5140,f9296]) ).
fof(f9296,plain,
( spl63_378
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_378])]) ).
fof(f5140,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ semiring(X2) ),
inference(cnf_transformation,[],[f2949]) ).
fof(f2949,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ semiring(X2) ),
inference(ennf_transformation,[],[f2049]) ).
fof(f2049,plain,
! [X0,X1,X2] :
( semiring(X2)
=> times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X0,X2,X1] :
( semiring(X1)
=> times_times(X1,X0,X2) = times_times(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_arg2) ).
fof(f9294,plain,
spl63_377,
inference(avatar_split_clause,[],[f5139,f9292]) ).
fof(f9292,plain,
( spl63_377
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_377])]) ).
fof(f5139,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ semiring(X2) ),
inference(cnf_transformation,[],[f2948]) ).
fof(f2948,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ semiring(X2) ),
inference(ennf_transformation,[],[f2048]) ).
fof(f2048,plain,
! [X0,X1,X2] :
( semiring(X2)
=> times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X0,X2,X1] :
( semiring(X1)
=> times_times(X1,X0,X2) = ti(X1,times_times(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_2_res) ).
fof(f9290,plain,
spl63_376,
inference(avatar_split_clause,[],[f5138,f9288]) ).
fof(f9288,plain,
( spl63_376
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ monoid_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_376])]) ).
fof(f5138,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ monoid_add(X2) ),
inference(cnf_transformation,[],[f2947]) ).
fof(f2947,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ monoid_add(X2) ),
inference(ennf_transformation,[],[f2047]) ).
fof(f2047,plain,
! [X0,X1,X2] :
( monoid_add(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X2,X1] :
( monoid_add(X1)
=> plus_plus(X1,ti(X1,X0),X2) = plus_plus(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
fof(f9286,plain,
spl63_375,
inference(avatar_split_clause,[],[f5137,f9284]) ).
fof(f9284,plain,
( spl63_375
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ monoid_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_375])]) ).
fof(f5137,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ monoid_add(X2) ),
inference(cnf_transformation,[],[f2946]) ).
fof(f2946,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ monoid_add(X2) ),
inference(ennf_transformation,[],[f2046]) ).
fof(f2046,plain,
! [X0,X1,X2] :
( monoid_add(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X0,X2,X1] :
( monoid_add(X1)
=> plus_plus(X1,X0,X2) = plus_plus(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
fof(f9282,plain,
spl63_374,
inference(avatar_split_clause,[],[f5136,f9280]) ).
fof(f9280,plain,
( spl63_374
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ monoid_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_374])]) ).
fof(f5136,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ monoid_add(X2) ),
inference(cnf_transformation,[],[f2945]) ).
fof(f2945,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ monoid_add(X2) ),
inference(ennf_transformation,[],[f2045]) ).
fof(f2045,plain,
! [X0,X1,X2] :
( monoid_add(X2)
=> plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1)) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X2,X1] :
( monoid_add(X1)
=> plus_plus(X1,X0,X2) = ti(X1,plus_plus(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
fof(f9278,plain,
spl63_373,
inference(avatar_split_clause,[],[f5135,f9276]) ).
fof(f9276,plain,
( spl63_373
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ ab_semigroup_mult(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_373])]) ).
fof(f5135,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ ab_semigroup_mult(X2) ),
inference(cnf_transformation,[],[f2944]) ).
fof(f2944,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1)
| ~ ab_semigroup_mult(X2) ),
inference(ennf_transformation,[],[f2044]) ).
fof(f2044,plain,
! [X0,X1,X2] :
( ab_semigroup_mult(X2)
=> times_times(X2,X0,X1) = times_times(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0,X2,X1] :
( ab_semigroup_mult(X1)
=> times_times(X1,ti(X1,X0),X2) = times_times(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_5_arg1) ).
fof(f9274,plain,
( ~ spl63_372
| ~ spl63_190
| ~ spl63_259 ),
inference(avatar_split_clause,[],[f8433,f8275,f7941,f9271]) ).
fof(f9271,plain,
( spl63_372
<=> pls = minus_minus(int,pls,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_372])]) ).
fof(f7941,plain,
( spl63_190
<=> pls = plus_plus(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_190])]) ).
fof(f8275,plain,
( spl63_259
<=> ! [X0] : pls != minus_minus(int,plus_plus(int,X0,X0),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_259])]) ).
fof(f8433,plain,
( pls != minus_minus(int,pls,min)
| ~ spl63_190
| ~ spl63_259 ),
inference(superposition,[],[f8276,f7943]) ).
fof(f7943,plain,
( pls = plus_plus(int,pls,pls)
| ~ spl63_190 ),
inference(avatar_component_clause,[],[f7941]) ).
fof(f8276,plain,
( ! [X0] : pls != minus_minus(int,plus_plus(int,X0,X0),min)
| ~ spl63_259 ),
inference(avatar_component_clause,[],[f8275]) ).
fof(f9269,plain,
spl63_371,
inference(avatar_split_clause,[],[f5134,f9267]) ).
fof(f9267,plain,
( spl63_371
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ ab_semigroup_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_371])]) ).
fof(f5134,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ ab_semigroup_add(X2) ),
inference(cnf_transformation,[],[f2943]) ).
fof(f2943,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ ab_semigroup_add(X2) ),
inference(ennf_transformation,[],[f2043]) ).
fof(f2043,plain,
! [X0,X1,X2] :
( ab_semigroup_add(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X2,X1] :
( ab_semigroup_add(X1)
=> plus_plus(X1,ti(X1,X0),X2) = plus_plus(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
fof(f9265,plain,
spl63_370,
inference(avatar_split_clause,[],[f5133,f9263]) ).
fof(f9263,plain,
( spl63_370
<=> ! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ ab_semigroup_mult(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_370])]) ).
fof(f5133,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ ab_semigroup_mult(X2) ),
inference(cnf_transformation,[],[f2942]) ).
fof(f2942,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1))
| ~ ab_semigroup_mult(X2) ),
inference(ennf_transformation,[],[f2042]) ).
fof(f2042,plain,
! [X0,X1,X2] :
( ab_semigroup_mult(X2)
=> times_times(X2,X0,X1) = times_times(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X2,X1] :
( ab_semigroup_mult(X1)
=> times_times(X1,X0,X2) = times_times(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_5_arg2) ).
fof(f9261,plain,
spl63_369,
inference(avatar_split_clause,[],[f5132,f9259]) ).
fof(f5132,plain,
! [X2,X0,X1] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ ab_semigroup_mult(X2) ),
inference(cnf_transformation,[],[f2941]) ).
fof(f2941,plain,
! [X0,X1,X2] :
( times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1))
| ~ ab_semigroup_mult(X2) ),
inference(ennf_transformation,[],[f2041]) ).
fof(f2041,plain,
! [X0,X1,X2] :
( ab_semigroup_mult(X2)
=> times_times(X2,X0,X1) = ti(X2,times_times(X2,X0,X1)) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X0,X2,X1] :
( ab_semigroup_mult(X1)
=> times_times(X1,X0,X2) = ti(X1,times_times(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_5_res) ).
fof(f9257,plain,
spl63_368,
inference(avatar_split_clause,[],[f5131,f9255]) ).
fof(f9255,plain,
( spl63_368
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ ab_semigroup_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_368])]) ).
fof(f5131,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ ab_semigroup_add(X2) ),
inference(cnf_transformation,[],[f2940]) ).
fof(f2940,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ ab_semigroup_add(X2) ),
inference(ennf_transformation,[],[f2040]) ).
fof(f2040,plain,
! [X0,X1,X2] :
( ab_semigroup_add(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X2,X1] :
( ab_semigroup_add(X1)
=> plus_plus(X1,X0,X2) = plus_plus(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg2) ).
fof(f9253,plain,
spl63_367,
inference(avatar_split_clause,[],[f5130,f9251]) ).
fof(f5130,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ ab_semigroup_add(X2) ),
inference(cnf_transformation,[],[f2939]) ).
fof(f2939,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ ab_semigroup_add(X2) ),
inference(ennf_transformation,[],[f2039]) ).
fof(f2039,plain,
! [X0,X1,X2] :
( ab_semigroup_add(X2)
=> plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1)) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X2,X1] :
( ab_semigroup_add(X1)
=> plus_plus(X1,X0,X2) = ti(X1,plus_plus(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
fof(f9249,plain,
spl63_366,
inference(avatar_split_clause,[],[f5129,f9247]) ).
fof(f9247,plain,
( spl63_366
<=> ! [X2,X0,X1] :
( minus_minus(X2,X0,X1) = minus_minus(X2,ti(X2,X0),X1)
| ~ group_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_366])]) ).
fof(f5129,plain,
! [X2,X0,X1] :
( minus_minus(X2,X0,X1) = minus_minus(X2,ti(X2,X0),X1)
| ~ group_add(X2) ),
inference(cnf_transformation,[],[f2938]) ).
fof(f2938,plain,
! [X0,X1,X2] :
( minus_minus(X2,X0,X1) = minus_minus(X2,ti(X2,X0),X1)
| ~ group_add(X2) ),
inference(ennf_transformation,[],[f2038]) ).
fof(f2038,plain,
! [X0,X1,X2] :
( group_add(X2)
=> minus_minus(X2,X0,X1) = minus_minus(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X2,X1] :
( group_add(X1)
=> minus_minus(X1,ti(X1,X0),X2) = minus_minus(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_0_arg1) ).
fof(f9245,plain,
spl63_365,
inference(avatar_split_clause,[],[f5128,f9243]) ).
fof(f9243,plain,
( spl63_365
<=> ! [X2,X0,X1] :
( minus_minus(X2,X0,X1) = minus_minus(X2,X0,ti(X2,X1))
| ~ group_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_365])]) ).
fof(f5128,plain,
! [X2,X0,X1] :
( minus_minus(X2,X0,X1) = minus_minus(X2,X0,ti(X2,X1))
| ~ group_add(X2) ),
inference(cnf_transformation,[],[f2937]) ).
fof(f2937,plain,
! [X0,X1,X2] :
( minus_minus(X2,X0,X1) = minus_minus(X2,X0,ti(X2,X1))
| ~ group_add(X2) ),
inference(ennf_transformation,[],[f2037]) ).
fof(f2037,plain,
! [X0,X1,X2] :
( group_add(X2)
=> minus_minus(X2,X0,X1) = minus_minus(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0,X2,X1] :
( group_add(X1)
=> minus_minus(X1,X0,X2) = minus_minus(X1,X0,ti(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_0_arg2) ).
fof(f9241,plain,
spl63_364,
inference(avatar_split_clause,[],[f5127,f9239]) ).
fof(f9239,plain,
( spl63_364
<=> ! [X2,X0,X1] :
( minus_minus(X2,X0,X1) = ti(X2,minus_minus(X2,X0,X1))
| ~ group_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_364])]) ).
fof(f5127,plain,
! [X2,X0,X1] :
( minus_minus(X2,X0,X1) = ti(X2,minus_minus(X2,X0,X1))
| ~ group_add(X2) ),
inference(cnf_transformation,[],[f2936]) ).
fof(f2936,plain,
! [X0,X1,X2] :
( minus_minus(X2,X0,X1) = ti(X2,minus_minus(X2,X0,X1))
| ~ group_add(X2) ),
inference(ennf_transformation,[],[f2036]) ).
fof(f2036,plain,
! [X0,X1,X2] :
( group_add(X2)
=> minus_minus(X2,X0,X1) = ti(X2,minus_minus(X2,X0,X1)) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X2,X1] :
( group_add(X1)
=> minus_minus(X1,X0,X2) = ti(X1,minus_minus(X1,X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_0_res) ).
fof(f9237,plain,
spl63_363,
inference(avatar_split_clause,[],[f4743,f9235]) ).
fof(f9235,plain,
( spl63_363
<=> ! [X0,X1] :
( power_power(X1,X0) = ti(fun(nat,X1),power_power(X1,X0))
| ~ power(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_363])]) ).
fof(f4743,plain,
! [X0,X1] :
( power_power(X1,X0) = ti(fun(nat,X1),power_power(X1,X0))
| ~ power(X1) ),
inference(cnf_transformation,[],[f2779]) ).
fof(f2779,plain,
! [X0,X1] :
( power_power(X1,X0) = ti(fun(nat,X1),power_power(X1,X0))
| ~ power(X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1] :
( power(X1)
=> power_power(X1,X0) = ti(fun(nat,X1),power_power(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_res) ).
fof(f9233,plain,
spl63_362,
inference(avatar_split_clause,[],[f4581,f9231]) ).
fof(f9231,plain,
( spl63_362
<=> ! [X0] :
( one_one(int) = abs_abs(int,X0)
| ti(int,X0) != number_number_of(int,min) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_362])]) ).
fof(f4581,plain,
! [X0] :
( one_one(int) = abs_abs(int,X0)
| ti(int,X0) != number_number_of(int,min) ),
inference(cnf_transformation,[],[f3369]) ).
fof(f9229,plain,
( spl63_361
| ~ spl63_186
| ~ spl63_250 ),
inference(avatar_split_clause,[],[f8390,f8238,f7924,f9227]) ).
fof(f9227,plain,
( spl63_361
<=> ! [X0] : pls = times_times(int,X0,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_361])]) ).
fof(f7924,plain,
( spl63_186
<=> ! [X0] : pls = times_times(int,pls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_186])]) ).
fof(f8238,plain,
( spl63_250
<=> ! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_250])]) ).
fof(f8390,plain,
( ! [X0] : pls = times_times(int,X0,pls)
| ~ spl63_186
| ~ spl63_250 ),
inference(superposition,[],[f8239,f7925]) ).
fof(f7925,plain,
( ! [X0] : pls = times_times(int,pls,X0)
| ~ spl63_186 ),
inference(avatar_component_clause,[],[f7924]) ).
fof(f8239,plain,
( ! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0)
| ~ spl63_250 ),
inference(avatar_component_clause,[],[f8238]) ).
fof(f9225,plain,
spl63_360,
inference(avatar_split_clause,[],[f4498,f9223]) ).
fof(f9223,plain,
( spl63_360
<=> ! [X0] :
( ord_less(X0) = ti(fun(X0,fun(X0,bool)),ord_less(X0))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_360])]) ).
fof(f4498,plain,
! [X0] :
( ord_less(X0) = ti(fun(X0,fun(X0,bool)),ord_less(X0))
| ~ order(X0) ),
inference(cnf_transformation,[],[f2691]) ).
fof(f2691,plain,
! [X0] :
( ord_less(X0) = ti(fun(X0,fun(X0,bool)),ord_less(X0))
| ~ order(X0) ),
inference(ennf_transformation,[],[f1681]) ).
fof(f1681,plain,
! [X0] :
( order(X0)
=> ord_less(X0) = ti(fun(X0,fun(X0,bool)),ord_less(X0)) ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X1] :
( order(X1)
=> ord_less(X1) = ti(fun(X1,fun(X1,bool)),ord_less(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_res) ).
fof(f9221,plain,
spl63_359,
inference(avatar_split_clause,[],[f4497,f9219]) ).
fof(f9219,plain,
( spl63_359
<=> ! [X0] :
( ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_359])]) ).
fof(f4497,plain,
! [X0] :
( ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0))
| ~ order(X0) ),
inference(cnf_transformation,[],[f2690]) ).
fof(f2690,plain,
! [X0] :
( ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0))
| ~ order(X0) ),
inference(ennf_transformation,[],[f1680]) ).
fof(f1680,plain,
! [X0] :
( order(X0)
=> ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0)) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X1] :
( order(X1)
=> ord_less_eq(X1) = ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(f9217,plain,
spl63_358,
inference(avatar_split_clause,[],[f4379,f9215]) ).
fof(f9215,plain,
( spl63_358
<=> ! [X0] :
( dvd_dvd(X0) = ti(fun(X0,fun(X0,bool)),dvd_dvd(X0))
| ~ dvd(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_358])]) ).
fof(f4379,plain,
! [X0] :
( dvd_dvd(X0) = ti(fun(X0,fun(X0,bool)),dvd_dvd(X0))
| ~ dvd(X0) ),
inference(cnf_transformation,[],[f2542]) ).
fof(f2542,plain,
! [X0] :
( dvd_dvd(X0) = ti(fun(X0,fun(X0,bool)),dvd_dvd(X0))
| ~ dvd(X0) ),
inference(ennf_transformation,[],[f1570]) ).
fof(f1570,plain,
! [X0] :
( dvd(X0)
=> dvd_dvd(X0) = ti(fun(X0,fun(X0,bool)),dvd_dvd(X0)) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X1] :
( dvd(X1)
=> dvd_dvd(X1) = ti(fun(X1,fun(X1,bool)),dvd_dvd(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Rings_Odvd__class_Odvd_res) ).
fof(f9213,plain,
spl63_357,
inference(avatar_split_clause,[],[f4355,f9211]) ).
fof(f9211,plain,
( spl63_357
<=> ! [X0,X1] :
( one_one(X0) = hAPP(nat,X0,power_power(X0,one_one(X0)),X1)
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_357])]) ).
fof(f4355,plain,
! [X0,X1] :
( one_one(X0) = hAPP(nat,X0,power_power(X0,one_one(X0)),X1)
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f2507]) ).
fof(f2507,plain,
! [X0] :
( ! [X1] : one_one(X0) = hAPP(nat,X0,power_power(X0,one_one(X0)),X1)
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f1548]) ).
fof(f1548,plain,
! [X0] :
( monoid_mult(X0)
=> ! [X1] : one_one(X0) = hAPP(nat,X0,power_power(X0,one_one(X0)),X1) ),
inference(rectify,[],[f264]) ).
fof(f264,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X14] : one_one(X1) = hAPP(nat,X1,power_power(X1,one_one(X1)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_power__one) ).
fof(f9209,plain,
spl63_356,
inference(avatar_split_clause,[],[f4096,f9207]) ).
fof(f9207,plain,
( spl63_356
<=> ! [X2,X0,X1] :
( ti(X0,X1) = plus_plus(X0,minus_minus(X0,X1,X2),X2)
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_356])]) ).
fof(f4096,plain,
! [X2,X0,X1] :
( ti(X0,X1) = plus_plus(X0,minus_minus(X0,X1,X2),X2)
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f2295]) ).
fof(f2295,plain,
! [X0] :
( ! [X1,X2] : ti(X0,X1) = plus_plus(X0,minus_minus(X0,X1,X2),X2)
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0] :
( group_add(X0)
=> ! [X1,X2] : ti(X0,X1) = plus_plus(X0,minus_minus(X0,X1,X2),X2) ),
inference(rectify,[],[f425]) ).
fof(f425,axiom,
! [X1] :
( group_add(X1)
=> ! [X30,X39] : ti(X1,X30) = plus_plus(X1,minus_minus(X1,X30,X39),X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_diff__add__cancel) ).
fof(f9205,plain,
spl63_355,
inference(avatar_split_clause,[],[f4095,f9203]) ).
fof(f9203,plain,
( spl63_355
<=> ! [X2,X0,X1] :
( ti(X0,X1) = minus_minus(X0,plus_plus(X0,X1,X2),X2)
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_355])]) ).
fof(f4095,plain,
! [X2,X0,X1] :
( ti(X0,X1) = minus_minus(X0,plus_plus(X0,X1,X2),X2)
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f2294]) ).
fof(f2294,plain,
! [X0] :
( ! [X1,X2] : ti(X0,X1) = minus_minus(X0,plus_plus(X0,X1,X2),X2)
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f1366]) ).
fof(f1366,plain,
! [X0] :
( group_add(X0)
=> ! [X1,X2] : ti(X0,X1) = minus_minus(X0,plus_plus(X0,X1,X2),X2) ),
inference(rectify,[],[f424]) ).
fof(f424,axiom,
! [X1] :
( group_add(X1)
=> ! [X30,X39] : ti(X1,X30) = minus_minus(X1,plus_plus(X1,X30,X39),X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_add__diff__cancel) ).
fof(f9201,plain,
spl63_354,
inference(avatar_split_clause,[],[f4009,f9199]) ).
fof(f9199,plain,
( spl63_354
<=> ! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_354])]) ).
fof(f4009,plain,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X0)),
inference(cnf_transformation,[],[f1307]) ).
fof(f1307,plain,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),X0)),
inference(rectify,[],[f349]) ).
fof(f349,axiom,
! [X7] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X7),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_zle__refl) ).
fof(f9197,plain,
spl63_353,
inference(avatar_split_clause,[],[f4008,f9195]) ).
fof(f4008,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)),
inference(cnf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)),
inference(rectify,[],[f670]) ).
fof(f670,axiom,
! [X14] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X14),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_le__refl) ).
fof(f9193,plain,
spl63_352,
inference(avatar_split_clause,[],[f4007,f9191]) ).
fof(f4007,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),X0)),
inference(cnf_transformation,[],[f1305]) ).
fof(f1305,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X0),X0)),
inference(rectify,[],[f940]) ).
fof(f940,axiom,
! [X9] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X9),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_dvd_Oorder__refl) ).
fof(f9189,plain,
spl63_351,
inference(avatar_split_clause,[],[f4006,f9187]) ).
fof(f9187,plain,
( spl63_351
<=> ! [X0] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_351])]) ).
fof(f4006,plain,
! [X0] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X0),X0)),
inference(cnf_transformation,[],[f1304]) ).
fof(f1304,plain,
! [X0] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X0),X0)),
inference(rectify,[],[f810]) ).
fof(f810,axiom,
! [X7] : hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X7),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_real__le__refl) ).
fof(f9185,plain,
( spl63_350
| ~ spl63_34
| ~ spl63_156
| ~ spl63_237 ),
inference(avatar_split_clause,[],[f8314,f8186,f7772,f7162,f9183]) ).
fof(f9183,plain,
( spl63_350
<=> ! [X0] : pls = minus_minus(int,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_350])]) ).
fof(f8314,plain,
( ! [X0] : pls = minus_minus(int,X0,X0)
| ~ spl63_34
| ~ spl63_156
| ~ spl63_237 ),
inference(forward_demodulation,[],[f8313,f7774]) ).
fof(f8313,plain,
( ! [X0] : zero_zero(int) = minus_minus(int,X0,X0)
| ~ spl63_34
| ~ spl63_237 ),
inference(resolution,[],[f8187,f7164]) ).
fof(f7164,plain,
( group_add(int)
| ~ spl63_34 ),
inference(avatar_component_clause,[],[f7162]) ).
fof(f9181,plain,
spl63_349,
inference(avatar_split_clause,[],[f4002,f9179]) ).
fof(f9179,plain,
( spl63_349
<=> ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_349])]) ).
fof(f4002,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X0)),
inference(cnf_transformation,[],[f1300]) ).
fof(f1300,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X0)),
inference(rectify,[],[f227]) ).
fof(f227,axiom,
! [X14] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X14),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_less__irrefl__nat) ).
fof(f9177,plain,
spl63_348,
inference(avatar_split_clause,[],[f3904,f9174]) ).
fof(f9174,plain,
( spl63_348
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_348])]) ).
fof(f3904,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)),
inference(cnf_transformation,[],[f850]) ).
fof(f850,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_rel__simps_I6_J) ).
fof(f9172,plain,
spl63_347,
inference(avatar_split_clause,[],[f3902,f9169]) ).
fof(f3902,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),pls)),
inference(cnf_transformation,[],[f856]) ).
fof(f856,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min),pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_rel__simps_I23_J) ).
fof(f9167,plain,
~ spl63_346,
inference(avatar_split_clause,[],[f3900,f9164]) ).
fof(f9164,plain,
( spl63_346
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_346])]) ).
fof(f3900,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(cnf_transformation,[],[f130]) ).
fof(f130,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
fof(f9162,plain,
~ spl63_345,
inference(avatar_split_clause,[],[f3899,f9159]) ).
fof(f9159,plain,
( spl63_345
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_345])]) ).
fof(f3899,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)),
inference(cnf_transformation,[],[f851]) ).
fof(f851,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),min)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_rel__simps_I3_J) ).
fof(f9157,plain,
~ spl63_344,
inference(avatar_split_clause,[],[f3898,f9154]) ).
fof(f9154,plain,
( spl63_344
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_344])]) ).
fof(f3898,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)),
inference(cnf_transformation,[],[f862]) ).
fof(f862,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min),min)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_rel__simps_I7_J) ).
fof(f9152,plain,
~ spl63_343,
inference(avatar_split_clause,[],[f3897,f9149]) ).
fof(f3897,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),min)),
inference(cnf_transformation,[],[f857]) ).
fof(f857,axiom,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),min)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_rel__simps_I20_J) ).
fof(f9141,plain,
spl63_342,
inference(avatar_split_clause,[],[f5449,f9139]) ).
fof(f9139,plain,
( spl63_342
<=> ! [X0] : plus_plus(int,X0,X0) = plus_plus(int,ti(int,X0),ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_342])]) ).
fof(f5449,plain,
! [X0] : plus_plus(int,X0,X0) = plus_plus(int,ti(int,X0),ti(int,X0)),
inference(definition_unfolding,[],[f3700,f3968,f3968]) ).
fof(f3700,plain,
! [X0] : bit0(ti(int,X0)) = bit0(X0),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] : bit0(ti(int,X0)) = bit0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
fof(f9060,plain,
spl63_341,
inference(avatar_split_clause,[],[f6324,f9058]) ).
fof(f9058,plain,
( spl63_341
<=> ! [X0] :
( pls != hAPP(nat,int,semiring_1_of_nat(int),X0)
| nat_1(pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_341])]) ).
fof(f6324,plain,
! [X0] :
( pls != hAPP(nat,int,semiring_1_of_nat(int),X0)
| nat_1(pls) = X0 ),
inference(forward_demodulation,[],[f6323,f3861]) ).
fof(f6323,plain,
! [X0] :
( nat_1(pls) = X0
| zero_zero(int) != hAPP(nat,int,semiring_1_of_nat(int),X0) ),
inference(forward_demodulation,[],[f4594,f5811]) ).
