TSTP Solution File: ITP146^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP146^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:53:14 EDT 2024
% Result : Theorem 4.65s 1.05s
% Output : Refutation 4.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 778
% Syntax : Number of formulae : 2795 ( 691 unt; 62 typ; 0 def)
% Number of atoms : 29390 (3600 equ; 0 cnn)
% Maximal formula atoms : 13 ( 10 avg)
% Number of connectives : 7597 (3221 ~;3354 |; 66 &; 0 @)
% ( 487 <=>; 469 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 105 ( 104 >; 1 *; 0 +; 0 <<)
% Number of symbols : 546 ( 543 usr; 506 con; 0-6 aty)
% Number of variables : 4161 ( 28 ^4116 !; 4 ?;4161 :)
% ( 13 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
set_a: $tType ).
thf(type_def_8,type,
set_real: $tType ).
thf(type_def_9,type,
real: $tType ).
thf(func_def_0,type,
set_real: $tType ).
thf(func_def_1,type,
set_a: $tType ).
thf(func_def_2,type,
real: $tType ).
thf(func_def_3,type,
a: $tType ).
thf(func_def_4,type,
auto_l612940ivl0_a: ( a > a ) > set_a > a > set_real ).
thf(func_def_5,type,
auto_ll_on_flow0_a: ( a > a ) > set_a > a > real > a ).
thf(func_def_6,type,
minus_minus_real: real > real > real ).
thf(func_def_7,type,
minus_minus_a: a > a > a ).
thf(func_def_8,type,
plus_plus_real: real > real > real ).
thf(func_def_9,type,
plus_plus_a: a > a > a ).
thf(func_def_10,type,
uminus_uminus_a_a: ( a > a ) > a > a ).
thf(func_def_11,type,
uminus_uminus_real: real > real ).
thf(func_def_12,type,
uminus_uminus_a: a > a ).
thf(func_def_13,type,
zero_zero_real: real ).
thf(func_def_14,type,
zero_zero_a: a ).
thf(func_def_15,type,
initia826609931terval: set_real > $o ).
thf(func_def_16,type,
bot_bot_set_real: set_real ).
thf(func_def_17,type,
ord_less_real: real > real > $o ).
thf(func_def_18,type,
ord_less_a: a > a > $o ).
thf(func_def_19,type,
top_top_set_real: set_real ).
thf(func_def_20,type,
period720806154rbit_a: ( a > a ) > set_a > a > $o ).
thf(func_def_21,type,
period1305449585riod_a: ( a > a ) > set_a > a > real ).
thf(func_def_22,type,
period138238489rbit_a: ( a > a ) > set_a > a > $o ).
thf(func_def_23,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_24,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_25,type,
member_real: real > set_real > $o ).
thf(func_def_26,type,
member_a: a > set_a > $o ).
thf(func_def_27,type,
x: set_a ).
thf(func_def_28,type,
d: real ).
thf(func_def_29,type,
f: a > a ).
thf(func_def_30,type,
i1: real ).
thf(func_def_31,type,
i2: real ).
thf(func_def_32,type,
ss: real ).
thf(func_def_33,type,
t: real ).
thf(func_def_34,type,
tt: real ).
thf(func_def_35,type,
x2: a ).
thf(func_def_36,type,
xx: a ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_42,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_48,type,
sK0: a > real ).
thf(func_def_49,type,
sK1: a > real ).
thf(func_def_50,type,
sK2: ( real > $o ) > ( real > $o ) > real ).
thf(func_def_51,type,
sK3: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_52,type,
sK4: a ).
thf(func_def_53,type,
sK5: a ).
thf(func_def_54,type,
sK6: a ).
thf(func_def_55,type,
sK7: a ).
thf(func_def_57,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_58,type,
vIMP: $o > $o > $o ).
thf(func_def_59,type,
sK9: a > real ).
thf(func_def_60,type,
sK10: a > real ).