fof(f4594,plain,
! [X0] :
( zero_zero(nat) = X0
| zero_zero(int) != hAPP(nat,int,semiring_1_of_nat(int),X0) ),
inference(cnf_transformation,[],[f3378]) ).
fof(f3378,plain,
! [X0] :
( ( zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),X0)
| zero_zero(nat) != X0 )
& ( zero_zero(nat) = X0
| zero_zero(int) != hAPP(nat,int,semiring_1_of_nat(int),X0) ) ),
inference(nnf_transformation,[],[f1734]) ).
fof(f1734,plain,
! [X0] :
( zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),X0)
<=> zero_zero(nat) = X0 ),
inference(rectify,[],[f125]) ).
fof(f125,axiom,
! [X16] :
( zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),X16)
<=> zero_zero(nat) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_int__eq__0__conv) ).
fof(f9056,plain,
( ~ spl63_340
| ~ spl63_324
| ~ spl63_327 ),
inference(avatar_split_clause,[],[f9014,f8824,f8812,f9053]) ).
fof(f9053,plain,
( spl63_340
<=> one_one(nat) = nat_1(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_340])]) ).
fof(f8812,plain,
( spl63_324
<=> ! [X0] : one_one(nat) = hAPP(nat,nat,power_power(nat,X0),nat_1(pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_324])]) ).
fof(f8824,plain,
( spl63_327
<=> ! [X0] : nat_1(pls) != hAPP(nat,nat,power_power(nat,X0),nat_1(pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_327])]) ).
fof(f9014,plain,
( one_one(nat) != nat_1(pls)
| ~ spl63_324
| ~ spl63_327 ),
inference(superposition,[],[f8825,f8813]) ).
fof(f8813,plain,
( ! [X0] : one_one(nat) = hAPP(nat,nat,power_power(nat,X0),nat_1(pls))
| ~ spl63_324 ),
inference(avatar_component_clause,[],[f8812]) ).
fof(f8825,plain,
( ! [X0] : nat_1(pls) != hAPP(nat,nat,power_power(nat,X0),nat_1(pls))
| ~ spl63_327 ),
inference(avatar_component_clause,[],[f8824]) ).
fof(f9051,plain,
spl63_339,
inference(avatar_split_clause,[],[f6100,f9049]) ).
fof(f9049,plain,
( spl63_339
<=> ! [X0] :
( zero_zero(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),nat_1(pls))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_339])]) ).
fof(f6100,plain,
! [X0] :
( zero_zero(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),nat_1(pls))
| ~ semiring_1(X0) ),
inference(forward_demodulation,[],[f4333,f5811]) ).
fof(f4333,plain,
! [X0] :
( zero_zero(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),zero_zero(nat))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f2484]) ).
fof(f2484,plain,
! [X0] :
( zero_zero(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),zero_zero(nat))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f1527]) ).
fof(f1527,plain,
! [X0] :
( semiring_1(X0)
=> zero_zero(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),zero_zero(nat)) ),
inference(rectify,[],[f286]) ).
fof(f286,axiom,
! [X1] :
( semiring_1(X1)
=> zero_zero(X1) = hAPP(nat,X1,semiring_1_of_nat(X1),zero_zero(nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_of__nat__0) ).
fof(f9047,plain,
spl63_338,
inference(avatar_split_clause,[],[f5639,f9045]) ).
fof(f9045,plain,
( spl63_338
<=> ! [X0,X1] : minus_minus(int,plus_plus(int,X0,X0),min) != plus_plus(int,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_338])]) ).
fof(f5639,plain,
! [X0,X1] : minus_minus(int,plus_plus(int,X0,X0),min) != plus_plus(int,X1,X1),
inference(definition_unfolding,[],[f4667,f5445,f3968]) ).
fof(f4667,plain,
! [X0,X1] : bit1(X0) != bit0(X1),
inference(cnf_transformation,[],[f1769]) ).
fof(f1769,plain,
! [X0,X1] : bit1(X0) != bit0(X1),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X19,X29] : bit1(X19) != bit0(X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_rel__simps_I50_J) ).
fof(f9043,plain,
spl63_337,
inference(avatar_split_clause,[],[f5330,f9041]) ).
fof(f9041,plain,
( spl63_337
<=> ! [X2,X0,X1] :
( X0 = X2
| plus_plus(nat,X0,X1) != plus_plus(nat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_337])]) ).
fof(f5330,plain,
! [X2,X0,X1] :
( X0 = X2
| plus_plus(nat,X0,X1) != plus_plus(nat,X2,X1) ),
inference(cnf_transformation,[],[f3644]) ).
fof(f3644,plain,
! [X0,X1,X2] :
( ( plus_plus(nat,X0,X1) = plus_plus(nat,X2,X1)
| X0 != X2 )
& ( X0 = X2
| plus_plus(nat,X0,X1) != plus_plus(nat,X2,X1) ) ),
inference(nnf_transformation,[],[f2187]) ).
fof(f2187,plain,
! [X0,X1,X2] :
( plus_plus(nat,X0,X1) = plus_plus(nat,X2,X1)
<=> X0 = X2 ),
inference(rectify,[],[f224]) ).
fof(f224,axiom,
! [X27,X11,X16] :
( plus_plus(nat,X27,X11) = plus_plus(nat,X16,X11)
<=> X16 = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_nat__add__right__cancel) ).
fof(f9039,plain,
spl63_336,
inference(avatar_split_clause,[],[f5328,f9037]) ).
fof(f9037,plain,
( spl63_336
<=> ! [X2,X0,X1] :
( X1 = X2
| plus_plus(nat,X0,X1) != plus_plus(nat,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_336])]) ).
fof(f5328,plain,
! [X2,X0,X1] :
( X1 = X2
| plus_plus(nat,X0,X1) != plus_plus(nat,X0,X2) ),
inference(cnf_transformation,[],[f3643]) ).
fof(f3643,plain,
! [X0,X1,X2] :
( ( plus_plus(nat,X0,X1) = plus_plus(nat,X0,X2)
| X1 != X2 )
& ( X1 = X2
| plus_plus(nat,X0,X1) != plus_plus(nat,X0,X2) ) ),
inference(nnf_transformation,[],[f2186]) ).
fof(f2186,plain,
! [X0,X1,X2] :
( plus_plus(nat,X0,X1) = plus_plus(nat,X0,X2)
<=> X1 = X2 ),
inference(rectify,[],[f223]) ).
fof(f223,axiom,
! [X11,X27,X16] :
( plus_plus(nat,X11,X27) = plus_plus(nat,X11,X16)
<=> X16 = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_nat__add__left__cancel) ).
fof(f9035,plain,
spl63_335,
inference(avatar_split_clause,[],[f4580,f9033]) ).
fof(f9033,plain,
( spl63_335
<=> ! [X0] :
( one_one(int) = abs_abs(int,X0)
| ti(int,X0) != one_one(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_335])]) ).
fof(f4580,plain,
! [X0] :
( one_one(int) = abs_abs(int,X0)
| ti(int,X0) != one_one(int) ),
inference(cnf_transformation,[],[f3369]) ).
fof(f9031,plain,
spl63_334,
inference(avatar_split_clause,[],[f4522,f9029]) ).
fof(f9029,plain,
( spl63_334
<=> ! [X0] :
( one_one(X0) = abs_abs(X0,number_number_of(X0,min))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_334])]) ).
fof(f4522,plain,
! [X0] :
( one_one(X0) = abs_abs(X0,number_number_of(X0,min))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2717]) ).
fof(f2717,plain,
! [X0] :
( one_one(X0) = abs_abs(X0,number_number_of(X0,min))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f2716]) ).
fof(f2716,plain,
! [X0] :
( one_one(X0) = abs_abs(X0,number_number_of(X0,min))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1700]) ).
fof(f1700,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> one_one(X0) = abs_abs(X0,number_number_of(X0,min)) ),
inference(rectify,[],[f1027]) ).
fof(f1027,axiom,
! [X1] :
( ( linordered_idom(X1)
& number_ring(X1) )
=> one_one(X1) = abs_abs(X1,number_number_of(X1,min)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_abs__minus__one) ).
fof(f9027,plain,
spl63_333,
inference(avatar_split_clause,[],[f4332,f9025]) ).
fof(f9025,plain,
( spl63_333
<=> ! [X0] :
( one_one(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),one_one(nat))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_333])]) ).
fof(f4332,plain,
! [X0] :
( one_one(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),one_one(nat))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f2483]) ).
fof(f2483,plain,
! [X0] :
( one_one(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),one_one(nat))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f1526]) ).
fof(f1526,plain,
! [X0] :
( semiring_1(X0)
=> one_one(X0) = hAPP(nat,X0,semiring_1_of_nat(X0),one_one(nat)) ),
inference(rectify,[],[f269]) ).
fof(f269,axiom,
! [X1] :
( semiring_1(X1)
=> one_one(X1) = hAPP(nat,X1,semiring_1_of_nat(X1),one_one(nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_of__nat__1) ).
fof(f9023,plain,
spl63_332,
inference(avatar_split_clause,[],[f4233,f9021]) ).
fof(f9021,plain,
( spl63_332
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_332])]) ).
fof(f4233,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2381]) ).
fof(f2381,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1443]) ).
fof(f1443,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1) ),
inference(rectify,[],[f182]) ).
fof(f182,axiom,
! [X1] :
( number_ring(X1)
=> ! [X30] : plus_plus(X1,number_number_of(X1,pls),X30) = ti(X1,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).
fof(f9019,plain,
spl63_331,
inference(avatar_split_clause,[],[f4232,f9017]) ).
fof(f9017,plain,
( spl63_331
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_331])]) ).
fof(f4232,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2380]) ).
fof(f2380,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1442]) ).
fof(f1442,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls)) ),
inference(rectify,[],[f183]) ).
fof(f183,axiom,
! [X1] :
( number_ring(X1)
=> ! [X30] : ti(X1,X30) = plus_plus(X1,X30,number_number_of(X1,pls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_add__numeral__0__right) ).
fof(f9013,plain,
( spl63_330
| ~ spl63_41
| ~ spl63_218 ),
inference(avatar_split_clause,[],[f8140,f8083,f7197,f9010]) ).
fof(f9010,plain,
( spl63_330
<=> zero_zero(real) = number_number_of(real,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_330])]) ).
fof(f8083,plain,
( spl63_218
<=> ! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_218])]) ).
fof(f8140,plain,
( zero_zero(real) = number_number_of(real,pls)
| ~ spl63_41
| ~ spl63_218 ),
inference(resolution,[],[f8084,f7199]) ).
fof(f8084,plain,
( ! [X0] :
( ~ number_ring(X0)
| zero_zero(X0) = number_number_of(X0,pls) )
| ~ spl63_218 ),
inference(avatar_component_clause,[],[f8083]) ).
fof(f8948,plain,
( spl63_329
| ~ spl63_161
| ~ spl63_201 ),
inference(avatar_split_clause,[],[f8055,f7998,f7793,f8946]) ).
fof(f8946,plain,
( spl63_329
<=> ! [X0] : sP9(nat_1(X0),ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_329])]) ).
fof(f7793,plain,
( spl63_161
<=> ! [X1] : sP9(nat_1(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_161])]) ).
fof(f7998,plain,
( spl63_201
<=> ! [X0] : nat_1(ti(int,X0)) = nat_1(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_201])]) ).
fof(f8055,plain,
( ! [X0] : sP9(nat_1(X0),ti(int,X0))
| ~ spl63_161
| ~ spl63_201 ),
inference(superposition,[],[f7794,f7999]) ).
fof(f7999,plain,
( ! [X0] : nat_1(ti(int,X0)) = nat_1(X0)
| ~ spl63_201 ),
inference(avatar_component_clause,[],[f7998]) ).
fof(f7794,plain,
( ! [X1] : sP9(nat_1(X1),X1)
| ~ spl63_161 ),
inference(avatar_component_clause,[],[f7793]) ).
fof(f8852,plain,
( spl63_328
| ~ spl63_75
| ~ spl63_202
| ~ spl63_248
| ~ spl63_289 ),
inference(avatar_split_clause,[],[f8847,f8663,f8230,f8002,f7367,f8850]) ).
fof(f8850,plain,
( spl63_328
<=> ! [X0] : ti(real,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_328])]) ).
fof(f7367,plain,
( spl63_75
<=> comm_monoid_mult(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_75])]) ).
fof(f8663,plain,
( spl63_289
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ comm_monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_289])]) ).
fof(f8847,plain,
( ! [X0] : ti(real,X0) = X0
| ~ spl63_75
| ~ spl63_202
| ~ spl63_248
| ~ spl63_289 ),
inference(forward_demodulation,[],[f8844,f8370]) ).
fof(f8844,plain,
( ! [X0] : times_times(real,X0,one_one(real)) = ti(real,X0)
| ~ spl63_75
| ~ spl63_289 ),
inference(resolution,[],[f8664,f7369]) ).
fof(f7369,plain,
( comm_monoid_mult(real)
| ~ spl63_75 ),
inference(avatar_component_clause,[],[f7367]) ).
fof(f8664,plain,
( ! [X0,X1] :
( ~ comm_monoid_mult(X0)
| ti(X0,X1) = times_times(X0,X1,one_one(X0)) )
| ~ spl63_289 ),
inference(avatar_component_clause,[],[f8663]) ).
fof(f8826,plain,
spl63_327,
inference(avatar_split_clause,[],[f6633,f8824]) ).
fof(f6633,plain,
! [X0] : nat_1(pls) != hAPP(nat,nat,power_power(nat,X0),nat_1(pls)),
inference(forward_demodulation,[],[f5758,f5811]) ).
fof(f5758,plain,
! [X0] : zero_zero(nat) != hAPP(nat,nat,power_power(nat,X0),zero_zero(nat)),
inference(equality_resolution,[],[f4931]) ).
fof(f4931,plain,
! [X0,X1] :
( zero_zero(nat) != X1
| zero_zero(nat) != hAPP(nat,nat,power_power(nat,X0),X1) ),
inference(cnf_transformation,[],[f3497]) ).
fof(f8822,plain,
spl63_326,
inference(avatar_split_clause,[],[f6601,f8820]) ).
fof(f8820,plain,
( spl63_326
<=> ! [X0,X1] :
( plus_plus(nat,X0,X1) != nat_1(pls)
| nat_1(pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_326])]) ).
fof(f6601,plain,
! [X0,X1] :
( plus_plus(nat,X0,X1) != nat_1(pls)
| nat_1(pls) = X0 ),
inference(forward_demodulation,[],[f6600,f5811]) ).
fof(f6600,plain,
! [X0,X1] :
( nat_1(pls) = X0
| zero_zero(nat) != plus_plus(nat,X0,X1) ),
inference(forward_demodulation,[],[f4906,f5811]) ).
fof(f4906,plain,
! [X0,X1] :
( zero_zero(nat) = X0
| zero_zero(nat) != plus_plus(nat,X0,X1) ),
inference(cnf_transformation,[],[f3478]) ).
fof(f3478,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,[],[f3477]) ).
fof(f3477,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,[],[f1934]) ).
fof(f1934,plain,
! [X0,X1] :
( zero_zero(nat) = plus_plus(nat,X0,X1)
<=> ( zero_zero(nat) = X1
& zero_zero(nat) = X0 ) ),
inference(rectify,[],[f252]) ).
fof(f252,axiom,
! [X27,X16] :
( zero_zero(nat) = plus_plus(nat,X27,X16)
<=> ( zero_zero(nat) = X16
& zero_zero(nat) = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_add__is__0) ).
fof(f8818,plain,
spl63_325,
inference(avatar_split_clause,[],[f6599,f8816]) ).
fof(f8816,plain,
( spl63_325
<=> ! [X0,X1] :
( plus_plus(nat,X0,X1) != nat_1(pls)
| nat_1(pls) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_325])]) ).
fof(f6599,plain,
! [X0,X1] :
( plus_plus(nat,X0,X1) != nat_1(pls)
| nat_1(pls) = X1 ),
inference(forward_demodulation,[],[f6598,f5811]) ).
fof(f6598,plain,
! [X0,X1] :
( nat_1(pls) = X1
| zero_zero(nat) != plus_plus(nat,X0,X1) ),
inference(forward_demodulation,[],[f4907,f5811]) ).
fof(f4907,plain,
! [X0,X1] :
( zero_zero(nat) = X1
| zero_zero(nat) != plus_plus(nat,X0,X1) ),
inference(cnf_transformation,[],[f3478]) ).
fof(f8814,plain,
spl63_324,
inference(avatar_split_clause,[],[f6423,f8812]) ).
fof(f8807,plain,
( spl63_323
| ~ spl63_162
| ~ spl63_201 ),
inference(avatar_split_clause,[],[f8054,f7998,f7797,f8805]) ).
fof(f8805,plain,
( spl63_323
<=> ! [X0] : sP10(nat_1(X0),ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_323])]) ).
fof(f7797,plain,
( spl63_162
<=> ! [X0] : sP10(nat_1(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_162])]) ).
fof(f8054,plain,
( ! [X0] : sP10(nat_1(X0),ti(int,X0))
| ~ spl63_162
| ~ spl63_201 ),
inference(superposition,[],[f7798,f7999]) ).
fof(f7798,plain,
( ! [X0] : sP10(nat_1(X0),X0)
| ~ spl63_162 ),
inference(avatar_component_clause,[],[f7797]) ).
fof(f8803,plain,
( spl63_322
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279
| ~ spl63_321 ),
inference(avatar_split_clause,[],[f8799,f8796,f8536,f8198,f8075,f7337,f8801]) ).
fof(f8796,plain,
( spl63_321
<=> ! [X0] :
( one_one(X0) = number_number_of(X0,minus_minus(int,pls,min))
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_321])]) ).
fof(f8799,plain,
( ! [X0] :
( one_one(X0) = number_number_of(X0,one_one(int))
| ~ number_semiring(X0) )
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279
| ~ spl63_321 ),
inference(forward_demodulation,[],[f8797,f8607]) ).
fof(f8797,plain,
( ! [X0] :
( one_one(X0) = number_number_of(X0,minus_minus(int,pls,min))
| ~ number_semiring(X0) )
| ~ spl63_321 ),
inference(avatar_component_clause,[],[f8796]) ).
fof(f8798,plain,
spl63_321,
inference(avatar_split_clause,[],[f6115,f8796]) ).
fof(f6115,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,minus_minus(int,pls,min))
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f5560,f5453]) ).
fof(f5560,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,minus_minus(int,plus_plus(int,pls,pls),min))
| ~ number_semiring(X0) ),
inference(definition_unfolding,[],[f4343,f5445]) ).
fof(f4343,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,bit1(pls))
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f2493]) ).
fof(f2493,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,bit1(pls))
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f1536]) ).
fof(f1536,plain,
! [X0] :
( number_semiring(X0)
=> one_one(X0) = number_number_of(X0,bit1(pls)) ),
inference(rectify,[],[f199]) ).
fof(f199,axiom,
! [X1] :
( number_semiring(X1)
=> one_one(X1) = number_number_of(X1,bit1(pls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_semiring__numeral__1__eq__1) ).
fof(f8792,plain,
( spl63_320
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279
| ~ spl63_319 ),
inference(avatar_split_clause,[],[f8788,f8785,f8536,f8198,f8075,f7337,f8790]) ).
fof(f8785,plain,
( spl63_319
<=> ! [X0] :
( one_one(X0) = number_number_of(X0,minus_minus(int,pls,min))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_319])]) ).
fof(f8788,plain,
( ! [X0] :
( one_one(X0) = number_number_of(X0,one_one(int))
| ~ number_ring(X0) )
| ~ spl63_69
| ~ spl63_216
| ~ spl63_240
| ~ spl63_279
| ~ spl63_319 ),
inference(forward_demodulation,[],[f8786,f8607]) ).
fof(f8786,plain,
( ! [X0] :
( one_one(X0) = number_number_of(X0,minus_minus(int,pls,min))
| ~ number_ring(X0) )
| ~ spl63_319 ),
inference(avatar_component_clause,[],[f8785]) ).
fof(f8787,plain,
spl63_319,
inference(avatar_split_clause,[],[f6071,f8785]) ).
fof(f6071,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,minus_minus(int,pls,min))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f5542,f5453]) ).
fof(f5542,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,minus_minus(int,plus_plus(int,pls,pls),min))
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f4229,f5445]) ).
fof(f4229,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,bit1(pls))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2377]) ).
fof(f2377,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,bit1(pls))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1439]) ).
fof(f1439,plain,
! [X0] :
( number_ring(X0)
=> one_one(X0) = number_number_of(X0,bit1(pls)) ),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X1] :
( number_ring(X1)
=> one_one(X1) = number_number_of(X1,bit1(pls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_numeral__1__eq__1) ).
fof(f8783,plain,
spl63_318,
inference(avatar_split_clause,[],[f5756,f8781]) ).
fof(f8781,plain,
( spl63_318
<=> ! [X1] : one_one(nat) = hAPP(nat,nat,power_power(nat,one_one(nat)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_318])]) ).
fof(f5756,plain,
! [X1] : one_one(nat) = hAPP(nat,nat,power_power(nat,one_one(nat)),X1),
inference(equality_resolution,[],[f4929]) ).
fof(f4929,plain,
! [X0,X1] :
( one_one(nat) = hAPP(nat,nat,power_power(nat,X0),X1)
| one_one(nat) != X0 ),
inference(cnf_transformation,[],[f3495]) ).
fof(f8779,plain,
spl63_317,
inference(avatar_split_clause,[],[f5600,f8777]) ).
fof(f8777,plain,
( spl63_317
<=> ! [X0] :
( ti(int,X0) = pls
| pls != plus_plus(int,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_317])]) ).
fof(f5600,plain,
! [X0] :
( ti(int,X0) = pls
| pls != plus_plus(int,X0,X0) ),
inference(definition_unfolding,[],[f4571,f3968]) ).
fof(f4571,plain,
! [X0] :
( ti(int,X0) = pls
| bit0(X0) != pls ),
inference(cnf_transformation,[],[f3364]) ).
fof(f3364,plain,
! [X0] :
( ( bit0(X0) = pls
| ti(int,X0) != pls )
& ( ti(int,X0) = pls
| bit0(X0) != pls ) ),
inference(nnf_transformation,[],[f1727]) ).
fof(f1727,plain,
! [X0] :
( bit0(X0) = pls
<=> ti(int,X0) = pls ),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X11] :
( pls = bit0(X11)
<=> pls = ti(int,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I44_J) ).
fof(f8775,plain,
spl63_316,
inference(avatar_split_clause,[],[f5599,f8773]) ).
fof(f8773,plain,
( spl63_316
<=> ! [X0] :
( pls = plus_plus(int,X0,X0)
| ti(int,X0) != pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_316])]) ).
fof(f5599,plain,
! [X0] :
( pls = plus_plus(int,X0,X0)
| ti(int,X0) != pls ),
inference(definition_unfolding,[],[f4572,f3968]) ).
fof(f4572,plain,
! [X0] :
( bit0(X0) = pls
| ti(int,X0) != pls ),
inference(cnf_transformation,[],[f3364]) ).
fof(f8771,plain,
spl63_315,
inference(avatar_split_clause,[],[f5503,f8769]) ).
fof(f8769,plain,
( spl63_315
<=> ! [X0] : minus_minus(int,X0,min) = minus_minus(int,ti(int,X0),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_315])]) ).
fof(f5503,plain,
! [X0] : minus_minus(int,X0,min) = minus_minus(int,ti(int,X0),min),
inference(definition_unfolding,[],[f3972,f3966,f3966]) ).
fof(f3972,plain,
! [X0] : succ(ti(int,X0)) = succ(X0),
inference(cnf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] : succ(ti(int,X0)) = succ(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Osucc_arg1) ).
fof(f8767,plain,
spl63_314,
inference(avatar_split_clause,[],[f5501,f8765]) ).
fof(f8765,plain,
( spl63_314
<=> ! [X0] : minus_minus(int,X0,min) = ti(int,minus_minus(int,X0,min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_314])]) ).
fof(f5501,plain,
! [X0] : minus_minus(int,X0,min) = ti(int,minus_minus(int,X0,min)),
inference(definition_unfolding,[],[f3965,f3966,f3966]) ).
fof(f3965,plain,
! [X0] : succ(X0) = ti(int,succ(X0)),
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] : succ(X0) = ti(int,succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Osucc_res) ).
fof(f8763,plain,
spl63_313,
inference(avatar_split_clause,[],[f5122,f8761]) ).
fof(f8761,plain,
( spl63_313
<=> ! [X2,X0,X1] :
( nat_1(X1) = nat_1(if(int,X2,X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_313])]) ).
fof(f5122,plain,
! [X2,X0,X1] :
( nat_1(X1) = nat_1(if(int,X2,X0,X1))
| hBOOL(X2) ),
inference(cnf_transformation,[],[f2933]) ).
fof(f2933,plain,
! [X0,X1,X2] :
( ( nat_1(X1) = nat_1(if(int,X2,X0,X1))
| hBOOL(X2) )
& ( nat_1(X0) = nat_1(if(int,X2,X0,X1))
| ~ hBOOL(X2) ) ),
inference(ennf_transformation,[],[f2033]) ).
fof(f2033,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(X2)
=> nat_1(X1) = nat_1(if(int,X2,X0,X1)) )
& ( hBOOL(X2)
=> nat_1(X0) = nat_1(if(int,X2,X0,X1)) ) ),
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X4,X5,X32] :
( ( ~ hBOOL(X32)
=> nat_1(if(int,X32,X4,X5)) = nat_1(X5) )
& ( hBOOL(X32)
=> nat_1(X4) = nat_1(if(int,X32,X4,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_nat__if__cong) ).
fof(f8759,plain,
spl63_312,
inference(avatar_split_clause,[],[f5121,f8757]) ).
fof(f8757,plain,
( spl63_312
<=> ! [X2,X0,X1] :
( nat_1(X0) = nat_1(if(int,X2,X0,X1))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_312])]) ).
fof(f5121,plain,
! [X2,X0,X1] :
( nat_1(X0) = nat_1(if(int,X2,X0,X1))
| ~ hBOOL(X2) ),
inference(cnf_transformation,[],[f2933]) ).
fof(f8755,plain,
spl63_311,
inference(avatar_split_clause,[],[f4888,f8753]) ).
fof(f8753,plain,
( spl63_311
<=> ! [X0,X1] :
( one_one(nat) = X1
| one_one(nat) != times_times(nat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_311])]) ).
fof(f4888,plain,
! [X0,X1] :
( one_one(nat) = X1
| one_one(nat) != times_times(nat,X0,X1) ),
inference(cnf_transformation,[],[f3467]) ).
fof(f3467,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,[],[f3466]) ).
fof(f3466,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,[],[f1929]) ).
fof(f1929,plain,
! [X0,X1] :
( one_one(nat) = times_times(nat,X0,X1)
<=> ( one_one(nat) = X1
& one_one(nat) = X0 ) ),
inference(rectify,[],[f723]) ).
fof(f723,axiom,
! [X16,X27] :
( one_one(nat) = times_times(nat,X16,X27)
<=> ( one_one(nat) = X27
& one_one(nat) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_nat__mult__eq__one) ).
fof(f8751,plain,
spl63_310,
inference(avatar_split_clause,[],[f4887,f8749]) ).
fof(f8749,plain,
( spl63_310
<=> ! [X0,X1] :
( one_one(nat) = X0
| one_one(nat) != times_times(nat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_310])]) ).
fof(f4887,plain,
! [X0,X1] :
( one_one(nat) = X0
| one_one(nat) != times_times(nat,X0,X1) ),
inference(cnf_transformation,[],[f3467]) ).
fof(f8747,plain,
spl63_309,
inference(avatar_split_clause,[],[f4742,f8745]) ).
fof(f8745,plain,
( spl63_309
<=> ! [X0,X1] :
( power_power(X1,ti(X1,X0)) = power_power(X1,X0)
| ~ power(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_309])]) ).
fof(f4742,plain,
! [X0,X1] :
( power_power(X1,ti(X1,X0)) = power_power(X1,X0)
| ~ power(X1) ),
inference(cnf_transformation,[],[f2778]) ).
fof(f2778,plain,
! [X0,X1] :
( power_power(X1,ti(X1,X0)) = power_power(X1,X0)
| ~ power(X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1] :
( power(X1)
=> power_power(X1,ti(X1,X0)) = power_power(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg1) ).
fof(f8743,plain,
spl63_308,
inference(avatar_split_clause,[],[f4741,f8741]) ).
fof(f8741,plain,
( spl63_308
<=> ! [X0,X1] :
( number_number_of(X1,ti(int,X0)) = number_number_of(X1,X0)
| ~ number(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_308])]) ).
fof(f4741,plain,
! [X0,X1] :
( number_number_of(X1,ti(int,X0)) = number_number_of(X1,X0)
| ~ number(X1) ),
inference(cnf_transformation,[],[f2777]) ).
fof(f2777,plain,
! [X0,X1] :
( number_number_of(X1,ti(int,X0)) = number_number_of(X1,X0)
| ~ number(X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
( number(X1)
=> number_number_of(X1,ti(int,X0)) = number_number_of(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
fof(f8739,plain,
spl63_307,
inference(avatar_split_clause,[],[f4740,f8737]) ).
fof(f8737,plain,
( spl63_307
<=> ! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_307])]) ).
fof(f4740,plain,
! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ),
inference(cnf_transformation,[],[f2776]) ).
fof(f2776,plain,
! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] :
( number(X1)
=> number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
fof(f8735,plain,
spl63_306,
inference(avatar_split_clause,[],[f4739,f8733]) ).
fof(f8733,plain,
( spl63_306
<=> ! [X0,X1] :
( abs_abs(X1,ti(X1,X0)) = abs_abs(X1,X0)
| ~ ordere142940540dd_abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_306])]) ).
fof(f4739,plain,
! [X0,X1] :
( abs_abs(X1,ti(X1,X0)) = abs_abs(X1,X0)
| ~ ordere142940540dd_abs(X1) ),
inference(cnf_transformation,[],[f2775]) ).
fof(f2775,plain,
! [X0,X1] :
( abs_abs(X1,ti(X1,X0)) = abs_abs(X1,X0)
| ~ ordere142940540dd_abs(X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ordere142940540dd_abs(X1)
=> abs_abs(X1,ti(X1,X0)) = abs_abs(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oabs__class_Oabs_arg1) ).
fof(f8731,plain,
spl63_305,
inference(avatar_split_clause,[],[f4738,f8729]) ).
fof(f8729,plain,
( spl63_305
<=> ! [X0,X1] :
( abs_abs(X1,X0) = ti(X1,abs_abs(X1,X0))
| ~ ordere142940540dd_abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_305])]) ).
fof(f4738,plain,
! [X0,X1] :
( abs_abs(X1,X0) = ti(X1,abs_abs(X1,X0))
| ~ ordere142940540dd_abs(X1) ),
inference(cnf_transformation,[],[f2774]) ).
fof(f2774,plain,
! [X0,X1] :
( abs_abs(X1,X0) = ti(X1,abs_abs(X1,X0))
| ~ ordere142940540dd_abs(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ordere142940540dd_abs(X1)
=> abs_abs(X1,X0) = ti(X1,abs_abs(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oabs__class_Oabs_res) ).
fof(f8727,plain,
spl63_304,
inference(avatar_split_clause,[],[f4689,f8725]) ).
fof(f8725,plain,
( spl63_304
<=> ! [X0,X1] : minus_minus(nat,X0,X1) = minus_minus(nat,ti(nat,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_304])]) ).
fof(f4689,plain,
! [X0,X1] : minus_minus(nat,X0,X1) = minus_minus(nat,ti(nat,X0),X1),
inference(cnf_transformation,[],[f1791]) ).
fof(f1791,plain,
! [X0,X1] : minus_minus(nat,X0,X1) = minus_minus(nat,ti(nat,X0),X1),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2] : minus_minus(nat,ti(nat,X0),X2) = minus_minus(nat,X0,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_1_arg1) ).
fof(f8722,plain,
spl63_303,
inference(avatar_split_clause,[],[f4687,f8720]) ).
fof(f8720,plain,
( spl63_303
<=> ! [X0,X1] : minus_minus(nat,X0,X1) = minus_minus(nat,X0,ti(nat,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_303])]) ).
fof(f4687,plain,
! [X0,X1] : minus_minus(nat,X0,X1) = minus_minus(nat,X0,ti(nat,X1)),
inference(cnf_transformation,[],[f1789]) ).
fof(f1789,plain,
! [X0,X1] : minus_minus(nat,X0,X1) = minus_minus(nat,X0,ti(nat,X1)),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X0,X2] : minus_minus(nat,X0,X2) = minus_minus(nat,X0,ti(nat,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_1_arg2) ).
fof(f8718,plain,
spl63_302,
inference(avatar_split_clause,[],[f4685,f8716]) ).
fof(f8716,plain,
( spl63_302
<=> ! [X0,X1] : zcong(X0,X1) = ti(fun(int,bool),zcong(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_302])]) ).
fof(f4685,plain,
! [X0,X1] : zcong(X0,X1) = ti(fun(int,bool),zcong(X0,X1)),
inference(cnf_transformation,[],[f1787]) ).
fof(f1787,plain,
! [X0,X1] : zcong(X0,X1) = ti(fun(int,bool),zcong(X0,X1)),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X0,X2] : zcong(X0,X2) = ti(fun(int,bool),zcong(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_res) ).
fof(f8714,plain,
spl63_301,
inference(avatar_split_clause,[],[f4460,f8712]) ).
fof(f8712,plain,
( spl63_301
<=> ! [X2,X0,X1] :
( times_times(X0,X2,X1) = times_times(X0,X1,X2)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_301])]) ).
fof(f4460,plain,
! [X2,X0,X1] :
( times_times(X0,X2,X1) = times_times(X0,X1,X2)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2649]) ).
fof(f2649,plain,
! [X0] :
( ! [X1,X2] : times_times(X0,X2,X1) = times_times(X0,X1,X2)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1644]) ).
fof(f1644,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2] : times_times(X0,X2,X1) = times_times(X0,X1,X2) ),
inference(rectify,[],[f337]) ).
fof(f337,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30,X39] : times_times(X1,X30,X39) = times_times(X1,X39,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f8710,plain,
spl63_300,
inference(avatar_split_clause,[],[f4459,f8708]) ).
fof(f8708,plain,
( spl63_300
<=> ! [X2,X0,X1] :
( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_300])]) ).
fof(f4459,plain,
! [X2,X0,X1] :
( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2648]) ).
fof(f2648,plain,
! [X0] :
( ! [X1,X2] : plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1643]) ).
fof(f1643,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1,X2] : plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) ),
inference(rectify,[],[f308]) ).
fof(f308,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30,X40] : plus_plus(X1,X30,X40) = plus_plus(X1,X40,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f8706,plain,
spl63_299,
inference(avatar_split_clause,[],[f4450,f8704]) ).
fof(f8704,plain,
( spl63_299
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_299])]) ).
fof(f4450,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2639]) ).
fof(f2639,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1634]) ).
fof(f1634,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : ti(X0,X1) = times_times(X0,one_one(X0),X1) ),
inference(rectify,[],[f449]) ).
fof(f449,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : ti(X1,X30) = times_times(X1,one_one(X1),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(f8702,plain,
spl63_298,
inference(avatar_split_clause,[],[f4449,f8700]) ).
fof(f8700,plain,
( spl63_298
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_298])]) ).
fof(f4449,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2638]) ).
fof(f2638,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1633]) ).
fof(f1633,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : ti(X0,X1) = times_times(X0,X1,one_one(X0)) ),
inference(rectify,[],[f446]) ).
fof(f446,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : ti(X1,X30) = times_times(X1,X30,one_one(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f8698,plain,
spl63_297,
inference(avatar_split_clause,[],[f4448,f8696]) ).
fof(f8696,plain,
( spl63_297
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_297])]) ).
fof(f4448,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2637]) ).
fof(f2637,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1632]) ).
fof(f1632,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1) ),
inference(rectify,[],[f316]) ).
fof(f316,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : ti(X1,X30) = plus_plus(X1,zero_zero(X1),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f8694,plain,
spl63_296,
inference(avatar_split_clause,[],[f4447,f8692]) ).
fof(f8692,plain,
( spl63_296
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_296])]) ).
fof(f4447,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2636]) ).
fof(f2636,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1631]) ).
fof(f1631,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0)) ),
inference(rectify,[],[f312]) ).
fof(f312,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : ti(X1,X30) = plus_plus(X1,X30,zero_zero(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(f8690,plain,
spl63_295,
inference(avatar_split_clause,[],[f4354,f8688]) ).
fof(f8688,plain,
( spl63_295
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_295])]) ).
fof(f4354,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f2506]) ).
fof(f2506,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f1547]) ).
fof(f1547,plain,
! [X0] :
( monoid_mult(X0)
=> ! [X1] : ti(X0,X1) = times_times(X0,one_one(X0),X1) ),
inference(rectify,[],[f450]) ).
fof(f450,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X30] : ti(X1,X30) = times_times(X1,one_one(X1),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_mult__1__left) ).
fof(f8686,plain,
spl63_294,
inference(avatar_split_clause,[],[f4353,f8684]) ).
fof(f8684,plain,
( spl63_294
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_294])]) ).
fof(f4353,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ monoid_mult(X0) ),
inference(cnf_transformation,[],[f2505]) ).
fof(f2505,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f1546]) ).
fof(f1546,plain,
! [X0] :
( monoid_mult(X0)
=> ! [X1] : ti(X0,X1) = times_times(X0,X1,one_one(X0)) ),
inference(rectify,[],[f447]) ).
fof(f447,axiom,
! [X1] :
( monoid_mult(X1)
=> ! [X30] : ti(X1,X30) = times_times(X1,X30,one_one(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_mult__1__right) ).
fof(f8681,plain,
spl63_293,
inference(avatar_split_clause,[],[f4331,f8679]) ).
fof(f8679,plain,
( spl63_293
<=> ! [X0] :
( semiring_1_of_nat(X0) = ti(fun(nat,X0),semiring_1_of_nat(X0))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_293])]) ).
fof(f4331,plain,
! [X0] :
( semiring_1_of_nat(X0) = ti(fun(nat,X0),semiring_1_of_nat(X0))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f2482]) ).
fof(f2482,plain,
! [X0] :
( semiring_1_of_nat(X0) = ti(fun(nat,X0),semiring_1_of_nat(X0))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f1525]) ).
fof(f1525,plain,
! [X0] :
( semiring_1(X0)
=> semiring_1_of_nat(X0) = ti(fun(nat,X0),semiring_1_of_nat(X0)) ),
inference(rectify,[],[f59]) ).
fof(f59,axiom,
! [X1] :
( semiring_1(X1)
=> semiring_1_of_nat(X1) = ti(fun(nat,X1),semiring_1_of_nat(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_res) ).
fof(f8677,plain,
spl63_292,
inference(avatar_split_clause,[],[f4296,f8675]) ).
fof(f8675,plain,
( spl63_292
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_292])]) ).
fof(f4296,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f2445]) ).
fof(f2445,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f1497]) ).
fof(f1497,plain,
! [X0] :
( monoid_add(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1) ),
inference(rectify,[],[f317]) ).
fof(f317,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X30] : ti(X1,X30) = plus_plus(X1,zero_zero(X1),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_add__0__left) ).
fof(f8673,plain,
spl63_291,
inference(avatar_split_clause,[],[f4295,f8671]) ).
fof(f8671,plain,
( spl63_291
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_291])]) ).
fof(f4295,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f2444]) ).
fof(f2444,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f1496]) ).
fof(f1496,plain,
! [X0] :
( monoid_add(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0)) ),
inference(rectify,[],[f313]) ).
fof(f313,axiom,
! [X1] :
( monoid_add(X1)
=> ! [X30] : ti(X1,X30) = plus_plus(X1,X30,zero_zero(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_add__0__right) ).
fof(f8669,plain,
spl63_290,
inference(avatar_split_clause,[],[f4273,f8667]) ).
fof(f8667,plain,
( spl63_290
<=> ! [X0,X1] :
( ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ comm_monoid_mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_290])]) ).
fof(f4273,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f2421]) ).
fof(f2421,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = times_times(X0,one_one(X0),X1)
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f1479]) ).
fof(f1479,plain,
! [X0] :
( comm_monoid_mult(X0)
=> ! [X1] : ti(X0,X1) = times_times(X0,one_one(X0),X1) ),
inference(rectify,[],[f448]) ).
fof(f448,axiom,
! [X1] :
( comm_monoid_mult(X1)
=> ! [X30] : ti(X1,X30) = times_times(X1,one_one(X1),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_mult__1) ).
fof(f8665,plain,
spl63_289,
inference(avatar_split_clause,[],[f4272,f8663]) ).
fof(f4272,plain,
! [X0,X1] :
( ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ comm_monoid_mult(X0) ),
inference(cnf_transformation,[],[f2420]) ).
fof(f2420,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = times_times(X0,X1,one_one(X0))
| ~ comm_monoid_mult(X0) ),
inference(ennf_transformation,[],[f1478]) ).
fof(f1478,plain,
! [X0] :
( comm_monoid_mult(X0)
=> ! [X1] : ti(X0,X1) = times_times(X0,X1,one_one(X0)) ),
inference(rectify,[],[f445]) ).
fof(f445,axiom,
! [X1] :
( comm_monoid_mult(X1)
=> ! [X30] : ti(X1,X30) = times_times(X1,X30,one_one(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_mult_Ocomm__neutral) ).
fof(f8661,plain,
spl63_288,
inference(avatar_split_clause,[],[f4265,f8659]) ).
fof(f8659,plain,
( spl63_288
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_288])]) ).
fof(f4265,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f2413]) ).
fof(f2413,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1)
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f1473]) ).
fof(f1473,plain,
! [X0] :
( comm_monoid_add(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,zero_zero(X0),X1) ),
inference(rectify,[],[f315]) ).
fof(f315,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X30] : ti(X1,X30) = plus_plus(X1,zero_zero(X1),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_add__0) ).
fof(f8657,plain,
spl63_287,
inference(avatar_split_clause,[],[f4264,f8655]) ).
fof(f8655,plain,
( spl63_287
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_287])]) ).
fof(f4264,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f2412]) ).
fof(f2412,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0))
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f1472]) ).
fof(f1472,plain,
! [X0] :
( comm_monoid_add(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,X1,zero_zero(X0)) ),
inference(rectify,[],[f311]) ).
fof(f311,axiom,
! [X1] :
( comm_monoid_add(X1)
=> ! [X30] : ti(X1,X30) = plus_plus(X1,X30,zero_zero(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_add_Ocomm__neutral) ).
fof(f8653,plain,
spl63_286,
inference(avatar_split_clause,[],[f4169,f8651]) ).
fof(f8651,plain,
( spl63_286
<=> ! [X0,X1] :
( abs_abs(X0,X1) = abs_abs(X0,abs_abs(X0,X1))
| ~ ordere142940540dd_abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_286])]) ).
fof(f4169,plain,
! [X0,X1] :
( abs_abs(X0,X1) = abs_abs(X0,abs_abs(X0,X1))
| ~ ordere142940540dd_abs(X0) ),
inference(cnf_transformation,[],[f2326]) ).
fof(f2326,plain,
! [X0] :
( ! [X1] : abs_abs(X0,X1) = abs_abs(X0,abs_abs(X0,X1))
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f1392]) ).
fof(f1392,plain,
! [X0] :
( ordere142940540dd_abs(X0)
=> ! [X1] : abs_abs(X0,X1) = abs_abs(X0,abs_abs(X0,X1)) ),
inference(rectify,[],[f1035]) ).
fof(f1035,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> ! [X30] : abs_abs(X1,X30) = abs_abs(X1,abs_abs(X1,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_abs__idempotent) ).
fof(f8649,plain,
spl63_285,
inference(avatar_split_clause,[],[f4094,f8647]) ).
fof(f8647,plain,
( spl63_285
<=> ! [X0,X1] :
( ti(X0,X1) = minus_minus(X0,X1,zero_zero(X0))
| ~ group_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_285])]) ).
fof(f4094,plain,
! [X0,X1] :
( ti(X0,X1) = minus_minus(X0,X1,zero_zero(X0))
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f2293]) ).
fof(f2293,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = minus_minus(X0,X1,zero_zero(X0))
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f1365]) ).
fof(f1365,plain,
! [X0] :
( group_add(X0)
=> ! [X1] : ti(X0,X1) = minus_minus(X0,X1,zero_zero(X0)) ),
inference(rectify,[],[f421]) ).
fof(f421,axiom,
! [X1] :
( group_add(X1)
=> ! [X30] : ti(X1,X30) = minus_minus(X1,X30,zero_zero(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_diff__0__right) ).
fof(f8635,plain,
spl63_284,
inference(avatar_split_clause,[],[f5447,f8633]) ).
fof(f8633,plain,
( spl63_284
<=> ! [X0] : plus_plus(int,X0,X0) = ti(int,plus_plus(int,X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_284])]) ).
fof(f5447,plain,
! [X0] : plus_plus(int,X0,X0) = ti(int,plus_plus(int,X0,X0)),
inference(definition_unfolding,[],[f3698,f3968,f3968]) ).
fof(f3698,plain,
! [X0] : bit0(X0) = ti(int,bit0(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] : bit0(X0) = ti(int,bit0(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
fof(f8581,plain,
( spl63_283
| ~ spl63_38
| ~ spl63_156
| ~ spl63_238 ),
inference(avatar_split_clause,[],[f8317,f8190,f7772,f7182,f8578]) ).
fof(f8578,plain,
( spl63_283
<=> pls = abs_abs(int,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_283])]) ).
fof(f7182,plain,
( spl63_38
<=> ordere142940540dd_abs(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_38])]) ).
fof(f8317,plain,
( pls = abs_abs(int,pls)
| ~ spl63_38
| ~ spl63_156
| ~ spl63_238 ),
inference(forward_demodulation,[],[f8316,f7774]) ).
fof(f8316,plain,
( zero_zero(int) = abs_abs(int,zero_zero(int))
| ~ spl63_38
| ~ spl63_238 ),
inference(resolution,[],[f8191,f7184]) ).
fof(f7184,plain,
( ordere142940540dd_abs(int)
| ~ spl63_38 ),
inference(avatar_component_clause,[],[f7182]) ).
fof(f8550,plain,
spl63_282,
inference(avatar_split_clause,[],[f6446,f8548]) ).
fof(f8548,plain,
( spl63_282
<=> ! [X0,X1] :
( nat_1(pls) = X1
| plus_plus(nat,X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_282])]) ).
fof(f6446,plain,
! [X0,X1] :
( nat_1(pls) = X1
| plus_plus(nat,X0,X1) != X0 ),
inference(forward_demodulation,[],[f4752,f5811]) ).
fof(f4752,plain,
! [X0,X1] :
( zero_zero(nat) = X1
| plus_plus(nat,X0,X1) != X0 ),
inference(cnf_transformation,[],[f2789]) ).
fof(f2789,plain,
! [X0,X1] :
( zero_zero(nat) = X1
| plus_plus(nat,X0,X1) != X0 ),
inference(ennf_transformation,[],[f1839]) ).
fof(f1839,plain,
! [X0,X1] :
( plus_plus(nat,X0,X1) = X0
=> zero_zero(nat) = X1 ),
inference(rectify,[],[f251]) ).
fof(f251,axiom,
! [X13,X14] :
( plus_plus(nat,X13,X14) = X13
=> zero_zero(nat) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_add__eq__self__zero) ).
fof(f8546,plain,
spl63_281,
inference(avatar_split_clause,[],[f6370,f8544]) ).
fof(f8544,plain,
( spl63_281
<=> ! [X0,X1] : minus_minus(nat,X0,plus_plus(nat,X0,X1)) = nat_1(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_281])]) ).
fof(f6370,plain,
! [X0,X1] : minus_minus(nat,X0,plus_plus(nat,X0,X1)) = nat_1(pls),
inference(forward_demodulation,[],[f4684,f5811]) ).
fof(f4684,plain,
! [X0,X1] : zero_zero(nat) = minus_minus(nat,X0,plus_plus(nat,X0,X1)),
inference(cnf_transformation,[],[f1786]) ).
fof(f1786,plain,
! [X0,X1] : zero_zero(nat) = minus_minus(nat,X0,plus_plus(nat,X0,X1)),
inference(rectify,[],[f551]) ).
fof(f551,axiom,
! [X14,X13] : zero_zero(nat) = minus_minus(nat,X14,plus_plus(nat,X14,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_diff__add__0) ).
fof(f8542,plain,
spl63_280,
inference(avatar_split_clause,[],[f5921,f8540]) ).
fof(f5921,plain,
! [X0] : pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(forward_demodulation,[],[f3996,f3861]) ).
fof(f3996,plain,
! [X0] : zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(cnf_transformation,[],[f1294]) ).
fof(f1294,plain,
! [X0] : zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(rectify,[],[f191]) ).
fof(f191,axiom,
! [X15] : zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X15),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_odd__nonzero) ).
fof(f8538,plain,
spl63_279,
inference(avatar_split_clause,[],[f5504,f8536]) ).
fof(f5504,plain,
! [X0] : minus_minus(int,X0,min) = plus_plus(int,X0,one_one(int)),
inference(definition_unfolding,[],[f3983,f3966]) ).
fof(f3983,plain,
! [X0] : succ(X0) = plus_plus(int,X0,one_one(int)),
inference(cnf_transformation,[],[f1282]) ).
fof(f1282,plain,
! [X0] : succ(X0) = plus_plus(int,X0,one_one(int)),
inference(rectify,[],[f617]) ).
fof(f617,axiom,
! [X19] : succ(X19) = plus_plus(int,X19,one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_succ__def) ).
fof(f8534,plain,
spl63_278,
inference(avatar_split_clause,[],[f4919,f8532]) ).
fof(f8532,plain,
( spl63_278
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X1)))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_278])]) ).
fof(f4919,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X1)))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f3486]) ).
fof(f3486,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,X0,nat_1(X1)))
| ~ sP12(X0,X1) )
& ( sP12(X0,X1)
| ~ hBOOL(hAPP(nat,bool,X0,nat_1(X1))) ) ),
inference(nnf_transformation,[],[f3219]) ).
fof(f3219,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X1)))
<=> sP12(X0,X1) ),
inference(definition_folding,[],[f2929,f3218]) ).
fof(f2929,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X1)))
<=> ( ( hBOOL(hAPP(nat,bool,X0,zero_zero(nat)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int))) )
& ! [X2] :
( hBOOL(hAPP(nat,bool,X0,X2))
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X2) ) ) ),
inference(ennf_transformation,[],[f1936]) ).
fof(f1936,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,X0,nat_1(X1)))
<=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),zero_zero(int)))
=> hBOOL(hAPP(nat,bool,X0,zero_zero(nat))) )
& ! [X2] :
( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X2)
=> hBOOL(hAPP(nat,bool,X0,X2)) ) ) ),
inference(rectify,[],[f621]) ).
fof(f621,axiom,
! [X32,X33] :
( hBOOL(hAPP(nat,bool,X32,nat_1(X33)))
<=> ( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X33),zero_zero(int)))
=> hBOOL(hAPP(nat,bool,X32,zero_zero(nat))) )
& ! [X42] :
( hAPP(nat,int,semiring_1_of_nat(int),X42) = ti(int,X33)
=> hBOOL(hAPP(nat,bool,X32,X42)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_split__nat) ).
fof(f8530,plain,
( spl63_277
| ~ spl63_197
| ~ spl63_236 ),
inference(avatar_split_clause,[],[f8309,f8182,f7981,f8528]) ).
fof(f7981,plain,
( spl63_197
<=> ! [X0] : nat_1(X0) = ti(nat,nat_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_197])]) ).
fof(f8309,plain,
( ! [X0] : ti(nat,X0) = X0
| ~ spl63_197
| ~ spl63_236 ),
inference(superposition,[],[f7982,f8183]) ).