thf(f17699,plain,
$false,
inference(avatar_sat_refutation,[],[f1940,f1944,f1977,f1982,f1987,f1992,f1996,f2000,f2004,f2010,f2014,f2018,f2022,f2026,f2030,f2034,f2038,f2042,f2046,f2050,f2055,f2060,f2065,f2070,f2075,f2080,f2084,f2092,f2096,f2100,f2104,f2108,f2112,f2116,f2120,f2149,f2154,f2158,f2162,f2166,f2170,f2174,f2178,f2182,f2186,f2190,f2247,f2251,f2258,f2262,f2266,f2270,f2274,f2278,f2282,f2429,f2433,f2442,f2447,f2452,f2456,f2508,f2513,f2518,f2523,f2527,f2548,f2552,f2556,f2560,f2567,f2713,f2719,f2725,f2729,f2733,f2737,f2741,f2745,f2749,f2753,f2757,f2761,f2765,f2769,f2773,f2777,f2781,f2786,f2790,f2794,f2798,f2802,f2806,f2810,f2818,f3800,f3804,f3880,f3886,f3890,f3894,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3973,f4008,f4258,f4264,f4269,f4282,f4284,f4286,f4290,f4302,f4306,f4310,f4314,f4318,f4340,f4344,f4348,f4352,f4366,f4370,f4374,f4392,f4396,f4402,f4406,f4410,f4414,f4418,f4422,f4426,f4433,f4438,f4441,f4490,f4494,f4540,f4546,f4553,f4565,f4573,f4584,f4594,f4599,f4603,f4612,f4616,f4622,f4626,f4643,f4647,f4651,f4670,f4674,f4682,f4694,f4710,f4725,f4731,f4735,f4739,f4744,f4748,f4782,f4786,f4818,f4843,f4885,f4889,f4935,f4940,f4948,f4952,f5014,f5018,f5022,f5074,f5082,f5086,f5144,f5164,f5184,f5188,f5211,f5271,f5275,f5372,f5376,f5487,f5511,f5533,f5557,f5579,f5585,f5624,f5694,f5698,f5703,f5707,f5711,f5715,f5719,f5723,f5727,f5731,f5735,f5814,f5818,f5822,f5827,f5832,f5837,f5994,f5999,f6003,f6063,f6067,f6071,f6075,f6079,f6083,f6087,f6091,f6095,f6099,f6103,f6107,f6111,f6115,f6463,f6711,f6715,f6733,f6737,f6741,f6745,f6749,f6753,f6757,f6761,f6765,f6769,f6774,f6778,f6782,f6786,f7023,f7027,f7031,f7035,f7039,f7043,f7047,f7051,f7055,f7059,f7063,f7067,f7071,f7075,f7079,f7083,f7087,f7091,f7095,f7099,f7180,f7939,f8503,f8507,f8511,f8597,f8601,f8605,f8609,f8613,f8617,f8621,f8625,f8629,f8633,f8637,f8641,f8645,f8654,f8662,f8679,f8946,f8992,f8996,f9000,f9004,f9008,f9012,f9016,f9020,f9024,f9028,f9032,f9036,f9040,f10446,f10450,f10454,f10458,f10463,f10467,f10471,f10475,f10479,f10483,f10487,f10491,f10495,f10499,f10504,f11577,f11581,f11585,f11589,f11593,f11597,f11601,f11602,f11696,f12321,f12325,f12329,f12333,f12337,f12954,f12959,f12964,f13008,f13013,f13075,f13079,f13083,f13088,f13093,f13097,f13170,f13175,f13225,f13230,f13299,f13304,f13309,f13314,f13319,f13323,f13327,f13331,f13335,f13339,f13343,f13347,f13351,f13355,f13359,f13424,f13428,f13432,f13436,f13440,f13444,f13448,f13452,f13456,f13460,f13464,f13468,f13472,f13476,f13480,f13484,f13488,f13492,f13496,f13500,f13504,f13508,f13512,f13516,f13729,f14235,f16077,f16502,f16506,f16510,f16514,f16518,f16522,f16526,f16530,f16534,f16538,f16893,f16941,f16946,f17027,f17031,f17035,f17039,f17043,f17049,f17053,f17057,f17061,f17065,f17069,f17073,f17077,f17081,f17085,f17090,f17094,f17098,f17102,f17106,f17110,f17114,f17118,f17122,f17126,f17130,f17190,f17194,f17198,f17202,f17206,f17210,f17214,f17218,f17222,f17227,f17233,f17237,f17241,f17245,f17249,f17253,f17257,f17261,f17265,f17269,f17274,f17278,f17282,f17286,f17290,f17294,f17298,f17302,f17306,f17310,f17314,f17365,f17369,f17373,f17377,f17381,f17385,f17389,f17393,f17397,f17401,f17406,f17413,f17418,f17419,f17500,f17504,f17517,f17522,f17525,f17531,f17536,f17556,f17565,f17569,f17575,f17604,f17614,f17627,f17634,f17698]) ).