fof(f7982,plain,
( ! [X0] : nat_1(X0) = ti(nat,nat_1(X0))
| ~ spl63_197 ),
inference(avatar_component_clause,[],[f7981]) ).
fof(f8526,plain,
spl63_276,
inference(avatar_split_clause,[],[f4918,f8524]) ).
fof(f8524,plain,
( spl63_276
<=> ! [X0,X1] :
( sP12(X0,X1)
| ~ hBOOL(hAPP(nat,bool,X0,nat_1(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_276])]) ).
fof(f4918,plain,
! [X0,X1] :
( sP12(X0,X1)
| ~ hBOOL(hAPP(nat,bool,X0,nat_1(X1))) ),
inference(cnf_transformation,[],[f3486]) ).
fof(f8522,plain,
spl63_275,
inference(avatar_split_clause,[],[f4903,f8520]) ).
fof(f8520,plain,
( spl63_275
<=> ! [X0,X1] :
( one_one(int) = times_times(int,X0,X1)
| ~ sP11(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_275])]) ).
fof(f4903,plain,
! [X0,X1] :
( one_one(int) = times_times(int,X0,X1)
| ~ sP11(X1,X0) ),
inference(cnf_transformation,[],[f3475]) ).
fof(f3475,plain,
! [X0,X1] :
( ( one_one(int) = times_times(int,X0,X1)
| ~ sP11(X1,X0) )
& ( sP11(X1,X0)
| one_one(int) != times_times(int,X0,X1) ) ),
inference(nnf_transformation,[],[f3217]) ).
fof(f3217,plain,
! [X0,X1] :
( one_one(int) = times_times(int,X0,X1)
<=> sP11(X1,X0) ),
inference(definition_folding,[],[f1932,f3216]) ).
fof(f1932,plain,
! [X0,X1] :
( one_one(int) = times_times(int,X0,X1)
<=> ( ( number_number_of(int,min) = ti(int,X1)
& ti(int,X0) = number_number_of(int,min) )
| ( one_one(int) = ti(int,X1)
& ti(int,X0) = one_one(int) ) ) ),
inference(rectify,[],[f883]) ).
fof(f883,axiom,
! [X27,X16] :
( one_one(int) = times_times(int,X27,X16)
<=> ( ( ti(int,X16) = number_number_of(int,min)
& ti(int,X27) = number_number_of(int,min) )
| ( one_one(int) = ti(int,X16)
& one_one(int) = ti(int,X27) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_zmult__eq__1__iff) ).
fof(f8518,plain,
spl63_274,
inference(avatar_split_clause,[],[f4902,f8516]) ).
fof(f8516,plain,
( spl63_274
<=> ! [X0,X1] :
( sP11(X1,X0)
| one_one(int) != times_times(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_274])]) ).
fof(f4902,plain,
! [X0,X1] :
( sP11(X1,X0)
| one_one(int) != times_times(int,X0,X1) ),
inference(cnf_transformation,[],[f3475]) ).
fof(f8514,plain,
spl63_273,
inference(avatar_split_clause,[],[f4446,f8512]) ).
fof(f8512,plain,
( spl63_273
<=> ! [X0,X1] :
( zero_zero(X0) = times_times(X0,zero_zero(X0),X1)
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_273])]) ).
fof(f4446,plain,
! [X0,X1] :
( zero_zero(X0) = times_times(X0,zero_zero(X0),X1)
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2635]) ).
fof(f2635,plain,
! [X0] :
( ! [X1] : zero_zero(X0) = times_times(X0,zero_zero(X0),X1)
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1630]) ).
fof(f1630,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : zero_zero(X0) = times_times(X0,zero_zero(X0),X1) ),
inference(rectify,[],[f432]) ).
fof(f432,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : zero_zero(X1) = times_times(X1,zero_zero(X1),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(f8510,plain,
spl63_272,
inference(avatar_split_clause,[],[f4445,f8508]) ).
fof(f8508,plain,
( spl63_272
<=> ! [X0,X1] :
( zero_zero(X0) = times_times(X0,X1,zero_zero(X0))
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_272])]) ).
fof(f4445,plain,
! [X0,X1] :
( zero_zero(X0) = times_times(X0,X1,zero_zero(X0))
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f2634]) ).
fof(f2634,plain,
! [X0] :
( ! [X1] : zero_zero(X0) = times_times(X0,X1,zero_zero(X0))
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f1629]) ).
fof(f1629,plain,
! [X0] :
( comm_semiring_1(X0)
=> ! [X1] : zero_zero(X0) = times_times(X0,X1,zero_zero(X0)) ),
inference(rectify,[],[f431]) ).
fof(f431,axiom,
! [X1] :
( comm_semiring_1(X1)
=> ! [X30] : zero_zero(X1) = times_times(X1,X30,zero_zero(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f8506,plain,
spl63_271,
inference(avatar_split_clause,[],[f4310,f8504]) ).
fof(f8504,plain,
( spl63_271
<=> ! [X0,X1] :
( zero_zero(X0) = times_times(X0,zero_zero(X0),X1)
| ~ mult_zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_271])]) ).
fof(f4310,plain,
! [X0,X1] :
( zero_zero(X0) = times_times(X0,zero_zero(X0),X1)
| ~ mult_zero(X0) ),
inference(cnf_transformation,[],[f2465]) ).
fof(f2465,plain,
! [X0] :
( ! [X1] : zero_zero(X0) = times_times(X0,zero_zero(X0),X1)
| ~ mult_zero(X0) ),
inference(ennf_transformation,[],[f1510]) ).
fof(f1510,plain,
! [X0] :
( mult_zero(X0)
=> ! [X1] : zero_zero(X0) = times_times(X0,zero_zero(X0),X1) ),
inference(rectify,[],[f426]) ).
fof(f426,axiom,
! [X1] :
( mult_zero(X1)
=> ! [X30] : zero_zero(X1) = times_times(X1,zero_zero(X1),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_mult__zero__left) ).
fof(f8502,plain,
spl63_270,
inference(avatar_split_clause,[],[f4309,f8500]) ).
fof(f4309,plain,
! [X0,X1] :
( zero_zero(X0) = times_times(X0,X1,zero_zero(X0))
| ~ mult_zero(X0) ),
inference(cnf_transformation,[],[f2464]) ).
fof(f2464,plain,
! [X0] :
( ! [X1] : zero_zero(X0) = times_times(X0,X1,zero_zero(X0))
| ~ mult_zero(X0) ),
inference(ennf_transformation,[],[f1509]) ).
fof(f1509,plain,
! [X0] :
( mult_zero(X0)
=> ! [X1] : zero_zero(X0) = times_times(X0,X1,zero_zero(X0)) ),
inference(rectify,[],[f427]) ).
fof(f427,axiom,
! [X1] :
( mult_zero(X1)
=> ! [X30] : zero_zero(X1) = times_times(X1,X30,zero_zero(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_mult__zero__right) ).
fof(f8498,plain,
spl63_269,
inference(avatar_split_clause,[],[f4036,f8496]) ).
fof(f8496,plain,
( spl63_269
<=> ! [X0] :
( ti(bool,X0) = fFalse
| ti(bool,X0) = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_269])]) ).
fof(f4036,plain,
! [X0] :
( ti(bool,X0) = fFalse
| ti(bool,X0) = fTrue ),
inference(cnf_transformation,[],[f1331]) ).
fof(f1331,plain,
! [X0] :
( ti(bool,X0) = fFalse
| ti(bool,X0) = fTrue ),
inference(rectify,[],[f1250]) ).
fof(f1250,axiom,
! [X84] :
( fFalse = ti(bool,X84)
| fTrue = ti(bool,X84) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
fof(f8494,plain,
spl63_268,
inference(avatar_split_clause,[],[f3889,f8491]) ).
fof(f8491,plain,
( spl63_268
<=> one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_268])]) ).
fof(f3889,plain,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
inference(cnf_transformation,[],[f122]) ).
fof(f122,axiom,
one_one(int) = hAPP(nat,int,semiring_1_of_nat(int),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_int__1) ).
fof(f8424,plain,
( ~ spl63_267
| ~ spl63_191
| ~ spl63_216 ),
inference(avatar_split_clause,[],[f8136,f8075,f7946,f8421]) ).
fof(f8421,plain,
( spl63_267
<=> min = ti(int,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_267])]) ).
fof(f8136,plain,
( min != ti(int,pls)
| ~ spl63_191
| ~ spl63_216 ),
inference(superposition,[],[f7947,f8076]) ).
fof(f8332,plain,
( spl63_266
| ~ spl63_161
| ~ spl63_185 ),
inference(avatar_split_clause,[],[f7954,f7919,f7793,f8329]) ).
fof(f8329,plain,
( spl63_266
<=> sP9(one_one(nat),one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_266])]) ).
fof(f7919,plain,
( spl63_185
<=> one_one(nat) = nat_1(one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_185])]) ).
fof(f7954,plain,
( sP9(one_one(nat),one_one(int))
| ~ spl63_161
| ~ spl63_185 ),
inference(superposition,[],[f7794,f7921]) ).
fof(f7921,plain,
( one_one(nat) = nat_1(one_one(int))
| ~ spl63_185 ),
inference(avatar_component_clause,[],[f7919]) ).
fof(f8306,plain,
( spl63_265
| ~ spl63_162
| ~ spl63_185 ),
inference(avatar_split_clause,[],[f7953,f7919,f7797,f8303]) ).
fof(f8303,plain,
( spl63_265
<=> sP10(one_one(nat),one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_265])]) ).
fof(f7953,plain,
( sP10(one_one(nat),one_one(int))
| ~ spl63_162
| ~ spl63_185 ),
inference(superposition,[],[f7798,f7921]) ).
fof(f8300,plain,
spl63_264,
inference(avatar_split_clause,[],[f6576,f8298]) ).
fof(f8298,plain,
( spl63_264
<=> ! [X1] :
( pls != ti(int,X1)
| sP10(nat_1(pls),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_264])]) ).
fof(f6576,plain,
! [X1] :
( pls != ti(int,X1)
| sP10(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6575,f5821]) ).
fof(f6575,plain,
! [X1] :
( ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),nat_1(pls))
| sP10(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6574,f5811]) ).
fof(f6574,plain,
! [X1] :
( sP10(nat_1(pls),X1)
| hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) != ti(int,X1) ),
inference(forward_demodulation,[],[f5742,f5811]) ).
fof(f5742,plain,
! [X1] :
( sP10(zero_zero(nat),X1)
| hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) != ti(int,X1) ),
inference(equality_resolution,[],[f4880]) ).
fof(f4880,plain,
! [X0,X1] :
( sP10(X0,X1)
| zero_zero(nat) != X0
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0) ),
inference(cnf_transformation,[],[f3462]) ).
fof(f8296,plain,
spl63_263,
inference(avatar_split_clause,[],[f6567,f8294]) ).
fof(f8294,plain,
( spl63_263
<=> ! [X1] :
( pls != ti(int,X1)
| sP9(nat_1(pls),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_263])]) ).
fof(f6567,plain,
! [X1] :
( pls != ti(int,X1)
| sP9(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6566,f5821]) ).
fof(f6566,plain,
! [X1] :
( ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),nat_1(pls))
| sP9(nat_1(pls),X1) ),
inference(forward_demodulation,[],[f6565,f5811]) ).
fof(f6565,plain,
! [X1] :
( sP9(nat_1(pls),X1)
| hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) != ti(int,X1) ),
inference(forward_demodulation,[],[f5739,f5811]) ).
fof(f5739,plain,
! [X1] :
( sP9(zero_zero(nat),X1)
| hAPP(nat,int,semiring_1_of_nat(int),zero_zero(nat)) != ti(int,X1) ),
inference(equality_resolution,[],[f4872]) ).
fof(f4872,plain,
! [X0,X1] :
( sP9(X0,X1)
| zero_zero(nat) != X0
| ti(int,X1) != hAPP(nat,int,semiring_1_of_nat(int),X0) ),
inference(cnf_transformation,[],[f3458]) ).
fof(f8292,plain,
spl63_262,
inference(avatar_split_clause,[],[f5821,f8289]) ).
fof(f8287,plain,
spl63_261,
inference(avatar_split_clause,[],[f5819,f8284]) ).
fof(f8284,plain,
( spl63_261
<=> one_one(int) = number_number_of(int,minus_minus(int,pls,min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_261])]) ).
fof(f5819,plain,
one_one(int) = number_number_of(int,minus_minus(int,pls,min)),
inference(forward_demodulation,[],[f5457,f5453]) ).
fof(f5457,plain,
one_one(int) = number_number_of(int,minus_minus(int,plus_plus(int,pls,pls),min)),
inference(definition_unfolding,[],[f3887,f5445]) ).
fof(f3887,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f135]) ).
fof(f135,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(f8282,plain,
spl63_260,
inference(avatar_split_clause,[],[f5817,f8279]) ).
fof(f8279,plain,
( spl63_260
<=> one_one(nat) = number_number_of(nat,minus_minus(int,pls,min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_260])]) ).
fof(f5817,plain,
one_one(nat) = number_number_of(nat,minus_minus(int,pls,min)),
inference(forward_demodulation,[],[f5455,f5453]) ).
fof(f5455,plain,
one_one(nat) = number_number_of(nat,minus_minus(int,plus_plus(int,pls,pls),min)),
inference(definition_unfolding,[],[f3885,f5445]) ).
fof(f3885,plain,
one_one(nat) = number_number_of(nat,bit1(pls)),
inference(cnf_transformation,[],[f137]) ).
fof(f137,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Numeral1__eq1__nat) ).
fof(f8277,plain,
spl63_259,
inference(avatar_split_clause,[],[f5499,f8275]) ).
fof(f5499,plain,
! [X0] : pls != minus_minus(int,plus_plus(int,X0,X0),min),
inference(definition_unfolding,[],[f3959,f5445]) ).
fof(f3959,plain,
! [X0] : bit1(X0) != pls,
inference(cnf_transformation,[],[f1263]) ).
fof(f1263,plain,
! [X0] : bit1(X0) != pls,
inference(rectify,[],[f165]) ).
fof(f165,axiom,
! [X29] : pls != bit1(X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_rel__simps_I39_J) ).
fof(f8273,plain,
spl63_258,
inference(avatar_split_clause,[],[f5451,f8270]) ).
fof(f8270,plain,
( spl63_258
<=> min = minus_minus(int,plus_plus(int,min,min),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_258])]) ).
fof(f5451,plain,
min = minus_minus(int,plus_plus(int,min,min),min),
inference(definition_unfolding,[],[f3858,f5445]) ).
fof(f3858,plain,
min = bit1(min),
inference(cnf_transformation,[],[f867]) ).
fof(f867,axiom,
min = bit1(min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_Bit1__Min) ).
fof(f8268,plain,
spl63_257,
inference(avatar_split_clause,[],[f5096,f8266]) ).
fof(f8266,plain,
( spl63_257
<=> ! [X2,X0,X1] : ti(X0,X2) = if(X0,fFalse,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_257])]) ).
fof(f5096,plain,
! [X2,X0,X1] : ti(X0,X2) = if(X0,fFalse,X1,X2),
inference(cnf_transformation,[],[f2008]) ).
fof(f2008,plain,
! [X0,X1,X2] : ti(X0,X2) = if(X0,fFalse,X1,X2),
inference(rectify,[],[f1249]) ).
fof(f1249,axiom,
! [X1,X9,X10] : ti(X1,X10) = if(X1,fFalse,X9,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
fof(f8264,plain,
spl63_256,
inference(avatar_split_clause,[],[f5095,f8262]) ).
fof(f8262,plain,
( spl63_256
<=> ! [X2,X0,X1] : ti(X0,X1) = if(X0,fTrue,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_256])]) ).
fof(f5095,plain,
! [X2,X0,X1] : ti(X0,X1) = if(X0,fTrue,X1,X2),
inference(cnf_transformation,[],[f2007]) ).
fof(f2007,plain,
! [X0,X1,X2] : ti(X0,X1) = if(X0,fTrue,X1,X2),
inference(rectify,[],[f1248]) ).
fof(f1248,axiom,
! [X1,X9,X10] : ti(X1,X9) = if(X1,fTrue,X9,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
fof(f8260,plain,
spl63_255,
inference(avatar_split_clause,[],[f4683,f8258]) ).
fof(f4683,plain,
! [X0,X1] : hBOOL(hAPP(int,bool,zcong(X0,X1),one_one(int))),
inference(cnf_transformation,[],[f1785]) ).
fof(f1785,plain,
! [X0,X1] : hBOOL(hAPP(int,bool,zcong(X0,X1),one_one(int))),
inference(rectify,[],[f984]) ).
fof(f984,axiom,
! [X30,X39] : hBOOL(hAPP(int,bool,zcong(X30,X39),one_one(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_zcong__1) ).
fof(f8256,plain,
spl63_254,
inference(avatar_split_clause,[],[f4682,f8254]) ).
fof(f8254,plain,
( spl63_254
<=> ! [X0,X1] : minus_minus(nat,plus_plus(nat,X0,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_254])]) ).
fof(f4682,plain,
! [X0,X1] : minus_minus(nat,plus_plus(nat,X0,X1),X1) = X0,
inference(cnf_transformation,[],[f1784]) ).
fof(f1784,plain,
! [X0,X1] : minus_minus(nat,plus_plus(nat,X0,X1),X1) = X0,
inference(rectify,[],[f463]) ).
fof(f463,axiom,
! [X13,X14] : minus_minus(nat,plus_plus(nat,X13,X14),X14) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_diff__add__inverse2) ).
fof(f8252,plain,
spl63_253,
inference(avatar_split_clause,[],[f4681,f8250]) ).
fof(f8250,plain,
( spl63_253
<=> ! [X0,X1] : minus_minus(nat,plus_plus(nat,X0,X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_253])]) ).
fof(f4681,plain,
! [X0,X1] : minus_minus(nat,plus_plus(nat,X0,X1),X0) = X1,
inference(cnf_transformation,[],[f1783]) ).
fof(f1783,plain,
! [X0,X1] : minus_minus(nat,plus_plus(nat,X0,X1),X0) = X1,
inference(rectify,[],[f464]) ).
fof(f464,axiom,
! [X14,X13] : minus_minus(nat,plus_plus(nat,X14,X13),X14) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_diff__add__inverse) ).
fof(f8248,plain,
spl63_252,
inference(avatar_split_clause,[],[f4680,f8246]) ).
fof(f8246,plain,
( spl63_252
<=> ! [X0,X1] : zcong(X0,X1) = zcong(ti(int,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_252])]) ).
fof(f4680,plain,
! [X0,X1] : zcong(X0,X1) = zcong(ti(int,X0),X1),
inference(cnf_transformation,[],[f1782]) ).
fof(f1782,plain,
! [X0,X1] : zcong(X0,X1) = zcong(ti(int,X0),X1),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X0,X2] : zcong(ti(int,X0),X2) = zcong(X0,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_arg1) ).
fof(f8244,plain,
spl63_251,
inference(avatar_split_clause,[],[f4679,f8242]) ).
fof(f8242,plain,
( spl63_251
<=> ! [X0,X1] : legendre(X0,X1) = legendre(ti(int,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_251])]) ).
fof(f4679,plain,
! [X0,X1] : legendre(X0,X1) = legendre(ti(int,X0),X1),
inference(cnf_transformation,[],[f1781]) ).
fof(f1781,plain,
! [X0,X1] : legendre(X0,X1) = legendre(ti(int,X0),X1),
inference(rectify,[],[f64]) ).
fof(f64,axiom,
! [X0,X2] : legendre(ti(int,X0),X2) = legendre(X0,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_arg1) ).
fof(f8240,plain,
spl63_250,
inference(avatar_split_clause,[],[f4678,f8238]) ).
fof(f4678,plain,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
inference(cnf_transformation,[],[f1780]) ).
fof(f1780,plain,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
inference(rectify,[],[f350]) ).
fof(f350,axiom,
! [X15,X7] : times_times(int,X15,X7) = times_times(int,X7,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_zmult__commute) ).
fof(f8236,plain,
spl63_249,
inference(avatar_split_clause,[],[f4677,f8234]) ).
fof(f8234,plain,
( spl63_249
<=> ! [X0,X1] : times_times(nat,X0,X1) = times_times(nat,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_249])]) ).
fof(f4677,plain,
! [X0,X1] : times_times(nat,X0,X1) = times_times(nat,X1,X0),
inference(cnf_transformation,[],[f1779]) ).
fof(f1779,plain,
! [X0,X1] : times_times(nat,X0,X1) = times_times(nat,X1,X0),
inference(rectify,[],[f673]) ).
fof(f673,axiom,
! [X13,X14] : times_times(nat,X13,X14) = times_times(nat,X14,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_nat__mult__commute) ).
fof(f8232,plain,
spl63_248,
inference(avatar_split_clause,[],[f4676,f8230]) ).
fof(f4676,plain,
! [X0,X1] : times_times(real,X0,X1) = times_times(real,X1,X0),
inference(cnf_transformation,[],[f1778]) ).
fof(f1778,plain,
! [X0,X1] : times_times(real,X0,X1) = times_times(real,X1,X0),
inference(rectify,[],[f811]) ).
fof(f811,axiom,
! [X15,X7] : times_times(real,X15,X7) = times_times(real,X7,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_real__mult__commute) ).
fof(f8228,plain,
spl63_247,
inference(avatar_split_clause,[],[f4675,f8226]) ).
fof(f4675,plain,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(cnf_transformation,[],[f1777]) ).
fof(f1777,plain,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X15,X7] : plus_plus(int,X15,X7) = plus_plus(int,X7,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
fof(f8224,plain,
spl63_246,
inference(avatar_split_clause,[],[f4674,f8222]) ).
fof(f8222,plain,
( spl63_246
<=> ! [X0,X1] : plus_plus(nat,X0,X1) = plus_plus(nat,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_246])]) ).
fof(f4674,plain,
! [X0,X1] : plus_plus(nat,X0,X1) = plus_plus(nat,X1,X0),
inference(cnf_transformation,[],[f1776]) ).
fof(f1776,plain,
! [X0,X1] : plus_plus(nat,X0,X1) = plus_plus(nat,X1,X0),
inference(rectify,[],[f220]) ).
fof(f220,axiom,
! [X13,X14] : plus_plus(nat,X13,X14) = plus_plus(nat,X14,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_nat__add__commute) ).
fof(f8220,plain,
spl63_245,
inference(avatar_split_clause,[],[f4673,f8218]) ).
fof(f8218,plain,
( spl63_245
<=> ! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_245])]) ).
fof(f4673,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(cnf_transformation,[],[f1775]) ).
fof(f1775,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(rectify,[],[f1247]) ).
fof(f1247,axiom,
! [X82,X83] : ti(X82,X83) = ti(X82,ti(X82,X83)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
fof(f8216,plain,
spl63_244,
inference(avatar_split_clause,[],[f4672,f8214]) ).
fof(f8214,plain,
( spl63_244
<=> ! [X0,X1] : zcong(X0,X1) = zcong(X0,ti(int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_244])]) ).
fof(f4672,plain,
! [X0,X1] : zcong(X0,X1) = zcong(X0,ti(int,X1)),
inference(cnf_transformation,[],[f1774]) ).
fof(f1774,plain,
! [X0,X1] : zcong(X0,X1) = zcong(X0,ti(int,X1)),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X0,X2] : zcong(X0,X2) = zcong(X0,ti(int,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozcong_arg2) ).
fof(f8212,plain,
spl63_243,
inference(avatar_split_clause,[],[f4671,f8210]) ).
fof(f8210,plain,
( spl63_243
<=> ! [X0,X1] : legendre(X0,X1) = ti(int,legendre(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_243])]) ).
fof(f4671,plain,
! [X0,X1] : legendre(X0,X1) = ti(int,legendre(X0,X1)),
inference(cnf_transformation,[],[f1773]) ).
fof(f1773,plain,
! [X0,X1] : legendre(X0,X1) = ti(int,legendre(X0,X1)),
inference(rectify,[],[f66]) ).
fof(f66,axiom,
! [X0,X2] : legendre(X0,X2) = ti(int,legendre(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_res) ).
fof(f8208,plain,
spl63_242,
inference(avatar_split_clause,[],[f4670,f8206]) ).
fof(f8206,plain,
( spl63_242
<=> ! [X0,X1] : legendre(X0,X1) = legendre(X0,ti(int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_242])]) ).
fof(f4670,plain,
! [X0,X1] : legendre(X0,X1) = legendre(X0,ti(int,X1)),
inference(cnf_transformation,[],[f1772]) ).
fof(f1772,plain,
! [X0,X1] : legendre(X0,X1) = legendre(X0,ti(int,X1)),
inference(rectify,[],[f65]) ).
fof(f65,axiom,
! [X0,X2] : legendre(X0,X2) = legendre(X0,ti(int,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OLegendre_arg2) ).
fof(f8204,plain,
spl63_241,
inference(avatar_split_clause,[],[f4263,f8202]) ).
fof(f8202,plain,
( spl63_241
<=> ! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_241])]) ).
fof(f4263,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero(X0) ),
inference(cnf_transformation,[],[f2411]) ).
fof(f2411,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero(X0) ),
inference(ennf_transformation,[],[f1471]) ).
fof(f1471,plain,
! [X0] :
( zero(X0)
=> zero_zero(X0) = ti(X0,zero_zero(X0)) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X1] :
( zero(X1)
=> zero_zero(X1) = ti(X1,zero_zero(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_res) ).
fof(f8200,plain,
spl63_240,
inference(avatar_split_clause,[],[f4262,f8198]) ).
fof(f4262,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ one(X0) ),
inference(cnf_transformation,[],[f2410]) ).
fof(f2410,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ one(X0) ),
inference(ennf_transformation,[],[f1470]) ).
fof(f1470,plain,
! [X0] :
( one(X0)
=> one_one(X0) = ti(X0,one_one(X0)) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1] :
( one(X1)
=> one_one(X1) = ti(X1,one_one(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
fof(f8196,plain,
spl63_239,
inference(avatar_split_clause,[],[f4190,f8194]) ).
fof(f4190,plain,
! [X0] :
( one_one(X0) = abs_abs(X0,one_one(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f2344]) ).
fof(f2344,plain,
! [X0] :
( one_one(X0) = abs_abs(X0,one_one(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f1410]) ).
fof(f1410,plain,
! [X0] :
( linordered_idom(X0)
=> one_one(X0) = abs_abs(X0,one_one(X0)) ),
inference(rectify,[],[f1031]) ).
fof(f1031,axiom,
! [X1] :
( linordered_idom(X1)
=> one_one(X1) = abs_abs(X1,one_one(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_abs__one) ).
fof(f8192,plain,
spl63_238,
inference(avatar_split_clause,[],[f4168,f8190]) ).
fof(f4168,plain,
! [X0] :
( zero_zero(X0) = abs_abs(X0,zero_zero(X0))
| ~ ordere142940540dd_abs(X0) ),
inference(cnf_transformation,[],[f2325]) ).
fof(f2325,plain,
! [X0] :
( zero_zero(X0) = abs_abs(X0,zero_zero(X0))
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f1391]) ).
fof(f1391,plain,
! [X0] :
( ordere142940540dd_abs(X0)
=> zero_zero(X0) = abs_abs(X0,zero_zero(X0)) ),
inference(rectify,[],[f1028]) ).
fof(f1028,axiom,
! [X1] :
( ordere142940540dd_abs(X1)
=> zero_zero(X1) = abs_abs(X1,zero_zero(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_abs__zero) ).
fof(f8188,plain,
spl63_237,
inference(avatar_split_clause,[],[f4093,f8186]) ).
fof(f4093,plain,
! [X0,X1] :
( zero_zero(X0) = minus_minus(X0,X1,X1)
| ~ group_add(X0) ),
inference(cnf_transformation,[],[f2292]) ).
fof(f2292,plain,
! [X0] :
( ! [X1] : zero_zero(X0) = minus_minus(X0,X1,X1)
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f1364]) ).
fof(f1364,plain,
! [X0] :
( group_add(X0)
=> ! [X1] : zero_zero(X0) = minus_minus(X0,X1,X1) ),
inference(rectify,[],[f420]) ).
fof(f420,axiom,
! [X1] :
( group_add(X1)
=> ! [X30] : zero_zero(X1) = minus_minus(X1,X30,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_diff__self) ).
fof(f8184,plain,
spl63_236,
inference(avatar_split_clause,[],[f3994,f8182]) ).
fof(f3994,plain,
! [X0] : nat_1(hAPP(nat,int,semiring_1_of_nat(int),X0)) = X0,
inference(cnf_transformation,[],[f1292]) ).
fof(f1292,plain,
! [X0] : nat_1(hAPP(nat,int,semiring_1_of_nat(int),X0)) = X0,
inference(rectify,[],[f444]) ).
fof(f444,axiom,
! [X14] : nat_1(hAPP(nat,int,semiring_1_of_nat(int),X14)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_nat__int) ).
fof(f8180,plain,
spl63_235,
inference(avatar_split_clause,[],[f3992,f8178]) ).
fof(f8178,plain,
( spl63_235
<=> ! [X0] : ti(int,X0) = times_times(int,one_one(int),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_235])]) ).
fof(f3992,plain,
! [X0] : ti(int,X0) = times_times(int,one_one(int),X0),
inference(cnf_transformation,[],[f1290]) ).
fof(f1290,plain,
! [X0] : ti(int,X0) = times_times(int,one_one(int),X0),
inference(rectify,[],[f476]) ).
fof(f476,axiom,
! [X15] : ti(int,X15) = times_times(int,one_one(int),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_zmult__1) ).
fof(f8176,plain,
spl63_234,
inference(avatar_split_clause,[],[f3991,f8174]) ).
fof(f8174,plain,
( spl63_234
<=> ! [X0] : ti(int,X0) = times_times(int,X0,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_234])]) ).
fof(f3991,plain,
! [X0] : ti(int,X0) = times_times(int,X0,one_one(int)),
inference(cnf_transformation,[],[f1289]) ).
fof(f1289,plain,
! [X0] : ti(int,X0) = times_times(int,X0,one_one(int)),
inference(rectify,[],[f477]) ).
fof(f477,axiom,
! [X15] : ti(int,X15) = times_times(int,X15,one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_zmult__1__right) ).
fof(f8172,plain,
spl63_233,
inference(avatar_split_clause,[],[f3989,f8170]) ).
fof(f8170,plain,
( spl63_233
<=> ! [X0] : quadRes(X0) = ti(fun(int,bool),quadRes(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_233])]) ).
fof(f3989,plain,
! [X0] : quadRes(X0) = ti(fun(int,bool),quadRes(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] : quadRes(X0) = ti(fun(int,bool),quadRes(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OQuadRes_res) ).
fof(f8168,plain,
( spl63_232
| ~ spl63_156
| ~ spl63_190
| ~ spl63_192
| ~ spl63_216
| ~ spl63_231 ),
inference(avatar_split_clause,[],[f8163,f8150,f8075,f7950,f7941,f7772,f8165]) ).
fof(f7950,plain,
( spl63_192
<=> ! [X0] : nat_1(X0) = number_number_of(nat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_192])]) ).
fof(f8150,plain,
( spl63_231
<=> zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,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_231])]) ).
fof(f8163,plain,
( pls = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,pls,min),min)))
| ~ spl63_156
| ~ spl63_190
| ~ spl63_192
| ~ spl63_216
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8162,f7774]) ).
fof(f8162,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,pls,min),min)))
| ~ spl63_190
| ~ spl63_192
| ~ spl63_216
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8161,f7943]) ).
fof(f8161,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,plus_plus(int,pls,pls),min),min)))
| ~ spl63_192
| ~ spl63_216
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8160,f5503]) ).
fof(f8160,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,ti(int,plus_plus(int,pls,pls)),min),min)))
| ~ spl63_192
| ~ spl63_216
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8159,f8076]) ).
fof(f8159,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,plus_plus(int,pls,plus_plus(int,pls,pls)),min),min)))
| ~ spl63_192
| ~ spl63_216
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8158,f4675]) ).
fof(f8158,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,plus_plus(int,plus_plus(int,pls,pls),pls),min),min)))
| ~ spl63_192
| ~ spl63_216
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8157,f5503]) ).
fof(f8157,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,ti(int,plus_plus(int,plus_plus(int,pls,pls),pls)),min),min)))
| ~ spl63_192
| ~ spl63_216
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8156,f8076]) ).
fof(f8156,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,plus_plus(int,pls,plus_plus(int,plus_plus(int,pls,pls),pls)),min),min)))
| ~ spl63_192
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8155,f5104]) ).
fof(f8155,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(minus_minus(int,minus_minus(int,plus_plus(int,plus_plus(int,pls,pls),plus_plus(int,pls,pls)),min),min)))
| ~ spl63_192
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8154,f5502]) ).
fof(f8154,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min))))
| ~ spl63_192
| ~ spl63_231 ),
inference(forward_demodulation,[],[f8152,f7951]) ).
fof(f7951,plain,
( ! [X0] : nat_1(X0) = number_number_of(nat,X0)
| ~ spl63_192 ),
inference(avatar_component_clause,[],[f7950]) ).
fof(f8152,plain,
( zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min))))
| ~ spl63_231 ),
inference(avatar_component_clause,[],[f8150]) ).
fof(f8153,plain,
spl63_231,
inference(avatar_split_clause,[],[f5446,f8150]) ).
fof(f5446,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,plus_plus(int,minus_minus(int,plus_plus(int,pls,pls),min),minus_minus(int,plus_plus(int,pls,pls),min)))),
inference(definition_unfolding,[],[f3695,f3968,f5445]) ).
fof(f3695,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1253]) ).
fof(f1253,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))),
inference(flattening,[],[f1252]) ).
fof(f1252,negated_conjecture,
~ ( zero_zero(int) != hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) ),
inference(negated_conjecture,[],[f1251]) ).
fof(f1251,conjecture,
zero_zero(int) != hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f8133,plain,
spl63_230,
inference(avatar_split_clause,[],[f5920,f8131]) ).
fof(f5920,plain,
! [X0] : hBOOL(hAPP(int,bool,zcong(X0,pls),X0)),
inference(forward_demodulation,[],[f3995,f3861]) ).
fof(f3995,plain,
! [X0] : hBOOL(hAPP(int,bool,zcong(X0,zero_zero(int)),X0)),
inference(cnf_transformation,[],[f1293]) ).
fof(f1293,plain,
! [X0] : hBOOL(hAPP(int,bool,zcong(X0,zero_zero(int)),X0)),
inference(rectify,[],[f914]) ).
fof(f914,axiom,
! [X13] : hBOOL(hAPP(int,bool,zcong(X13,zero_zero(int)),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_zcong__id) ).
fof(f8129,plain,
spl63_229,
inference(avatar_split_clause,[],[f5913,f8127]) ).
fof(f8127,plain,
( spl63_229
<=> ! [X0] : nat_1(pls) = times_times(nat,nat_1(pls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_229])]) ).
fof(f5913,plain,
! [X0] : nat_1(pls) = times_times(nat,nat_1(pls),X0),
inference(forward_demodulation,[],[f3982,f5811]) ).
fof(f3982,plain,
! [X0] : zero_zero(nat) = times_times(nat,zero_zero(nat),X0),
inference(cnf_transformation,[],[f1281]) ).
fof(f1281,plain,
! [X0] : zero_zero(nat) = times_times(nat,zero_zero(nat),X0),
inference(rectify,[],[f692]) ).
fof(f692,axiom,
! [X14] : zero_zero(nat) = times_times(nat,zero_zero(nat),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_mult__0) ).
fof(f8125,plain,
spl63_228,
inference(avatar_split_clause,[],[f5912,f8123]) ).
fof(f8123,plain,
( spl63_228
<=> ! [X0] : nat_1(pls) = times_times(nat,X0,nat_1(pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_228])]) ).
fof(f5912,plain,
! [X0] : nat_1(pls) = times_times(nat,X0,nat_1(pls)),
inference(forward_demodulation,[],[f3981,f5811]) ).
fof(f3981,plain,
! [X0] : zero_zero(nat) = times_times(nat,X0,zero_zero(nat)),
inference(cnf_transformation,[],[f1280]) ).
fof(f1280,plain,
! [X0] : zero_zero(nat) = times_times(nat,X0,zero_zero(nat)),
inference(rectify,[],[f693]) ).
fof(f693,axiom,
! [X13] : zero_zero(nat) = times_times(nat,X13,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_mult__0__right) ).
fof(f8121,plain,
spl63_227,
inference(avatar_split_clause,[],[f5911,f8119]) ).
fof(f5911,plain,
! [X0] : nat_1(pls) = minus_minus(nat,nat_1(pls),X0),
inference(forward_demodulation,[],[f3980,f5811]) ).
fof(f3980,plain,
! [X0] : zero_zero(nat) = minus_minus(nat,zero_zero(nat),X0),
inference(cnf_transformation,[],[f1279]) ).
fof(f1279,plain,
! [X0] : zero_zero(nat) = minus_minus(nat,zero_zero(nat),X0),
inference(rectify,[],[f436]) ).
fof(f436,axiom,
! [X14] : zero_zero(nat) = minus_minus(nat,zero_zero(nat),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_diff__0__eq__0) ).
fof(f8117,plain,
spl63_226,
inference(avatar_split_clause,[],[f5313,f8115]) ).
fof(f8115,plain,
( spl63_226
<=> ! [X2,X0,X1] :
( sP16(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_226])]) ).
fof(f5313,plain,
! [X2,X0,X1] :
( sP16(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f3628]) ).
fof(f8113,plain,
spl63_225,
inference(avatar_split_clause,[],[f5312,f8111]) ).
fof(f8111,plain,
( spl63_225
<=> ! [X2,X0,X1] :
( sP16(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_225])]) ).
fof(f5312,plain,
! [X2,X0,X1] :
( sP16(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f3628]) ).
fof(f8109,plain,
spl63_224,
inference(avatar_split_clause,[],[f5306,f8107]) ).
fof(f8107,plain,
( spl63_224
<=> ! [X2,X0,X1] :
( sP15(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_224])]) ).
fof(f5306,plain,
! [X2,X0,X1] :
( sP15(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f3623]) ).
fof(f8105,plain,
spl63_223,
inference(avatar_split_clause,[],[f5305,f8103]) ).
fof(f8103,plain,
( spl63_223
<=> ! [X2,X0,X1] :
( sP15(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_223])]) ).
fof(f5305,plain,
! [X2,X0,X1] :
( sP15(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f3623]) ).
fof(f8101,plain,
spl63_222,
inference(avatar_split_clause,[],[f4669,f8099]) ).
fof(f4669,plain,
! [X0,X1] : hBOOL(hAPP(int,bool,zcong(X0,X0),X1)),
inference(cnf_transformation,[],[f1771]) ).
fof(f1771,plain,
! [X0,X1] : hBOOL(hAPP(int,bool,zcong(X0,X0),X1)),
inference(rectify,[],[f980]) ).
fof(f980,axiom,
! [X19,X13] : hBOOL(hAPP(int,bool,zcong(X19,X19),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_zcong__refl) ).
fof(f8097,plain,
spl63_221,
inference(avatar_split_clause,[],[f4593,f8095]) ).
fof(f8095,plain,
( spl63_221
<=> ! [X0] :
( hBOOL(hAPP(int,bool,zprime,X0))
| ~ sP8(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_221])]) ).
fof(f4593,plain,
! [X0] :
( hBOOL(hAPP(int,bool,zprime,X0))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f3377]) ).
fof(f3377,plain,
! [X0] :
( ( hBOOL(hAPP(int,bool,zprime,X0))
| ~ sP8(X0) )
& ( sP8(X0)
| ~ hBOOL(hAPP(int,bool,zprime,X0)) ) ),
inference(nnf_transformation,[],[f3211]) ).
fof(f3211,plain,
! [X0] :
( hBOOL(hAPP(int,bool,zprime,X0))
<=> sP8(X0) ),
inference(definition_folding,[],[f2765,f3210]) ).
fof(f2765,plain,
! [X0] :
( hBOOL(hAPP(int,bool,zprime,X0))
<=> ( ! [X1] :
( ti(int,X0) = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) ) ),
inference(flattening,[],[f2764]) ).
fof(f2764,plain,
! [X0] :
( hBOOL(hAPP(int,bool,zprime,X0))
<=> ( ! [X1] :
( ti(int,X0) = ti(int,X1)
| one_one(int) = ti(int,X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) ) ),
inference(ennf_transformation,[],[f1733]) ).
fof(f1733,plain,
! [X0] :
( hBOOL(hAPP(int,bool,zprime,X0))
<=> ( ! [X1] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X1),X0))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
=> ( ti(int,X0) = ti(int,X1)
| one_one(int) = ti(int,X1) ) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X0)) ) ),
inference(rectify,[],[f999]) ).
fof(f999,axiom,
! [X73] :
( hBOOL(hAPP(int,bool,zprime,X73))
<=> ( ! [X75] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X75),X73))
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X75)) )
=> ( ti(int,X75) = ti(int,X73)
| one_one(int) = ti(int,X75) ) )
& hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_zprime__def) ).
fof(f8093,plain,
spl63_220,
inference(avatar_split_clause,[],[f4592,f8091]) ).
fof(f8091,plain,
( spl63_220
<=> ! [X0] :
( sP8(X0)
| ~ hBOOL(hAPP(int,bool,zprime,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_220])]) ).
fof(f4592,plain,
! [X0] :
( sP8(X0)
| ~ hBOOL(hAPP(int,bool,zprime,X0)) ),
inference(cnf_transformation,[],[f3377]) ).
fof(f8089,plain,
spl63_219,
inference(avatar_split_clause,[],[f4342,f8087]) ).
fof(f8087,plain,
( spl63_219
<=> ! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_219])]) ).
fof(f4342,plain,
! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f2492]) ).
fof(f2492,plain,
! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f1535]) ).
fof(f1535,plain,
! [X0] :
( number_semiring(X0)
=> zero_zero(X0) = number_number_of(X0,pls) ),
inference(rectify,[],[f179]) ).
fof(f179,axiom,
! [X1] :
( number_semiring(X1)
=> zero_zero(X1) = number_number_of(X1,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_semiring__numeral__0__eq__0) ).
fof(f8085,plain,
spl63_218,
inference(avatar_split_clause,[],[f4227,f8083]) ).
fof(f4227,plain,
! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f2375]) ).
fof(f2375,plain,
! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f1437]) ).
fof(f1437,plain,
! [X0] :
( number_ring(X0)
=> zero_zero(X0) = number_number_of(X0,pls) ),
inference(rectify,[],[f180]) ).
fof(f180,axiom,
! [X1] :
( number_ring(X1)
=> zero_zero(X1) = number_number_of(X1,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_number__of__Pls) ).
fof(f8081,plain,
spl63_217,
inference(avatar_split_clause,[],[f3988,f8079]) ).
fof(f3988,plain,
! [X0] : ti(int,X0) = plus_plus(int,X0,pls),
inference(cnf_transformation,[],[f1287]) ).
fof(f1287,plain,
! [X0] : ti(int,X0) = plus_plus(int,X0,pls),
inference(rectify,[],[f173]) ).
fof(f173,axiom,
! [X19] : plus_plus(int,X19,pls) = ti(int,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
fof(f8077,plain,
spl63_216,
inference(avatar_split_clause,[],[f3985,f8075]) ).
fof(f3985,plain,
! [X0] : ti(int,X0) = plus_plus(int,pls,X0),
inference(cnf_transformation,[],[f1284]) ).
fof(f1284,plain,
! [X0] : ti(int,X0) = plus_plus(int,pls,X0),
inference(rectify,[],[f174]) ).
fof(f174,axiom,
! [X19] : ti(int,X19) = plus_plus(int,pls,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__Pls) ).
fof(f8073,plain,
spl63_215,
inference(avatar_split_clause,[],[f3984,f8071]) ).
fof(f8071,plain,
( spl63_215
<=> ! [X0] : ti(int,X0) = minus_minus(int,X0,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_215])]) ).
fof(f3984,plain,
! [X0] : ti(int,X0) = minus_minus(int,X0,pls),
inference(cnf_transformation,[],[f1283]) ).
fof(f1283,plain,
! [X0] : ti(int,X0) = minus_minus(int,X0,pls),
inference(rectify,[],[f688]) ).
fof(f688,axiom,
! [X19] : ti(int,X19) = minus_minus(int,X19,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_diff__bin__simps_I1_J) ).
fof(f8069,plain,
spl63_214,
inference(avatar_split_clause,[],[f3888,f8066]) ).
fof(f8066,plain,
( spl63_214
<=> tn = minus_minus(nat,nat_1(t),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_214])]) ).
fof(f3888,plain,
tn = minus_minus(nat,nat_1(t),one_one(nat)),
inference(cnf_transformation,[],[f334]) ).
fof(f334,axiom,
tn = minus_minus(nat,nat_1(t),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_tn) ).
fof(f8060,plain,
( spl63_213
| ~ spl63_36
| ~ spl63_160 ),
inference(avatar_split_clause,[],[f7817,f7789,f7172,f8057]) ).
fof(f8057,plain,
( spl63_213
<=> sP7(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_213])]) ).
fof(f7172,plain,
( spl63_36
<=> linord581940658strict(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_36])]) ).
fof(f7789,plain,
( spl63_160
<=> ! [X0] :
( sP7(X0)
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_160])]) ).
fof(f7817,plain,
( sP7(int)
| ~ spl63_36
| ~ spl63_160 ),
inference(resolution,[],[f7790,f7174]) ).
fof(f7174,plain,
( linord581940658strict(int)
| ~ spl63_36 ),
inference(avatar_component_clause,[],[f7172]) ).
fof(f7790,plain,
( ! [X0] :
( ~ linord581940658strict(X0)
| sP7(X0) )
| ~ spl63_160 ),
inference(avatar_component_clause,[],[f7789]) ).
fof(f8045,plain,
spl63_212,
inference(avatar_split_clause,[],[f5910,f8043]) ).
fof(f8043,plain,
( spl63_212
<=> ! [X0] : plus_plus(nat,nat_1(pls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_212])]) ).
fof(f5910,plain,
! [X0] : plus_plus(nat,nat_1(pls),X0) = X0,
inference(forward_demodulation,[],[f3976,f5811]) ).
fof(f3976,plain,
! [X0] : plus_plus(nat,zero_zero(nat),X0) = X0,
inference(cnf_transformation,[],[f1275]) ).
fof(f1275,plain,
! [X0] : plus_plus(nat,zero_zero(nat),X0) = X0,
inference(rectify,[],[f254]) ).
fof(f254,axiom,
! [X14] : plus_plus(nat,zero_zero(nat),X14) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_plus__nat_Oadd__0) ).
fof(f8041,plain,
spl63_211,
inference(avatar_split_clause,[],[f5909,f8039]) ).
fof(f8039,plain,
( spl63_211
<=> ! [X0] : plus_plus(nat,X0,nat_1(pls)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_211])]) ).
fof(f5909,plain,
! [X0] : plus_plus(nat,X0,nat_1(pls)) = X0,
inference(forward_demodulation,[],[f3975,f5811]) ).
fof(f3975,plain,
! [X0] : plus_plus(nat,X0,zero_zero(nat)) = X0,
inference(cnf_transformation,[],[f1274]) ).
fof(f1274,plain,
! [X0] : plus_plus(nat,X0,zero_zero(nat)) = X0,
inference(rectify,[],[f253]) ).
fof(f253,axiom,
! [X13] : plus_plus(nat,X13,zero_zero(nat)) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Nat_Oadd__0__right) ).
fof(f8037,plain,
spl63_210,
inference(avatar_split_clause,[],[f5908,f8035]) ).
fof(f8035,plain,
( spl63_210
<=> ! [X0] : minus_minus(nat,X0,nat_1(pls)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_210])]) ).
fof(f5908,plain,
! [X0] : minus_minus(nat,X0,nat_1(pls)) = X0,
inference(forward_demodulation,[],[f3974,f5811]) ).
fof(f3974,plain,
! [X0] : minus_minus(nat,X0,zero_zero(nat)) = X0,
inference(cnf_transformation,[],[f1273]) ).
fof(f1273,plain,
! [X0] : minus_minus(nat,X0,zero_zero(nat)) = X0,
inference(rectify,[],[f435]) ).
fof(f435,axiom,
! [X13] : minus_minus(nat,X13,zero_zero(nat)) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_minus__nat_Odiff__0) ).
fof(f8033,plain,
( spl63_209
| ~ spl63_35
| ~ spl63_160 ),
inference(avatar_split_clause,[],[f7816,f7789,f7167,f8030]) ).
fof(f8030,plain,
( spl63_209
<=> sP7(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_209])]) ).
fof(f7167,plain,
( spl63_35
<=> linord581940658strict(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_35])]) ).
fof(f7816,plain,
( sP7(real)
| ~ spl63_35
| ~ spl63_160 ),
inference(resolution,[],[f7790,f7169]) ).
fof(f7169,plain,
( linord581940658strict(real)
| ~ spl63_35 ),
inference(avatar_component_clause,[],[f7167]) ).
fof(f8028,plain,
spl63_208,
inference(avatar_split_clause,[],[f5907,f8026]) ).
fof(f8026,plain,
( spl63_208
<=> ! [X0] : minus_minus(nat,X0,X0) = nat_1(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_208])]) ).
fof(f5907,plain,
! [X0] : minus_minus(nat,X0,X0) = nat_1(pls),
inference(forward_demodulation,[],[f3963,f5811]) ).
fof(f3963,plain,
! [X0] : zero_zero(nat) = minus_minus(nat,X0,X0),
inference(cnf_transformation,[],[f1267]) ).
fof(f1267,plain,
! [X0] : zero_zero(nat) = minus_minus(nat,X0,X0),
inference(rectify,[],[f434]) ).
fof(f434,axiom,
! [X13] : zero_zero(nat) = minus_minus(nat,X13,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_diff__self__eq__0) ).
fof(f8024,plain,
spl63_207,
inference(avatar_split_clause,[],[f4882,f8022]) ).
fof(f8022,plain,
( spl63_207
<=> ! [X0,X1] :
( nat_1(X0) = X1
| ~ sP10(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_207])]) ).
fof(f4882,plain,
! [X0,X1] :
( nat_1(X0) = X1
| ~ sP10(X1,X0) ),
inference(cnf_transformation,[],[f3463]) ).
fof(f3463,plain,
! [X0,X1] :
( ( nat_1(X0) = X1
| ~ sP10(X1,X0) )
& ( sP10(X1,X0)
| nat_1(X0) != X1 ) ),
inference(nnf_transformation,[],[f3215]) ).
fof(f3215,plain,
! [X0,X1] :
( nat_1(X0) = X1
<=> sP10(X1,X0) ),
inference(definition_folding,[],[f2928,f3214]) ).
fof(f2928,plain,
! [X0,X1] :
( nat_1(X0) = X1
<=> ( ( zero_zero(nat) = X1
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) )
& ( ti(int,X0) = hAPP(nat,int,semiring_1_of_nat(int),X1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0)) ) ) ),
inference(ennf_transformation,[],[f1926]) ).
fof(f1926,plain,
! [X0,X1] :
( nat_1(X0) = X1
<=> ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0))
=> zero_zero(nat) = X1 )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X0))
=> ti(int,X0) = hAPP(nat,int,semiring_1_of_nat(int),X1) ) ) ),
inference(rectify,[],[f493]) ).
fof(f493,axiom,
! [X23,X27] :
( nat_1(X23) = X27
<=> ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X23))
=> zero_zero(nat) = X27 )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X23))
=> hAPP(nat,int,semiring_1_of_nat(int),X27) = ti(int,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_nat__eq__iff) ).
fof(f8020,plain,
spl63_206,
inference(avatar_split_clause,[],[f4874,f8018]) ).
fof(f8018,plain,
( spl63_206
<=> ! [X0,X1] :
( nat_1(X1) = X0
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_206])]) ).
fof(f4874,plain,
! [X0,X1] :
( nat_1(X1) = X0
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f3459]) ).
fof(f3459,plain,
! [X0,X1] :
( ( nat_1(X1) = X0
| ~ sP9(X0,X1) )
& ( sP9(X0,X1)
| nat_1(X1) != X0 ) ),
inference(nnf_transformation,[],[f3213]) ).
fof(f3213,plain,
! [X0,X1] :
( nat_1(X1) = X0
<=> sP9(X0,X1) ),
inference(definition_folding,[],[f2927,f3212]) ).
fof(f2927,plain,
! [X0,X1] :
( nat_1(X1) = X0
<=> ( ( zero_zero(nat) = X0
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) )
& ( ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1)) ) ) ),
inference(ennf_transformation,[],[f1925]) ).
fof(f1925,plain,
! [X0,X1] :
( nat_1(X1) = X0
<=> ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
=> zero_zero(nat) = X0 )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X1))
=> ti(int,X1) = hAPP(nat,int,semiring_1_of_nat(int),X0) ) ) ),
inference(rectify,[],[f492]) ).
fof(f492,axiom,
! [X27,X23] :
( nat_1(X23) = X27
<=> ( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X23))
=> zero_zero(nat) = X27 )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X23))
=> hAPP(nat,int,semiring_1_of_nat(int),X27) = ti(int,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_nat__eq__iff2) ).
fof(f8016,plain,
spl63_205,
inference(avatar_split_clause,[],[f4278,f8014]) ).
fof(f8014,plain,
( spl63_205
<=> ! [X0] :
( zero_zero(X0) != one_one(X0)
| ~ zero_neq_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_205])]) ).
fof(f4278,plain,
! [X0] :
( zero_zero(X0) != one_one(X0)
| ~ zero_neq_one(X0) ),
inference(cnf_transformation,[],[f2427]) ).
fof(f2427,plain,
! [X0] :
( zero_zero(X0) != one_one(X0)
| ~ zero_neq_one(X0) ),
inference(ennf_transformation,[],[f1484]) ).
fof(f1484,plain,
! [X0] :
( zero_neq_one(X0)
=> zero_zero(X0) != one_one(X0) ),
inference(rectify,[],[f262]) ).
fof(f262,axiom,
! [X1] :
( zero_neq_one(X1)
=> one_one(X1) != zero_zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_zero__neq__one) ).
fof(f8012,plain,
spl63_204,
inference(avatar_split_clause,[],[f3979,f8010]) ).
fof(f3979,plain,
! [X0] : times_times(nat,one_one(nat),X0) = X0,
inference(cnf_transformation,[],[f1278]) ).
fof(f1278,plain,
! [X0] : times_times(nat,one_one(nat),X0) = X0,
inference(rectify,[],[f727]) ).
fof(f727,axiom,
! [X14] : times_times(nat,one_one(nat),X14) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_nat__mult__1) ).
fof(f8008,plain,
spl63_203,
inference(avatar_split_clause,[],[f3978,f8006]) ).
fof(f8006,plain,
( spl63_203
<=> ! [X0] : times_times(nat,X0,one_one(nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_203])]) ).
fof(f3978,plain,
! [X0] : times_times(nat,X0,one_one(nat)) = X0,
inference(cnf_transformation,[],[f1277]) ).
fof(f1277,plain,
! [X0] : times_times(nat,X0,one_one(nat)) = X0,
inference(rectify,[],[f725]) ).
fof(f725,axiom,
! [X14] : times_times(nat,X14,one_one(nat)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_nat__mult__1__right) ).
fof(f8004,plain,
spl63_202,
inference(avatar_split_clause,[],[f3977,f8002]) ).
fof(f3977,plain,
! [X0] : times_times(real,one_one(real),X0) = X0,
inference(cnf_transformation,[],[f1276]) ).
fof(f1276,plain,
! [X0] : times_times(real,one_one(real),X0) = X0,
inference(rectify,[],[f730]) ).
fof(f730,axiom,
! [X15] : times_times(real,one_one(real),X15) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_real__mult__1) ).
fof(f8000,plain,
spl63_201,
inference(avatar_split_clause,[],[f3973,f7998]) ).
fof(f7996,plain,
spl63_200,
inference(avatar_split_clause,[],[f3971,f7994]) ).
fof(f7994,plain,
( spl63_200
<=> ! [X0] : quadRes(ti(int,X0)) = quadRes(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_200])]) ).
fof(f3971,plain,
! [X0] : quadRes(ti(int,X0)) = quadRes(X0),
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] : quadRes(ti(int,X0)) = quadRes(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Residues_OQuadRes_arg1) ).
fof(f7992,plain,
spl63_199,
inference(avatar_split_clause,[],[f3970,f7990]) ).
fof(f7990,plain,
( spl63_199
<=> ! [X0] : ti(int,X0) = number_number_of(int,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_199])]) ).
fof(f7988,plain,
( spl63_198
| ~ spl63_36
| ~ spl63_159 ),
inference(avatar_split_clause,[],[f7815,f7785,f7172,f7985]) ).
fof(f7985,plain,
( spl63_198
<=> sP5(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_198])]) ).
fof(f7785,plain,
( spl63_159
<=> ! [X0] :
( sP5(X0)
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_159])]) ).
fof(f7815,plain,
( sP5(int)
| ~ spl63_36
| ~ spl63_159 ),
inference(resolution,[],[f7786,f7174]) ).
fof(f7786,plain,
( ! [X0] :
( ~ linord581940658strict(X0)
| sP5(X0) )
| ~ spl63_159 ),
inference(avatar_component_clause,[],[f7785]) ).
fof(f7983,plain,
spl63_197,
inference(avatar_split_clause,[],[f3967,f7981]) ).
fof(f3967,plain,
! [X0] : nat_1(X0) = ti(nat,nat_1(X0)),
inference(cnf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] : nat_1(X0) = ti(nat,nat_1(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onat_res) ).
fof(f7979,plain,
spl63_196,
inference(avatar_split_clause,[],[f3964,f7977]) ).
fof(f7977,plain,
( spl63_196
<=> ! [X0] : undefined(X0) = ti(X0,undefined(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_196])]) ).
fof(f3964,plain,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
inference(cnf_transformation,[],[f1268]) ).
fof(f1268,plain,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X1] : undefined(X1) = ti(X1,undefined(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(f7975,plain,
spl63_195,
inference(avatar_split_clause,[],[f3884,f7972]) ).
fof(f7972,plain,
( spl63_195
<=> zprime = ti(fun(int,bool),zprime) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_195])]) ).
fof(f3884,plain,
zprime = ti(fun(int,bool),zprime),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
zprime = ti(fun(int,bool),zprime),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozprime_res) ).
fof(f7970,plain,
spl63_194,
inference(avatar_split_clause,[],[f3883,f7967]) ).
fof(f7967,plain,
( spl63_194
<=> twoSqu658283162sum2sq = ti(fun(int,bool),twoSqu658283162sum2sq) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_194])]) ).
fof(f3883,plain,
twoSqu658283162sum2sq = ti(fun(int,bool),twoSqu658283162sum2sq),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
twoSqu658283162sum2sq = ti(fun(int,bool),twoSqu658283162sum2sq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__lldtdwpyrp_Ois__sum2sq_res) ).
fof(f7959,plain,
( spl63_193
| ~ spl63_35
| ~ spl63_159 ),
inference(avatar_split_clause,[],[f7814,f7785,f7167,f7956]) ).
fof(f7956,plain,
( spl63_193
<=> sP5(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_193])]) ).
fof(f7814,plain,
( sP5(real)
| ~ spl63_35
| ~ spl63_159 ),
inference(resolution,[],[f7786,f7169]) ).
fof(f7952,plain,
spl63_192,
inference(avatar_split_clause,[],[f5915,f7950]) ).
fof(f7948,plain,
spl63_191,
inference(avatar_split_clause,[],[f5497,f7946]) ).
fof(f5497,plain,
! [X0] : min != plus_plus(int,X0,X0),
inference(definition_unfolding,[],[f3957,f3968]) ).
fof(f3957,plain,
! [X0] : bit0(X0) != min,
inference(cnf_transformation,[],[f1261]) ).
fof(f1261,plain,
! [X0] : bit0(X0) != min,
inference(rectify,[],[f863]) ).
fof(f863,axiom,
! [X29] : min != bit0(X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_rel__simps_I42_J) ).
fof(f7944,plain,
spl63_190,
inference(avatar_split_clause,[],[f5453,f7941]) ).
fof(f7939,plain,
spl63_189,
inference(avatar_split_clause,[],[f5452,f7936]) ).
fof(f7936,plain,
( spl63_189
<=> pls = minus_minus(int,min,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_189])]) ).
fof(f5452,plain,
pls = minus_minus(int,min,min),
inference(definition_unfolding,[],[f3859,f3966]) ).
fof(f3859,plain,
pls = succ(min),
inference(cnf_transformation,[],[f874]) ).
fof(f874,axiom,
pls = succ(min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_776_succ__Min) ).
fof(f7934,plain,
spl63_188,
inference(avatar_split_clause,[],[f4576,f7932]) ).
fof(f7932,plain,
( spl63_188
<=> ! [X0] :
( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_188])]) ).
fof(f4576,plain,
! [X0] :
( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f3366]) ).
fof(f3366,plain,
! [X0] :
( ( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) )
& ( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( hBOOL(ti(bool,X0))
<=> hBOOL(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(f7930,plain,
spl63_187,
inference(avatar_split_clause,[],[f4575,f7928]) ).
fof(f7928,plain,
( spl63_187
<=> ! [X0] :
( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_187])]) ).
fof(f4575,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ),
inference(cnf_transformation,[],[f3366]) ).
fof(f7926,plain,
spl63_186,
inference(avatar_split_clause,[],[f3961,f7924]) ).
fof(f3961,plain,
! [X0] : pls = times_times(int,pls,X0),
inference(cnf_transformation,[],[f1265]) ).
fof(f1265,plain,
! [X0] : pls = times_times(int,pls,X0),
inference(rectify,[],[f468]) ).
fof(f468,axiom,
! [X7] : pls = times_times(int,pls,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_mult__Pls) ).
fof(f7922,plain,
spl63_185,
inference(avatar_split_clause,[],[f3876,f7919]) ).
fof(f3876,plain,
one_one(nat) = nat_1(one_one(int)),
inference(cnf_transformation,[],[f528]) ).
fof(f528,axiom,
one_one(nat) = nat_1(one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_transfer__nat__int__numerals_I2_J) ).
fof(f7917,plain,
( spl63_184
| ~ spl63_36
| ~ spl63_158 ),
inference(avatar_split_clause,[],[f7813,f7781,f7172,f7914]) ).
fof(f7914,plain,
( spl63_184
<=> sP3(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_184])]) ).
fof(f7781,plain,
( spl63_158
<=> ! [X0] :
( sP3(X0)
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_158])]) ).
fof(f7813,plain,
( sP3(int)
| ~ spl63_36
| ~ spl63_158 ),
inference(resolution,[],[f7782,f7174]) ).
fof(f7782,plain,
( ! [X0] :
( ~ linord581940658strict(X0)
| sP3(X0) )
| ~ spl63_158 ),
inference(avatar_component_clause,[],[f7781]) ).
fof(f7912,plain,
( spl63_183
| ~ spl63_35
| ~ spl63_158 ),
inference(avatar_split_clause,[],[f7812,f7781,f7167,f7909]) ).
fof(f7909,plain,
( spl63_183
<=> sP3(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_183])]) ).
fof(f7812,plain,
( sP3(real)
| ~ spl63_35
| ~ spl63_158 ),
inference(resolution,[],[f7782,f7169]) ).
fof(f7907,plain,
~ spl63_182,
inference(avatar_split_clause,[],[f5816,f7904]) ).
fof(f7904,plain,
( spl63_182
<=> pls = number_number_of(int,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_182])]) ).
fof(f5816,plain,
pls != number_number_of(int,min),
inference(forward_demodulation,[],[f3882,f5815]) ).
fof(f5815,plain,
pls = number_number_of(int,pls),
inference(forward_demodulation,[],[f3881,f3861]) ).
fof(f3881,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f117]) ).
fof(f117,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
fof(f3882,plain,
number_number_of(int,pls) != number_number_of(int,min),
inference(cnf_transformation,[],[f859]) ).
fof(f859,axiom,
number_number_of(int,pls) != number_number_of(int,min),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_eq__number__of__Pls__Min) ).
fof(f7902,plain,
spl63_181,
inference(avatar_split_clause,[],[f5815,f7899]) ).
fof(f7899,plain,
( spl63_181
<=> pls = number_number_of(int,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_181])]) ).
fof(f7897,plain,
spl63_180,
inference(avatar_split_clause,[],[f5811,f7894]) ).
fof(f7892,plain,
spl63_179,
inference(avatar_split_clause,[],[f3874,f7889]) ).
fof(f7887,plain,
spl63_178,
inference(avatar_split_clause,[],[f3873,f7884]) ).
fof(f7884,plain,
( spl63_178
<=> m = ti(int,m) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_178])]) ).
fof(f3873,plain,
m = ti(int,m),
inference(cnf_transformation,[],[f89]) ).
fof(f89,axiom,
m = ti(int,m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_m_res) ).
fof(f7882,plain,
spl63_177,
inference(avatar_split_clause,[],[f3872,f7879]) ).
fof(f7879,plain,
( spl63_177
<=> s = ti(int,s) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_177])]) ).
fof(f3872,plain,
s = ti(int,s),
inference(cnf_transformation,[],[f93]) ).
fof(f93,axiom,
s = ti(int,s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_s_____res) ).
fof(f7877,plain,
spl63_176,
inference(avatar_split_clause,[],[f3871,f7874]) ).
fof(f7874,plain,
( spl63_176
<=> t = ti(int,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_176])]) ).
fof(f3871,plain,
t = ti(int,t),
inference(cnf_transformation,[],[f94]) ).
fof(f94,axiom,
t = ti(int,t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
fof(f7872,plain,
spl63_175,
inference(avatar_split_clause,[],[f3870,f7869]) ).
fof(f7869,plain,
( spl63_175
<=> s1 = ti(int,s1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_175])]) ).
fof(f3870,plain,
s1 = ti(int,s1),
inference(cnf_transformation,[],[f92]) ).
fof(f92,axiom,
s1 = ti(int,s1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_s1_____res) ).
fof(f7867,plain,
spl63_174,
inference(avatar_split_clause,[],[f3869,f7864]) ).
fof(f7864,plain,
( spl63_174
<=> y = ti(int,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_174])]) ).
fof(f3869,plain,
y = ti(int,y),
inference(cnf_transformation,[],[f97]) ).
fof(f97,axiom,
y = ti(int,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_y_____res) ).
fof(f7862,plain,
spl63_173,
inference(avatar_split_clause,[],[f3868,f7859]) ).
fof(f7859,plain,
( spl63_173
<=> x = ti(int,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_173])]) ).
fof(f3868,plain,
x = ti(int,x),
inference(cnf_transformation,[],[f96]) ).
fof(f96,axiom,
x = ti(int,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_x_____res) ).
fof(f7857,plain,
spl63_172,
inference(avatar_split_clause,[],[f3867,f7854]) ).
fof(f7854,plain,
( spl63_172
<=> tn = ti(nat,tn) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_172])]) ).
fof(f3867,plain,
tn = ti(nat,tn),
inference(cnf_transformation,[],[f95]) ).
fof(f95,axiom,
tn = ti(nat,tn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_tn_____res) ).
fof(f7852,plain,
spl63_171,
inference(avatar_split_clause,[],[f3866,f7849]) ).
fof(f7849,plain,
( spl63_171
<=> fFalse = ti(bool,fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_171])]) ).
fof(f3866,plain,
fFalse = ti(bool,fFalse),
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
fFalse = ti(bool,fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
fof(f7847,plain,
spl63_170,
inference(avatar_split_clause,[],[f3865,f7844]) ).
fof(f7844,plain,
( spl63_170
<=> fTrue = ti(bool,fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_170])]) ).
fof(f3865,plain,
fTrue = ti(bool,fTrue),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
fTrue = ti(bool,fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
fof(f7842,plain,
spl63_169,
inference(avatar_split_clause,[],[f3864,f7839]) ).
fof(f7839,plain,
( spl63_169
<=> m1 = ti(int,m1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_169])]) ).
fof(f3864,plain,
m1 = ti(int,m1),
inference(cnf_transformation,[],[f90]) ).
fof(f90,axiom,
m1 = ti(int,m1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_m1_____res) ).
fof(f7837,plain,
~ spl63_168,
inference(avatar_split_clause,[],[f3862,f7834]) ).
fof(f7834,plain,
( spl63_168
<=> zero_zero(real) = one_one(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_168])]) ).
fof(f3862,plain,
zero_zero(real) != one_one(real),
inference(cnf_transformation,[],[f214]) ).
fof(f214,axiom,
zero_zero(real) != one_one(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_real__zero__not__eq__one) ).
fof(f7832,plain,
( spl63_167
| ~ spl63_36
| ~ spl63_157 ),
inference(avatar_split_clause,[],[f7806,f7777,f7172,f7829]) ).
fof(f7829,plain,
( spl63_167
<=> sP1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_167])]) ).
fof(f7777,plain,
( spl63_157
<=> ! [X0] :
( sP1(X0)
| ~ linord581940658strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_157])]) ).
fof(f7806,plain,
( sP1(int)
| ~ spl63_36
| ~ spl63_157 ),
inference(resolution,[],[f7778,f7174]) ).
fof(f7778,plain,
( ! [X0] :
( ~ linord581940658strict(X0)
| sP1(X0) )
| ~ spl63_157 ),
inference(avatar_component_clause,[],[f7777]) ).
fof(f7827,plain,
spl63_166,
inference(avatar_split_clause,[],[f3697,f7824]) ).
fof(f7824,plain,
( spl63_166
<=> pls = ti(int,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_166])]) ).
fof(f3697,plain,
pls = ti(int,pls),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
pls = ti(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
fof(f7822,plain,
spl63_165,
inference(avatar_split_clause,[],[f3696,f7819]) ).
fof(f7819,plain,
( spl63_165
<=> n = ti(nat,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_165])]) ).
fof(f3696,plain,
n = ti(nat,n),
inference(cnf_transformation,[],[f91]) ).
fof(f91,axiom,
n = ti(nat,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_n_____res) ).
fof(f7811,plain,
( spl63_164
| ~ spl63_35
| ~ spl63_157 ),
inference(avatar_split_clause,[],[f7805,f7777,f7167,f7808]) ).
fof(f7808,plain,
( spl63_164
<=> sP1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_164])]) ).
fof(f7805,plain,
( sP1(real)
| ~ spl63_35
| ~ spl63_157 ),
inference(resolution,[],[f7778,f7169]) ).
fof(f7804,plain,
~ spl63_163,
inference(avatar_split_clause,[],[f5810,f7801]) ).
fof(f7801,plain,
( spl63_163
<=> pls = one_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_163])]) ).
fof(f5810,plain,
pls != one_one(int),
inference(forward_demodulation,[],[f3863,f3861]) ).
fof(f3863,plain,
zero_zero(int) != one_one(int),
inference(cnf_transformation,[],[f172]) ).
fof(f172,axiom,
zero_zero(int) != one_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_int__0__neq__1) ).
fof(f7799,plain,
spl63_162,
inference(avatar_split_clause,[],[f5744,f7797]) ).
fof(f5744,plain,
! [X0] : sP10(nat_1(X0),X0),
inference(equality_resolution,[],[f4881]) ).
fof(f4881,plain,
! [X0,X1] :
( sP10(X1,X0)
| nat_1(X0) != X1 ),
inference(cnf_transformation,[],[f3463]) ).
fof(f7795,plain,
spl63_161,
inference(avatar_split_clause,[],[f5741,f7793]) ).
fof(f5741,plain,
! [X1] : sP9(nat_1(X1),X1),
inference(equality_resolution,[],[f4873]) ).
fof(f4873,plain,
! [X0,X1] :
( sP9(X0,X1)
| nat_1(X1) != X0 ),
inference(cnf_transformation,[],[f3459]) ).
fof(f7791,plain,
spl63_160,
inference(avatar_split_clause,[],[f4167,f7789]) ).
fof(f4167,plain,
! [X0] :
( sP7(X0)
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f3209]) ).
fof(f3209,plain,
! [X0] :
( sP7(X0)
| ~ linord581940658strict(X0) ),
inference(definition_folding,[],[f2324,f3208,f3207]) ).
fof(f3207,plain,
! [X1,X3,X0,X2] :
( sP6(X1,X3,X0,X2)
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f3208,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X2)),times_times(X0,X3,X2)))
<=> sP6(X1,X3,X0,X2) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f2324,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X2)),times_times(X0,X3,X2)))
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X2)) ) ) )
| ~ linord581940658strict(X0) ),
inference(ennf_transformation,[],[f1390]) ).
fof(f1390,plain,
! [X0] :
( linord581940658strict(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X2)),times_times(X0,X3,X2)))
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X2)) ) ) ) ),
inference(rectify,[],[f508]) ).
fof(f508,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X45,X41] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),times_times(X1,X6,X45)),times_times(X1,X41,X45)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X6))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X45),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X41))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X45)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_mult__less__cancel__right__disj) ).
fof(f7787,plain,
spl63_159,
inference(avatar_split_clause,[],[f4158,f7785]) ).
fof(f4158,plain,
! [X0] :
( sP5(X0)
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f3206]) ).
fof(f3206,plain,
! [X0] :
( sP5(X0)
| ~ linord581940658strict(X0) ),
inference(definition_folding,[],[f2323,f3205,f3204]) ).
fof(f3204,plain,
! [X2,X3,X0,X1] :
( sP4(X2,X3,X0,X1)
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f3205,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X2)),times_times(X0,X1,X3)))
<=> sP4(X2,X3,X0,X1) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f2323,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X2)),times_times(X0,X1,X3)))
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1)) ) ) )
| ~ linord581940658strict(X0) ),
inference(ennf_transformation,[],[f1389]) ).
fof(f1389,plain,
! [X0] :
( linord581940658strict(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),times_times(X0,X1,X2)),times_times(X0,X1,X3)))
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1)) ) ) ) ),
inference(rectify,[],[f509]) ).
fof(f509,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X45,X6,X41] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),times_times(X1,X45,X6)),times_times(X1,X45,X41)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X41),X6))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X45),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X41))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X45)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_mult__less__cancel__left__disj) ).
fof(f7783,plain,
spl63_158,
inference(avatar_split_clause,[],[f4133,f7781]) ).
fof(f4133,plain,
! [X0] :
( sP3(X0)
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f3203]) ).
fof(f3203,plain,
! [X0] :
( sP3(X0)
| ~ linord581940658strict(X0) ),
inference(definition_folding,[],[f2312,f3202,f3201]) ).
fof(f3201,plain,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f3202,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),times_times(X0,X1,X2)),zero_zero(X0)))
<=> sP2(X2,X0,X1) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f2312,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),times_times(X0,X1,X2)),zero_zero(X0)))
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1)) ) ) )
| ~ linord581940658strict(X0) ),
inference(ennf_transformation,[],[f1380]) ).
fof(f1380,plain,
! [X0] :
( linord581940658strict(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),times_times(X0,X1,X2)),zero_zero(X0)))
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1)) ) ) ) ),
inference(rectify,[],[f388]) ).
fof(f388,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X41] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),times_times(X1,X6,X41)),zero_zero(X1)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_mult__le__0__iff) ).
fof(f7779,plain,
spl63_157,
inference(avatar_split_clause,[],[f4124,f7777]) ).
fof(f4124,plain,
! [X0] :
( sP1(X0)
| ~ linord581940658strict(X0) ),
inference(cnf_transformation,[],[f3200]) ).
fof(f3200,plain,
! [X0] :
( sP1(X0)
| ~ linord581940658strict(X0) ),
inference(definition_folding,[],[f2311,f3199,f3198]) ).
fof(f3198,plain,
! [X0,X2,X1] :
( sP0(X0,X2,X1)
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3199,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),times_times(X0,X1,X2)))
<=> sP0(X0,X2,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f2311,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),times_times(X0,X1,X2)))
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1)) ) ) )
| ~ linord581940658strict(X0) ),
inference(ennf_transformation,[],[f1379]) ).
fof(f1379,plain,
! [X0] :
( linord581940658strict(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),times_times(X0,X1,X2)))
<=> ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0))) )
| ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1)) ) ) ) ),
inference(rectify,[],[f389]) ).
fof(f389,axiom,
! [X1] :
( linord581940658strict(X1)
=> ! [X6,X41] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),times_times(X1,X6,X41)))
<=> ( ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X41),zero_zero(X1)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),zero_zero(X1))) )
| ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X41))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X6)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_zero__le__mult__iff) ).
fof(f7775,plain,
spl63_156,
inference(avatar_split_clause,[],[f3861,f7772]) ).
fof(f7770,plain,
~ spl63_155,
inference(avatar_split_clause,[],[f3856,f7767]) ).
fof(f3856,plain,
min != pls,
inference(cnf_transformation,[],[f866]) ).
fof(f866,axiom,
min != pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_rel__simps_I37_J) ).
fof(f7765,plain,
spl63_154,
inference(avatar_split_clause,[],[f3855,f7762]) ).
fof(f7762,plain,
( spl63_154
<=> order(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_154])]) ).
fof(f3855,plain,
order(int),
inference(cnf_transformation,[],[f1139]) ).
fof(f1139,axiom,
order(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
fof(f7760,plain,
spl63_153,
inference(avatar_split_clause,[],[f3854,f7757]) ).
fof(f7757,plain,
( spl63_153
<=> order(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_153])]) ).
fof(f3854,plain,
order(nat),
inference(cnf_transformation,[],[f1181]) ).
fof(f1181,axiom,
order(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
fof(f7755,plain,
spl63_152,
inference(avatar_split_clause,[],[f3853,f7752]) ).
fof(f7752,plain,
( spl63_152
<=> order(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_152])]) ).
fof(f3853,plain,
order(bool),
inference(cnf_transformation,[],[f1188]) ).
fof(f1188,axiom,
order(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
fof(f7750,plain,
spl63_151,
inference(avatar_split_clause,[],[f3852,f7747]) ).
fof(f7747,plain,
( spl63_151
<=> order(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_151])]) ).
fof(f3852,plain,
order(real),
inference(cnf_transformation,[],[f1235]) ).
fof(f1235,axiom,
order(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oorder) ).
fof(f7745,plain,
spl63_150,
inference(avatar_split_clause,[],[f3851,f7742]) ).
fof(f7742,plain,
( spl63_150
<=> comm_semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_150])]) ).
fof(f3851,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f1123]) ).
fof(f1123,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
fof(f7740,plain,
spl63_149,
inference(avatar_split_clause,[],[f3850,f7737]) ).
fof(f7737,plain,
( spl63_149
<=> comm_semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_149])]) ).
fof(f3850,plain,
comm_semiring_1(nat),
inference(cnf_transformation,[],[f1170]) ).
fof(f1170,axiom,
comm_semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
fof(f7735,plain,
spl63_148,
inference(avatar_split_clause,[],[f3849,f7732]) ).
fof(f7732,plain,
( spl63_148
<=> comm_semiring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_148])]) ).
fof(f3849,plain,
comm_semiring_1(real),
inference(cnf_transformation,[],[f1219]) ).
fof(f1219,axiom,
comm_semiring_1(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
fof(f7730,plain,
spl63_147,
inference(avatar_split_clause,[],[f3848,f7727]) ).
fof(f3848,plain,
linordered_semidom(int),
inference(cnf_transformation,[],[f1113]) ).
fof(f1113,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
fof(f7725,plain,
spl63_146,
inference(avatar_split_clause,[],[f3847,f7722]) ).
fof(f7722,plain,
( spl63_146
<=> linordered_semidom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_146])]) ).
fof(f3847,plain,
linordered_semidom(nat),
inference(cnf_transformation,[],[f1163]) ).
fof(f1163,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
fof(f7720,plain,
spl63_145,
inference(avatar_split_clause,[],[f3846,f7717]) ).
fof(f7717,plain,
( spl63_145
<=> linordered_semidom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_145])]) ).
fof(f3846,plain,
linordered_semidom(real),
inference(cnf_transformation,[],[f1209]) ).
fof(f1209,axiom,
linordered_semidom(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
fof(f7715,plain,
spl63_144,
inference(avatar_split_clause,[],[f3845,f7712]) ).
fof(f7712,plain,
( spl63_144
<=> linord20386208strict(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_144])]) ).
fof(f3845,plain,
linord20386208strict(int),
inference(cnf_transformation,[],[f1098]) ).
fof(f1098,axiom,
linord20386208strict(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__strict) ).
fof(f7710,plain,
spl63_143,
inference(avatar_split_clause,[],[f3844,f7707]) ).
fof(f7707,plain,
( spl63_143
<=> linord20386208strict(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_143])]) ).
fof(f3844,plain,
linord20386208strict(nat),
inference(cnf_transformation,[],[f1155]) ).
fof(f1155,axiom,
linord20386208strict(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring__strict) ).
fof(f7705,plain,
spl63_142,
inference(avatar_split_clause,[],[f3843,f7702]) ).
fof(f7702,plain,
( spl63_142
<=> linord20386208strict(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_142])]) ).
fof(f3843,plain,
linord20386208strict(real),
inference(cnf_transformation,[],[f1194]) ).
fof(f1194,axiom,
linord20386208strict(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) ).
fof(f7700,plain,
spl63_141,
inference(avatar_split_clause,[],[f3842,f7697]) ).
fof(f7697,plain,
( spl63_141
<=> dvd(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_141])]) ).
fof(f3842,plain,
dvd(int),
inference(cnf_transformation,[],[f1150]) ).
fof(f1150,axiom,
dvd(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Odvd) ).
fof(f7695,plain,
spl63_140,
inference(avatar_split_clause,[],[f3841,f7692]) ).
fof(f3841,plain,
power(int),
inference(cnf_transformation,[],[f1144]) ).
fof(f1144,axiom,
power(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
fof(f7690,plain,
spl63_139,
inference(avatar_split_clause,[],[f3840,f7687]) ).
fof(f7687,plain,
( spl63_139
<=> dvd(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_139])]) ).
fof(f3840,plain,
dvd(nat),
inference(cnf_transformation,[],[f1187]) ).
fof(f1187,axiom,
dvd(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Odvd) ).
fof(f7685,plain,
spl63_138,
inference(avatar_split_clause,[],[f3839,f7682]) ).
fof(f7682,plain,
( spl63_138
<=> power(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_138])]) ).
fof(f3839,plain,
power(nat),
inference(cnf_transformation,[],[f1183]) ).
fof(f1183,axiom,
power(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
fof(f7680,plain,
spl63_137,
inference(avatar_split_clause,[],[f3838,f7677]) ).
fof(f7677,plain,
( spl63_137
<=> dvd(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_137])]) ).
fof(f3838,plain,
dvd(real),
inference(cnf_transformation,[],[f1246]) ).
fof(f1246,axiom,
dvd(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Odvd) ).
fof(f7675,plain,
spl63_136,
inference(avatar_split_clause,[],[f3837,f7672]) ).
fof(f7672,plain,
( spl63_136
<=> power(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_136])]) ).
fof(f3837,plain,
power(real),
inference(cnf_transformation,[],[f1240]) ).
fof(f1240,axiom,
power(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
fof(f7670,plain,
spl63_135,
inference(avatar_split_clause,[],[f3836,f7667]) ).
fof(f7667,plain,
( spl63_135
<=> ordere216010020id_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_135])]) ).
fof(f3836,plain,
ordere216010020id_add(int),
inference(cnf_transformation,[],[f1101]) ).
fof(f1101,axiom,
ordere216010020id_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
fof(f7665,plain,
spl63_134,
inference(avatar_split_clause,[],[f3835,f7662]) ).
fof(f7662,plain,
( spl63_134
<=> ordere216010020id_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_134])]) ).
fof(f3835,plain,
ordere216010020id_add(nat),
inference(cnf_transformation,[],[f1157]) ).
fof(f1157,axiom,
ordere216010020id_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
fof(f7660,plain,
spl63_133,
inference(avatar_split_clause,[],[f3834,f7657]) ).
fof(f7657,plain,
( spl63_133
<=> ordere216010020id_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_133])]) ).
fof(f3834,plain,
ordere216010020id_add(real),
inference(cnf_transformation,[],[f1197]) ).
fof(f1197,axiom,
ordere216010020id_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) ).
fof(f7655,plain,
spl63_132,
inference(avatar_split_clause,[],[f3833,f7652]) ).
fof(f7652,plain,
( spl63_132
<=> monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_132])]) ).
fof(f3833,plain,
monoid_mult(int),
inference(cnf_transformation,[],[f1131]) ).
fof(f1131,axiom,
monoid_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
fof(f7650,plain,
spl63_131,
inference(avatar_split_clause,[],[f3832,f7647]) ).
fof(f7647,plain,
( spl63_131
<=> monoid_mult(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_131])]) ).
fof(f3832,plain,
monoid_mult(nat),
inference(cnf_transformation,[],[f1176]) ).
fof(f1176,axiom,
monoid_mult(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
fof(f7645,plain,
spl63_130,
inference(avatar_split_clause,[],[f3831,f7642]) ).
fof(f7642,plain,
( spl63_130
<=> monoid_mult(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_130])]) ).
fof(f3831,plain,
monoid_mult(real),
inference(cnf_transformation,[],[f1227]) ).
fof(f1227,axiom,
monoid_mult(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
fof(f7640,plain,
spl63_129,
inference(avatar_split_clause,[],[f3830,f7637]) ).
fof(f7637,plain,
( spl63_129
<=> number_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_129])]) ).
fof(f3830,plain,
number_semiring(int),
inference(cnf_transformation,[],[f1126]) ).
fof(f1126,axiom,
number_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
fof(f7635,plain,
spl63_128,
inference(avatar_split_clause,[],[f3829,f7632]) ).
fof(f3829,plain,
number_semiring(nat),
inference(cnf_transformation,[],[f1173]) ).
fof(f1173,axiom,
number_semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
fof(f7630,plain,
spl63_127,
inference(avatar_split_clause,[],[f3828,f7627]) ).
fof(f7627,plain,
( spl63_127
<=> number_semiring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_127])]) ).
fof(f3828,plain,
number_semiring(real),
inference(cnf_transformation,[],[f1222]) ).
fof(f1222,axiom,
number_semiring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
fof(f7625,plain,
spl63_126,
inference(avatar_split_clause,[],[f3827,f7622]) ).
fof(f7622,plain,
( spl63_126
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_126])]) ).
fof(f3827,plain,
semiring_1(int),
inference(cnf_transformation,[],[f1134]) ).
fof(f1134,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
fof(f7620,plain,
spl63_125,
inference(avatar_split_clause,[],[f3826,f7617]) ).
fof(f7617,plain,
( spl63_125
<=> number(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_125])]) ).
fof(f3826,plain,
number(int),
inference(cnf_transformation,[],[f1148]) ).
fof(f1148,axiom,
number(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
fof(f7615,plain,
spl63_124,
inference(avatar_split_clause,[],[f3825,f7612]) ).
fof(f7612,plain,
( spl63_124
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_124])]) ).
fof(f3825,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f1178]) ).
fof(f1178,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
fof(f7610,plain,
spl63_123,
inference(avatar_split_clause,[],[f3824,f7607]) ).
fof(f7607,plain,
( spl63_123
<=> number(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_123])]) ).
fof(f3824,plain,
number(nat),
inference(cnf_transformation,[],[f1185]) ).
fof(f1185,axiom,
number(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
fof(f7605,plain,
spl63_122,
inference(avatar_split_clause,[],[f3823,f7602]) ).
fof(f7602,plain,
( spl63_122
<=> number(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_122])]) ).
fof(f3823,plain,
number(real),
inference(cnf_transformation,[],[f1244]) ).
fof(f1244,axiom,
number(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
fof(f7600,plain,
spl63_121,
inference(avatar_split_clause,[],[f3822,f7597]) ).
fof(f7597,plain,
( spl63_121
<=> semiring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_121])]) ).
fof(f3822,plain,
semiring_1(real),
inference(cnf_transformation,[],[f1230]) ).
fof(f1230,axiom,
semiring_1(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
fof(f7595,plain,
spl63_120,
inference(avatar_split_clause,[],[f3821,f7592]) ).
fof(f7592,plain,
( spl63_120
<=> ordere236663937imp_le(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_120])]) ).
fof(f3821,plain,
ordere236663937imp_le(int),
inference(cnf_transformation,[],[f1095]) ).
fof(f1095,axiom,
ordere236663937imp_le(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f7590,plain,
spl63_119,
inference(avatar_split_clause,[],[f3820,f7587]) ).
fof(f7587,plain,
( spl63_119
<=> ordere236663937imp_le(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_119])]) ).
fof(f3820,plain,
ordere236663937imp_le(nat),
inference(cnf_transformation,[],[f1153]) ).
fof(f1153,axiom,
ordere236663937imp_le(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f7585,plain,
spl63_118,
inference(avatar_split_clause,[],[f3819,f7582]) ).
fof(f7582,plain,
( spl63_118
<=> ordere236663937imp_le(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_118])]) ).
fof(f3819,plain,
ordere236663937imp_le(real),
inference(cnf_transformation,[],[f1191]) ).
fof(f1191,axiom,
ordere236663937imp_le(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f7580,plain,
spl63_117,
inference(avatar_split_clause,[],[f3818,f7577]) ).
fof(f7577,plain,
( spl63_117
<=> mult_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_117])]) ).
fof(f3818,plain,
mult_zero(int),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,axiom,
mult_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
fof(f7575,plain,
spl63_116,
inference(avatar_split_clause,[],[f3817,f7572]) ).
fof(f7572,plain,
( spl63_116
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_116])]) ).
fof(f3817,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
fof(f7570,plain,
spl63_115,
inference(avatar_split_clause,[],[f3816,f7567]) ).
fof(f7567,plain,
( spl63_115
<=> no_zero_divisors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_115])]) ).
fof(f3816,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f1119]) ).
fof(f1119,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
fof(f7565,plain,
spl63_114,
inference(avatar_split_clause,[],[f3815,f7562]) ).
fof(f7562,plain,
( spl63_114
<=> cancel_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_114])]) ).
fof(f3815,plain,
cancel_semigroup_add(nat),
inference(cnf_transformation,[],[f1161]) ).
fof(f1161,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
fof(f7560,plain,
spl63_113,
inference(avatar_split_clause,[],[f3814,f7557]) ).
fof(f7557,plain,
( spl63_113
<=> mult_zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_113])]) ).
fof(f3814,plain,
mult_zero(nat),
inference(cnf_transformation,[],[f1180]) ).
fof(f1180,axiom,
mult_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
fof(f7555,plain,
spl63_112,
inference(avatar_split_clause,[],[f3813,f7552]) ).
fof(f7552,plain,
( spl63_112
<=> no_zero_divisors(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_112])]) ).
fof(f3813,plain,
no_zero_divisors(nat),
inference(cnf_transformation,[],[f1168]) ).
fof(f1168,axiom,
no_zero_divisors(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
fof(f7550,plain,
spl63_111,
inference(avatar_split_clause,[],[f3812,f7547]) ).
fof(f3812,plain,
mult_zero(real),
inference(cnf_transformation,[],[f1233]) ).
fof(f1233,axiom,
mult_zero(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
fof(f7545,plain,
spl63_110,
inference(avatar_split_clause,[],[f3811,f7542]) ).
fof(f7542,plain,
( spl63_110
<=> cancel_semigroup_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_110])]) ).
fof(f3811,plain,
cancel_semigroup_add(real),
inference(cnf_transformation,[],[f1207]) ).
fof(f1207,axiom,
cancel_semigroup_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) ).
fof(f7540,plain,
spl63_109,
inference(avatar_split_clause,[],[f3810,f7537]) ).
fof(f7537,plain,
( spl63_109
<=> no_zero_divisors(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_109])]) ).
fof(f3810,plain,
no_zero_divisors(real),
inference(cnf_transformation,[],[f1215]) ).
fof(f1215,axiom,
no_zero_divisors(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
fof(f7535,plain,
spl63_108,
inference(avatar_split_clause,[],[f3809,f7532]) ).
fof(f7532,plain,
( spl63_108
<=> semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_108])]) ).
fof(f3809,plain,
semiring(int),
inference(cnf_transformation,[],[f1142]) ).
fof(f1142,axiom,
semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
fof(f7530,plain,
spl63_107,
inference(avatar_split_clause,[],[f3808,f7527]) ).
fof(f7527,plain,
( spl63_107
<=> semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_107])]) ).
fof(f3808,plain,
semiring(nat),
inference(cnf_transformation,[],[f1182]) ).
fof(f1182,axiom,
semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
fof(f7525,plain,
spl63_106,
inference(avatar_split_clause,[],[f3807,f7522]) ).
fof(f7522,plain,
( spl63_106
<=> semiring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_106])]) ).
fof(f3807,plain,
semiring(real),
inference(cnf_transformation,[],[f1238]) ).
fof(f1238,axiom,
semiring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring) ).
fof(f7520,plain,
spl63_105,
inference(avatar_split_clause,[],[f3806,f7517]) ).
fof(f7517,plain,
( spl63_105
<=> ordere453448008miring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_105])]) ).
fof(f3806,plain,
ordere453448008miring(int),
inference(cnf_transformation,[],[f1105]) ).
fof(f1105,axiom,
ordere453448008miring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__cancel__semiring) ).
fof(f7515,plain,
spl63_104,
inference(avatar_split_clause,[],[f3805,f7512]) ).
fof(f7512,plain,
( spl63_104
<=> ordere223160158up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_104])]) ).
fof(f3805,plain,
ordere223160158up_add(int),
inference(cnf_transformation,[],[f1094]) ).
fof(f1094,axiom,
ordere223160158up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f7510,plain,
spl63_103,
inference(avatar_split_clause,[],[f3804,f7507]) ).
fof(f7507,plain,
( spl63_103
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_103])]) ).
fof(f3804,plain,
monoid_add(int),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,axiom,
monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
fof(f7505,plain,
spl63_102,
inference(avatar_split_clause,[],[f3803,f7502]) ).
fof(f7502,plain,
( spl63_102
<=> ordere223160158up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_102])]) ).
fof(f3803,plain,
ordere223160158up_add(nat),
inference(cnf_transformation,[],[f1152]) ).
fof(f1152,axiom,
ordere223160158up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f7500,plain,
spl63_101,
inference(avatar_split_clause,[],[f3802,f7497]) ).
fof(f7497,plain,
( spl63_101
<=> monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_101])]) ).
fof(f3802,plain,
monoid_add(nat),
inference(cnf_transformation,[],[f1177]) ).
fof(f1177,axiom,
monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
fof(f7495,plain,
spl63_100,
inference(avatar_split_clause,[],[f3801,f7492]) ).
fof(f7492,plain,
( spl63_100
<=> ordere453448008miring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_100])]) ).
fof(f3801,plain,
ordere453448008miring(nat),
inference(cnf_transformation,[],[f1159]) ).
fof(f1159,axiom,
ordere453448008miring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__cancel__semiring) ).
fof(f7490,plain,
spl63_99,
inference(avatar_split_clause,[],[f3800,f7487]) ).
fof(f7487,plain,
( spl63_99
<=> ordere453448008miring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_99])]) ).
fof(f3800,plain,
ordere453448008miring(real),
inference(cnf_transformation,[],[f1201]) ).
fof(f1201,axiom,
ordere453448008miring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oordered__cancel__semiring) ).
fof(f7485,plain,
spl63_98,
inference(avatar_split_clause,[],[f3799,f7482]) ).
fof(f7482,plain,
( spl63_98
<=> monoid_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_98])]) ).
fof(f3799,plain,
monoid_add(real),
inference(cnf_transformation,[],[f1229]) ).
fof(f1229,axiom,
monoid_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__add) ).
fof(f7480,plain,
spl63_97,
inference(avatar_split_clause,[],[f3798,f7477]) ).
fof(f7477,plain,
( spl63_97
<=> ordere223160158up_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_97])]) ).
fof(f3798,plain,
ordere223160158up_add(real),
inference(cnf_transformation,[],[f1190]) ).
fof(f1190,axiom,
ordere223160158up_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f7475,plain,
spl63_96,
inference(avatar_split_clause,[],[f3797,f7472]) ).
fof(f7472,plain,
( spl63_96
<=> ordered_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_96])]) ).
fof(f3797,plain,
ordered_semiring(int),
inference(cnf_transformation,[],[f1117]) ).
fof(f1117,axiom,
ordered_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__semiring) ).
fof(f7470,plain,
spl63_95,
inference(avatar_split_clause,[],[f3796,f7467]) ).
fof(f3796,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f1116]) ).
fof(f1116,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
fof(f7465,plain,
spl63_94,
inference(avatar_split_clause,[],[f3795,f7462]) ).
fof(f3795,plain,
ab_semigroup_mult(int),
inference(cnf_transformation,[],[f1114]) ).
fof(f1114,axiom,
ab_semigroup_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
fof(f7460,plain,
spl63_93,
inference(avatar_split_clause,[],[f3794,f7457]) ).
fof(f7457,plain,
( spl63_93
<=> zero_neq_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_93])]) ).
fof(f3794,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f1128]) ).
fof(f1128,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
fof(f7455,plain,
spl63_92,
inference(avatar_split_clause,[],[f3793,f7452]) ).
fof(f7452,plain,
( spl63_92
<=> semiri456707255roduct(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_92])]) ).
fof(f3793,plain,
semiri456707255roduct(int),
inference(cnf_transformation,[],[f1093]) ).
fof(f1093,axiom,
semiri456707255roduct(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
fof(f7450,plain,
spl63_91,
inference(avatar_split_clause,[],[f3792,f7447]) ).
fof(f7447,plain,
( spl63_91
<=> ab_semigroup_mult(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_91])]) ).
fof(f3792,plain,
ab_semigroup_mult(nat),
inference(cnf_transformation,[],[f1164]) ).
fof(f1164,axiom,
ab_semigroup_mult(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).
fof(f7445,plain,
spl63_90,
inference(avatar_split_clause,[],[f3791,f7442]) ).
fof(f7442,plain,
( spl63_90
<=> ordered_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_90])]) ).
fof(f3791,plain,
ordered_semiring(nat),
inference(cnf_transformation,[],[f1167]) ).
fof(f1167,axiom,
ordered_semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__semiring) ).
fof(f7440,plain,
spl63_89,
inference(avatar_split_clause,[],[f3790,f7437]) ).
fof(f7437,plain,
( spl63_89
<=> semiri456707255roduct(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_89])]) ).
fof(f3790,plain,
semiri456707255roduct(nat),
inference(cnf_transformation,[],[f1151]) ).
fof(f1151,axiom,
semiri456707255roduct(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
fof(f7435,plain,
spl63_88,
inference(avatar_split_clause,[],[f3789,f7432]) ).
fof(f7432,plain,
( spl63_88
<=> zero_neq_one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_88])]) ).
fof(f3789,plain,
zero_neq_one(nat),
inference(cnf_transformation,[],[f1174]) ).
fof(f1174,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
fof(f7430,plain,
spl63_87,
inference(avatar_split_clause,[],[f3788,f7427]) ).
fof(f7427,plain,
( spl63_87
<=> ab_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_87])]) ).
fof(f3788,plain,
ab_semigroup_add(nat),
inference(cnf_transformation,[],[f1166]) ).
fof(f1166,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
fof(f7425,plain,
spl63_86,
inference(avatar_split_clause,[],[f3787,f7422]) ).
fof(f7422,plain,
( spl63_86
<=> zero_neq_one(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_86])]) ).
fof(f3787,plain,
zero_neq_one(real),
inference(cnf_transformation,[],[f1224]) ).
fof(f1224,axiom,
zero_neq_one(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
fof(f7420,plain,
spl63_85,
inference(avatar_split_clause,[],[f3786,f7417]) ).
fof(f7417,plain,
( spl63_85
<=> ab_semigroup_mult(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_85])]) ).
fof(f3786,plain,
ab_semigroup_mult(real),
inference(cnf_transformation,[],[f1210]) ).
fof(f1210,axiom,
ab_semigroup_mult(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__mult) ).
fof(f7415,plain,
spl63_84,
inference(avatar_split_clause,[],[f3785,f7412]) ).
fof(f7412,plain,
( spl63_84
<=> ordered_semiring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_84])]) ).
fof(f3785,plain,
ordered_semiring(real),
inference(cnf_transformation,[],[f1213]) ).
fof(f1213,axiom,
ordered_semiring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oordered__semiring) ).
fof(f7410,plain,
spl63_83,
inference(avatar_split_clause,[],[f3784,f7407]) ).
fof(f7407,plain,
( spl63_83
<=> ab_semigroup_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_83])]) ).
fof(f3784,plain,
ab_semigroup_add(real),
inference(cnf_transformation,[],[f1212]) ).
fof(f1212,axiom,
ab_semigroup_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__add) ).
fof(f7405,plain,
spl63_82,
inference(avatar_split_clause,[],[f3783,f7402]) ).
fof(f7402,plain,
( spl63_82
<=> semiri456707255roduct(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_82])]) ).
fof(f3783,plain,
semiri456707255roduct(real),
inference(cnf_transformation,[],[f1189]) ).
fof(f1189,axiom,
semiri456707255roduct(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) ).
fof(f7400,plain,
spl63_81,
inference(avatar_split_clause,[],[f3782,f7397]) ).
fof(f7397,plain,
( spl63_81
<=> comm_monoid_mult(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_81])]) ).
fof(f3782,plain,
comm_monoid_mult(int),
inference(cnf_transformation,[],[f1115]) ).
fof(f1115,axiom,
comm_monoid_mult(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
fof(f7395,plain,
spl63_80,
inference(avatar_split_clause,[],[f3781,f7392]) ).
fof(f7392,plain,
( spl63_80
<=> ordere779506340up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_80])]) ).
fof(f3781,plain,
ordere779506340up_add(int),
inference(cnf_transformation,[],[f1099]) ).
fof(f1099,axiom,
ordere779506340up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
fof(f7390,plain,
spl63_79,
inference(avatar_split_clause,[],[f3780,f7387]) ).
fof(f7387,plain,
( spl63_79
<=> semiring_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_79])]) ).
fof(f3780,plain,
semiring_0(int),
inference(cnf_transformation,[],[f1135]) ).
fof(f1135,axiom,
semiring_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
fof(f7385,plain,
spl63_78,
inference(avatar_split_clause,[],[f3779,f7382]) ).
fof(f7382,plain,
( spl63_78
<=> comm_monoid_mult(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_78])]) ).
fof(f3779,plain,
comm_monoid_mult(nat),
inference(cnf_transformation,[],[f1165]) ).
fof(f1165,axiom,
comm_monoid_mult(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
fof(f7380,plain,
spl63_77,
inference(avatar_split_clause,[],[f3778,f7377]) ).
fof(f7377,plain,
( spl63_77
<=> ordere779506340up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_77])]) ).
fof(f3778,plain,
ordere779506340up_add(nat),
inference(cnf_transformation,[],[f1156]) ).
fof(f1156,axiom,
ordere779506340up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
fof(f7375,plain,
spl63_76,
inference(avatar_split_clause,[],[f3777,f7372]) ).
fof(f7372,plain,
( spl63_76
<=> semiring_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_76])]) ).
fof(f3777,plain,
semiring_0(nat),
inference(cnf_transformation,[],[f1179]) ).
fof(f1179,axiom,
semiring_0(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
fof(f7370,plain,
spl63_75,
inference(avatar_split_clause,[],[f3776,f7367]) ).
fof(f3776,plain,
comm_monoid_mult(real),
inference(cnf_transformation,[],[f1211]) ).
fof(f1211,axiom,
comm_monoid_mult(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) ).
fof(f7365,plain,
spl63_74,
inference(avatar_split_clause,[],[f3775,f7362]) ).
fof(f7362,plain,
( spl63_74
<=> ordere779506340up_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_74])]) ).
fof(f3775,plain,
ordere779506340up_add(real),
inference(cnf_transformation,[],[f1195]) ).
fof(f1195,axiom,
ordere779506340up_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) ).
fof(f7360,plain,
spl63_73,
inference(avatar_split_clause,[],[f3774,f7357]) ).
fof(f7357,plain,
( spl63_73
<=> semiring_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_73])]) ).
fof(f3774,plain,
semiring_0(real),
inference(cnf_transformation,[],[f1231]) ).
fof(f1231,axiom,
semiring_0(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__0) ).
fof(f7355,plain,
spl63_72,
inference(avatar_split_clause,[],[f3773,f7352]) ).
fof(f7352,plain,
( spl63_72
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_72])]) ).
fof(f3773,plain,
zero(int),
inference(cnf_transformation,[],[f1145]) ).
fof(f1145,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
fof(f7350,plain,
spl63_71,
inference(avatar_split_clause,[],[f3772,f7347]) ).
fof(f7347,plain,
( spl63_71
<=> linordered_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_71])]) ).
fof(f3772,plain,
linordered_semiring(int),
inference(cnf_transformation,[],[f1112]) ).
fof(f1112,axiom,
linordered_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring) ).
fof(f7345,plain,
spl63_70,
inference(avatar_split_clause,[],[f3771,f7342]) ).
fof(f7342,plain,
( spl63_70
<=> comm_monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_70])]) ).
fof(f3771,plain,
comm_monoid_add(int),
inference(cnf_transformation,[],[f1120]) ).
fof(f1120,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
fof(f7340,plain,
spl63_69,
inference(avatar_split_clause,[],[f3770,f7337]) ).
fof(f3770,plain,
one(int),
inference(cnf_transformation,[],[f1149]) ).
fof(f1149,axiom,
one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
fof(f7335,plain,
spl63_68,
inference(avatar_split_clause,[],[f3769,f7332]) ).
fof(f7332,plain,
( spl63_68
<=> comm_monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_68])]) ).
fof(f3769,plain,
comm_monoid_add(nat),
inference(cnf_transformation,[],[f1169]) ).
fof(f1169,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
fof(f7330,plain,
spl63_67,
inference(avatar_split_clause,[],[f3768,f7327]) ).
fof(f7327,plain,
( spl63_67
<=> one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_67])]) ).
fof(f3768,plain,
one(nat),
inference(cnf_transformation,[],[f1186]) ).
fof(f1186,axiom,
one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
fof(f7325,plain,
spl63_66,
inference(avatar_split_clause,[],[f3767,f7322]) ).
fof(f7322,plain,
( spl63_66
<=> linordered_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_66])]) ).
fof(f3767,plain,
linordered_semiring(nat),
inference(cnf_transformation,[],[f1162]) ).
fof(f1162,axiom,
linordered_semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring) ).
fof(f7320,plain,
spl63_65,
inference(avatar_split_clause,[],[f3766,f7317]) ).
fof(f7317,plain,
( spl63_65
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_65])]) ).
fof(f3766,plain,
zero(nat),
inference(cnf_transformation,[],[f1184]) ).
fof(f1184,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
fof(f7315,plain,
spl63_64,
inference(avatar_split_clause,[],[f3765,f7312]) ).
fof(f7312,plain,
( spl63_64
<=> comm_monoid_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_64])]) ).
fof(f3765,plain,
comm_monoid_add(real),
inference(cnf_transformation,[],[f1216]) ).
fof(f1216,axiom,
comm_monoid_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__add) ).
fof(f7310,plain,
spl63_63,
inference(avatar_split_clause,[],[f3764,f7307]) ).
fof(f7307,plain,
( spl63_63
<=> one(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_63])]) ).
fof(f3764,plain,
one(real),
inference(cnf_transformation,[],[f1245]) ).
fof(f1245,axiom,
one(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oone) ).
fof(f7305,plain,
spl63_62,
inference(avatar_split_clause,[],[f3763,f7302]) ).
fof(f7302,plain,
( spl63_62
<=> zero(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_62])]) ).
fof(f3763,plain,
zero(real),
inference(cnf_transformation,[],[f1241]) ).
fof(f1241,axiom,
zero(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
fof(f7300,plain,
spl63_61,
inference(avatar_split_clause,[],[f3762,f7297]) ).
fof(f7297,plain,
( spl63_61
<=> linordered_semiring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_61])]) ).
fof(f3762,plain,
linordered_semiring(real),
inference(cnf_transformation,[],[f1208]) ).
fof(f1208,axiom,
linordered_semiring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semiring) ).
fof(f7295,plain,
spl63_60,
inference(avatar_split_clause,[],[f3761,f7292]) ).
fof(f7292,plain,
( spl63_60
<=> semiring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_60])]) ).
fof(f3761,plain,
semiring_char_0(int),
inference(cnf_transformation,[],[f1125]) ).
fof(f1125,axiom,
semiring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
fof(f7290,plain,
spl63_59,
inference(avatar_split_clause,[],[f3760,f7287]) ).
fof(f7287,plain,
( spl63_59
<=> linorder(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_59])]) ).
fof(f3760,plain,
linorder(int),
inference(cnf_transformation,[],[f1130]) ).
fof(f1130,axiom,
linorder(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
fof(f7285,plain,
spl63_58,
inference(avatar_split_clause,[],[f3759,f7282]) ).
fof(f7282,plain,
( spl63_58
<=> comm_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_58])]) ).
fof(f3759,plain,
comm_semiring(int),
inference(cnf_transformation,[],[f1124]) ).
fof(f1124,axiom,
comm_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
fof(f7280,plain,
spl63_57,
inference(avatar_split_clause,[],[f3758,f7277]) ).
fof(f7277,plain,
( spl63_57
<=> ordere1490568538miring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_57])]) ).
fof(f3758,plain,
ordere1490568538miring(int),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,axiom,
ordere1490568538miring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__comm__semiring) ).
fof(f7275,plain,
spl63_56,
inference(avatar_split_clause,[],[f3757,f7272]) ).
fof(f7272,plain,
( spl63_56
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_56])]) ).
fof(f3757,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f1103]) ).
fof(f1103,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
fof(f7270,plain,
spl63_55,
inference(avatar_split_clause,[],[f3756,f7267]) ).
fof(f7267,plain,
( spl63_55
<=> linord893533164strict(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_55])]) ).
fof(f3756,plain,
linord893533164strict(int),
inference(cnf_transformation,[],[f1096]) ).
fof(f1096,axiom,
linord893533164strict(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) ).
fof(f7265,plain,
spl63_54,
inference(avatar_split_clause,[],[f3755,f7262]) ).
fof(f7262,plain,
( spl63_54
<=> comm_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_54])]) ).
fof(f3755,plain,
comm_semiring(nat),
inference(cnf_transformation,[],[f1171]) ).
fof(f1171,axiom,
comm_semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring) ).
fof(f7260,plain,
spl63_53,
inference(avatar_split_clause,[],[f3754,f7257]) ).
fof(f7257,plain,
( spl63_53
<=> semiring_char_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_53])]) ).
fof(f3754,plain,
semiring_char_0(nat),
inference(cnf_transformation,[],[f1172]) ).
fof(f1172,axiom,
semiring_char_0(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
fof(f7255,plain,
spl63_52,
inference(avatar_split_clause,[],[f3753,f7252]) ).
fof(f7252,plain,
( spl63_52
<=> cancel146912293up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_52])]) ).
fof(f3753,plain,
cancel146912293up_add(nat),
inference(cnf_transformation,[],[f1158]) ).
fof(f1158,axiom,
cancel146912293up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
fof(f7250,plain,
spl63_51,
inference(avatar_split_clause,[],[f3752,f7247]) ).
fof(f7247,plain,
( spl63_51
<=> linord893533164strict(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_51])]) ).
fof(f3752,plain,
linord893533164strict(nat),
inference(cnf_transformation,[],[f1154]) ).
fof(f1154,axiom,
linord893533164strict(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).
fof(f7245,plain,
spl63_50,
inference(avatar_split_clause,[],[f3751,f7242]) ).
fof(f7242,plain,
( spl63_50
<=> ordere1490568538miring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_50])]) ).
fof(f3751,plain,
ordere1490568538miring(nat),
inference(cnf_transformation,[],[f1160]) ).
fof(f1160,axiom,
ordere1490568538miring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Oordered__comm__semiring) ).
fof(f7240,plain,
spl63_49,
inference(avatar_split_clause,[],[f3750,f7237]) ).
fof(f7237,plain,
( spl63_49
<=> linorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_49])]) ).
fof(f3750,plain,
linorder(nat),
inference(cnf_transformation,[],[f1175]) ).
fof(f1175,axiom,
linorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
fof(f7235,plain,
spl63_48,
inference(avatar_split_clause,[],[f3749,f7232]) ).
fof(f7232,plain,
( spl63_48
<=> ordere1490568538miring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_48])]) ).
fof(f3749,plain,
ordere1490568538miring(real),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,axiom,
ordere1490568538miring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oordered__comm__semiring) ).
fof(f7230,plain,
spl63_47,
inference(avatar_split_clause,[],[f3748,f7227]) ).
fof(f7227,plain,
( spl63_47
<=> linord893533164strict(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_47])]) ).
fof(f3748,plain,
linord893533164strict(real),
inference(cnf_transformation,[],[f1192]) ).
fof(f1192,axiom,
linord893533164strict(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) ).
fof(f7225,plain,
spl63_46,
inference(avatar_split_clause,[],[f3747,f7222]) ).
fof(f7222,plain,
( spl63_46
<=> semiring_char_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_46])]) ).
fof(f3747,plain,
semiring_char_0(real),
inference(cnf_transformation,[],[f1221]) ).
fof(f1221,axiom,
semiring_char_0(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Nat_Osemiring__char__0) ).
fof(f7220,plain,
spl63_45,
inference(avatar_split_clause,[],[f3746,f7217]) ).
fof(f7217,plain,
( spl63_45
<=> comm_semiring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_45])]) ).
fof(f3746,plain,
comm_semiring(real),
inference(cnf_transformation,[],[f1220]) ).
fof(f1220,axiom,
comm_semiring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring) ).
fof(f7215,plain,
spl63_44,
inference(avatar_split_clause,[],[f3745,f7212]) ).
fof(f7212,plain,
( spl63_44
<=> linorder(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_44])]) ).
fof(f3745,plain,
linorder(real),
inference(cnf_transformation,[],[f1226]) ).
fof(f1226,axiom,
linorder(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
fof(f7210,plain,
spl63_43,
inference(avatar_split_clause,[],[f3744,f7207]) ).
fof(f7207,plain,
( spl63_43
<=> cancel146912293up_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_43])]) ).
fof(f3744,plain,
cancel146912293up_add(real),
inference(cnf_transformation,[],[f1199]) ).
fof(f1199,axiom,
cancel146912293up_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) ).
fof(f7205,plain,
spl63_42,
inference(avatar_split_clause,[],[f3743,f7202]) ).
fof(f3743,plain,
number_ring(int),
inference(cnf_transformation,[],[f1141]) ).
fof(f1141,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(f7200,plain,
spl63_41,
inference(avatar_split_clause,[],[f3742,f7197]) ).
fof(f3742,plain,
number_ring(real),
inference(cnf_transformation,[],[f1237]) ).
fof(f1237,axiom,
number_ring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
fof(f7195,plain,
spl63_40,
inference(avatar_split_clause,[],[f3741,f7192]) ).
fof(f3741,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f1122]) ).
fof(f1122,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(f7190,plain,
spl63_39,
inference(avatar_split_clause,[],[f3740,f7187]) ).
fof(f3740,plain,
linordered_idom(real),
inference(cnf_transformation,[],[f1218]) ).
fof(f1218,axiom,
linordered_idom(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
fof(f7185,plain,
spl63_38,
inference(avatar_split_clause,[],[f3739,f7182]) ).
fof(f3739,plain,
ordere142940540dd_abs(int),
inference(cnf_transformation,[],[f1100]) ).
fof(f1100,axiom,
ordere142940540dd_abs(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add__abs) ).
fof(f7180,plain,
spl63_37,
inference(avatar_split_clause,[],[f3738,f7177]) ).
fof(f3738,plain,
ordere142940540dd_abs(real),
inference(cnf_transformation,[],[f1196]) ).
fof(f1196,axiom,
ordere142940540dd_abs(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__group__add__abs) ).
fof(f7175,plain,
spl63_36,
inference(avatar_split_clause,[],[f3737,f7172]) ).
fof(f3737,plain,
linord581940658strict(int),
inference(cnf_transformation,[],[f1106]) ).
fof(f1106,axiom,
linord581940658strict(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
fof(f7170,plain,
spl63_35,
inference(avatar_split_clause,[],[f3736,f7167]) ).
fof(f3736,plain,
linord581940658strict(real),
inference(cnf_transformation,[],[f1202]) ).
fof(f1202,axiom,
linord581940658strict(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring__strict) ).
fof(f7165,plain,
spl63_34,
inference(avatar_split_clause,[],[f3735,f7162]) ).
fof(f3735,plain,
group_add(int),
inference(cnf_transformation,[],[f1136]) ).
fof(f1136,axiom,
group_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
fof(f7160,plain,
spl63_33,
inference(avatar_split_clause,[],[f3734,f7157]) ).
fof(f7157,plain,
( spl63_33
<=> ordered_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_33])]) ).
fof(f3734,plain,
ordered_ring(int),
inference(cnf_transformation,[],[f1129]) ).
fof(f1129,axiom,
ordered_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring) ).
fof(f7155,plain,
spl63_32,
inference(avatar_split_clause,[],[f3733,f7152]) ).
fof(f7152,plain,
( spl63_32
<=> ordered_ring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_32])]) ).
fof(f3733,plain,
ordered_ring(real),
inference(cnf_transformation,[],[f1225]) ).
fof(f1225,axiom,
ordered_ring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oordered__ring) ).
fof(f7150,plain,
spl63_31,
inference(avatar_split_clause,[],[f3732,f7147]) ).
fof(f3732,plain,
group_add(real),
inference(cnf_transformation,[],[f1232]) ).
fof(f1232,axiom,
group_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ogroup__add) ).
fof(f7145,plain,
spl63_30,
inference(avatar_split_clause,[],[f3731,f7142]) ).
fof(f7142,plain,
( spl63_30
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_30])]) ).
fof(f3731,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f1102]) ).
fof(f1102,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
fof(f7140,plain,
spl63_29,
inference(avatar_split_clause,[],[f3730,f7137]) ).
fof(f7137,plain,
( spl63_29
<=> linord219039673up_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_29])]) ).
fof(f3730,plain,
linord219039673up_add(real),
inference(cnf_transformation,[],[f1198]) ).
fof(f1198,axiom,
linord219039673up_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
fof(f7135,plain,
spl63_28,
inference(avatar_split_clause,[],[f3729,f7132]) ).
fof(f7132,plain,
( spl63_28
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_28])]) ).
fof(f3729,plain,
ring(int),
inference(cnf_transformation,[],[f1146]) ).
fof(f1146,axiom,
ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
fof(f7130,plain,
spl63_27,
inference(avatar_split_clause,[],[f3728,f7127]) ).
fof(f7127,plain,
( spl63_27
<=> ring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_27])]) ).
fof(f3728,plain,
ring(real),
inference(cnf_transformation,[],[f1242]) ).
fof(f1242,axiom,
ring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring) ).
fof(f7125,plain,
spl63_26,
inference(avatar_split_clause,[],[f3727,f7122]) ).
fof(f7122,plain,
( spl63_26
<=> linordered_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_26])]) ).
fof(f3727,plain,
linordered_ring(int),
inference(cnf_transformation,[],[f1121]) ).
fof(f1121,axiom,
linordered_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
fof(f7120,plain,
spl63_25,
inference(avatar_split_clause,[],[f3726,f7117]) ).
fof(f7117,plain,
( spl63_25
<=> ordered_ab_group_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_25])]) ).
fof(f3726,plain,
ordered_ab_group_add(int),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,axiom,
ordered_ab_group_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add) ).
fof(f7115,plain,
spl63_24,
inference(avatar_split_clause,[],[f3725,f7112]) ).
fof(f7112,plain,
( spl63_24
<=> ordered_ab_group_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_24])]) ).
fof(f3725,plain,
ordered_ab_group_add(real),
inference(cnf_transformation,[],[f1206]) ).
fof(f1206,axiom,
ordered_ab_group_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__group__add) ).
fof(f7110,plain,
spl63_23,
inference(avatar_split_clause,[],[f3724,f7107]) ).
fof(f7107,plain,
( spl63_23
<=> linordered_ring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_23])]) ).
fof(f3724,plain,
linordered_ring(real),
inference(cnf_transformation,[],[f1217]) ).
fof(f1217,axiom,
linordered_ring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring) ).
fof(f7105,plain,
spl63_22,
inference(avatar_split_clause,[],[f3723,f7102]) ).
fof(f7102,plain,
( spl63_22
<=> ab_group_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_22])]) ).
fof(f3723,plain,
ab_group_add(int),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,axiom,
ab_group_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).
fof(f7100,plain,
spl63_21,
inference(avatar_split_clause,[],[f3722,f7097]) ).
fof(f7097,plain,
( spl63_21
<=> ab_group_add(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_21])]) ).
fof(f3722,plain,
ab_group_add(real),
inference(cnf_transformation,[],[f1223]) ).
fof(f1223,axiom,
ab_group_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__group__add) ).
fof(f7095,plain,
spl63_20,
inference(avatar_split_clause,[],[f3721,f7092]) ).
fof(f7092,plain,
( spl63_20
<=> ring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_20])]) ).
fof(f3721,plain,
ring_1(int),
inference(cnf_transformation,[],[f1143]) ).
fof(f1143,axiom,
ring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
fof(f7090,plain,
spl63_19,
inference(avatar_split_clause,[],[f3720,f7087]) ).
fof(f7087,plain,
( spl63_19
<=> idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_19])]) ).
fof(f3720,plain,
idom(int),
inference(cnf_transformation,[],[f1147]) ).
fof(f1147,axiom,
idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oidom) ).
fof(f7085,plain,
spl63_18,
inference(avatar_split_clause,[],[f3719,f7082]) ).
fof(f3719,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f1104]) ).
fof(f1104,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(f7080,plain,
spl63_17,
inference(avatar_split_clause,[],[f3718,f7077]) ).
fof(f7077,plain,
( spl63_17
<=> comm_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_17])]) ).
fof(f3718,plain,
comm_ring(int),
inference(cnf_transformation,[],[f1138]) ).
fof(f1138,axiom,
comm_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring) ).
fof(f7075,plain,
spl63_16,
inference(avatar_split_clause,[],[f3717,f7072]) ).
fof(f7072,plain,
( spl63_16
<=> idom(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_16])]) ).
fof(f3717,plain,
idom(real),
inference(cnf_transformation,[],[f1243]) ).
fof(f1243,axiom,
idom(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oidom) ).
fof(f7070,plain,
spl63_15,
inference(avatar_split_clause,[],[f3716,f7067]) ).
fof(f7067,plain,
( spl63_15
<=> ring_11004092258visors(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_15])]) ).
fof(f3716,plain,
ring_11004092258visors(real),
inference(cnf_transformation,[],[f1200]) ).
fof(f1200,axiom,
ring_11004092258visors(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
fof(f7065,plain,
spl63_14,
inference(avatar_split_clause,[],[f3715,f7062]) ).
fof(f7062,plain,
( spl63_14
<=> ring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_14])]) ).
fof(f3715,plain,
ring_1(real),
inference(cnf_transformation,[],[f1239]) ).
fof(f1239,axiom,
ring_1(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1) ).
fof(f7060,plain,
spl63_13,
inference(avatar_split_clause,[],[f3714,f7057]) ).
fof(f7057,plain,
( spl63_13
<=> comm_ring(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_13])]) ).
fof(f3714,plain,
comm_ring(real),
inference(cnf_transformation,[],[f1234]) ).
fof(f1234,axiom,
comm_ring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__ring) ).
fof(f7055,plain,
spl63_12,
inference(avatar_split_clause,[],[f3713,f7052]) ).
fof(f7052,plain,
( spl63_12
<=> linord1278240602ring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_12])]) ).
fof(f3713,plain,
linord1278240602ring_1(int),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,axiom,
linord1278240602ring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__1) ).
fof(f7050,plain,
spl63_11,
inference(avatar_split_clause,[],[f3712,f7047]) ).
fof(f7047,plain,
( spl63_11
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_11])]) ).
fof(f3712,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f1140]) ).
fof(f1140,axiom,
ring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
fof(f7045,plain,
spl63_10,
inference(avatar_split_clause,[],[f3711,f7042]) ).
fof(f7042,plain,
( spl63_10
<=> comm_ring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_10])]) ).
fof(f3711,plain,
comm_ring_1(int),
inference(cnf_transformation,[],[f1132]) ).
fof(f1132,axiom,
comm_ring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring__1) ).
fof(f7040,plain,
spl63_9,
inference(avatar_split_clause,[],[f3710,f7037]) ).
fof(f7037,plain,
( spl63_9
<=> ring_n68954251visors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_9])]) ).
fof(f3710,plain,
ring_n68954251visors(int),
inference(cnf_transformation,[],[f1107]) ).
fof(f1107,axiom,
ring_n68954251visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
fof(f7035,plain,
spl63_8,
inference(avatar_split_clause,[],[f3709,f7032]) ).
fof(f7032,plain,
( spl63_8
<=> ordered_ring_abs(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_8])]) ).
fof(f3709,plain,
ordered_ring_abs(int),
inference(cnf_transformation,[],[f1118]) ).
fof(f1118,axiom,
ordered_ring_abs(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oordered__ring__abs) ).
fof(f7030,plain,
spl63_7,
inference(avatar_split_clause,[],[f3708,f7027]) ).
fof(f7027,plain,
( spl63_7
<=> linord626643107strict(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_7])]) ).
fof(f3708,plain,
linord626643107strict(int),
inference(cnf_transformation,[],[f1097]) ).
fof(f1097,axiom,
linord626643107strict(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__1__strict) ).
fof(f7025,plain,
spl63_6,
inference(avatar_split_clause,[],[f3707,f7022]) ).
fof(f7022,plain,
( spl63_6
<=> ring_char_0(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_6])]) ).
fof(f3707,plain,
ring_char_0(real),
inference(cnf_transformation,[],[f1236]) ).
fof(f1236,axiom,
ring_char_0(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
fof(f7020,plain,
spl63_5,
inference(avatar_split_clause,[],[f3706,f7017]) ).
fof(f7017,plain,
( spl63_5
<=> ring_n68954251visors(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_5])]) ).
fof(f3706,plain,
ring_n68954251visors(real),
inference(cnf_transformation,[],[f1203]) ).
fof(f1203,axiom,
ring_n68954251visors(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) ).
fof(f7015,plain,
spl63_4,
inference(avatar_split_clause,[],[f3705,f7012]) ).
fof(f7012,plain,
( spl63_4
<=> linord626643107strict(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_4])]) ).
fof(f3705,plain,
linord626643107strict(real),
inference(cnf_transformation,[],[f1193]) ).
fof(f1193,axiom,
linord626643107strict(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semiring__1__strict) ).
fof(f7010,plain,
spl63_3,
inference(avatar_split_clause,[],[f3704,f7007]) ).
fof(f7007,plain,
( spl63_3
<=> ordered_ring_abs(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_3])]) ).
fof(f3704,plain,
ordered_ring_abs(real),
inference(cnf_transformation,[],[f1214]) ).
fof(f1214,axiom,
ordered_ring_abs(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oordered__ring__abs) ).
fof(f7005,plain,
spl63_2,
inference(avatar_split_clause,[],[f3703,f7002]) ).
fof(f7002,plain,
( spl63_2
<=> comm_ring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_2])]) ).
fof(f3703,plain,
comm_ring_1(real),
inference(cnf_transformation,[],[f1228]) ).
fof(f1228,axiom,
comm_ring_1(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__ring__1) ).
fof(f7000,plain,
spl63_1,
inference(avatar_split_clause,[],[f3702,f6997]) ).
fof(f6997,plain,
( spl63_1
<=> linord1278240602ring_1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_1])]) ).
fof(f3702,plain,
linord1278240602ring_1(real),
inference(cnf_transformation,[],[f1205]) ).
fof(f1205,axiom,
linord1278240602ring_1(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semiring__1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.34 % Computer : n015.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri May 3 15:04:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (19276)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.47 % (19283)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)
% 0.21/0.47 % (19279)WARNING: value z3 for option sas not known
% 0.21/0.47 % (19277)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.47 % (19278)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.47 % (19280)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.47 % (19279)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)
% 0.21/0.47 % (19281)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)
% 0.21/0.47 % (19282)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)
% 1.73/0.73 % (19281)First to succeed.
% 2.37/0.76 % (19281)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19276"
% 2.37/0.77 % (19281)Refutation found. Thanks to Tanya!
% 2.37/0.77 % SZS status Theorem for theBenchmark
% 2.37/0.77 % SZS output start Proof for theBenchmark
% See solution above
% 2.37/0.79 % (19281)------------------------------
% 2.37/0.79 % (19281)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.37/0.79 % (19281)Termination reason: Refutation
% 2.37/0.79
% 2.37/0.79 % (19281)Memory used [KB]: 7356
% 2.37/0.79 % (19281)Time elapsed: 0.293 s
% 2.37/0.79 % (19281)Instructions burned: 779 (million)
% 2.37/0.79 % (19276)Success in time 0.422 s
%------------------------------------------------------------------------------