thf(f17698,plain,
( spl8_6
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_177
| ~ spl8_206 ),
inference(avatar_split_clause,[],[f5529,f5509,f4737,f4581,f4550,f2515,f2510,f2249,f1998,f1989]) ).
thf(f1989,plain,
( spl8_6
<=> ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
thf(f1998,plain,
( spl8_8
<=> ! [X0: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,uminus_uminus_real,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
thf(f2249,plain,
( spl8_48
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,uminus_uminus_real,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
thf(f2510,plain,
( spl8_63
<=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).
thf(f2515,plain,
( spl8_64
<=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,tt),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).
thf(f4550,plain,
( spl8_154
<=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_154])]) ).
thf(f4581,plain,
( spl8_157
<=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_157])]) ).
thf(f4737,plain,
( spl8_177
<=> ! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_177])]) ).
thf(f5509,plain,
( spl8_206
<=> ! [X2: real,X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_206])]) ).
thf(f5529,plain,
( ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_177
| ~ spl8_206 ),
inference(trivial_inequality_removal,[],[f5528]) ).
thf(f5528,plain,
( ( $true != $true )
| ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_177
| ~ spl8_206 ),
inference(forward_demodulation,[],[f5527,f2512]) ).
thf(f2512,plain,
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) = $true )
| ~ spl8_63 ),
inference(avatar_component_clause,[],[f2510]) ).
thf(f5527,plain,
( ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)) )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) != $true )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_177
| ~ spl8_206 ),
inference(forward_demodulation,[],[f5526,f4763]) ).
thf(f4763,plain,
( ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss)),vAPP(real,real,uminus_uminus_real,tt)) )
| ~ spl8_64
| ~ spl8_154
| ~ spl8_177 ),
inference(forward_demodulation,[],[f4760,f4552]) ).
thf(f4552,plain,
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss) )
| ~ spl8_154 ),
inference(avatar_component_clause,[],[f4550]) ).
thf(f4760,plain,
( ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt)),vAPP(real,real,uminus_uminus_real,tt)) )
| ~ spl8_64
| ~ spl8_177 ),
inference(trivial_inequality_removal,[],[f4755]) ).
thf(f4755,plain,
( ( $true != $true )
| ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt)),vAPP(real,real,uminus_uminus_real,tt)) )
| ~ spl8_64
| ~ spl8_177 ),
inference(superposition,[],[f4738,f2517]) ).
thf(f2517,plain,
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,tt),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) = $true )
| ~ spl8_64 ),
inference(avatar_component_clause,[],[f2515]) ).
thf(f4738,plain,
( ! [X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),vAPP(real,real,uminus_uminus_real,X0)) = X1 ) )
| ~ spl8_177 ),
inference(avatar_component_clause,[],[f4737]) ).
thf(f5526,plain,
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss)),vAPP(real,real,uminus_uminus_real,tt)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)) )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) != $true )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_157
| ~ spl8_206 ),
inference(forward_demodulation,[],[f5520,f2284]) ).
thf(f2284,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,uminus_uminus_real,X0)) )
| ~ spl8_8
| ~ spl8_48 ),
inference(superposition,[],[f2250,f1999]) ).
thf(f1999,plain,
( ! [X0: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,uminus_uminus_real,X0)) = X0 )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f1998]) ).
thf(f2250,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,uminus_uminus_real,X1)) )
| ~ spl8_48 ),
inference(avatar_component_clause,[],[f2249]) ).
thf(f5520,plain,
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss)),vAPP(real,real,uminus_uminus_real,tt)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,ss),vAPP(real,real,uminus_uminus_real,tt))) )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) != $true )
| ~ spl8_157
| ~ spl8_206 ),
inference(trivial_inequality_removal,[],[f5517]) ).
thf(f5517,plain,
( ( $true != $true )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss)),vAPP(real,real,uminus_uminus_real,tt)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,ss),vAPP(real,real,uminus_uminus_real,tt))) )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) != $true )
| ~ spl8_157
| ~ spl8_206 ),
inference(superposition,[],[f5510,f4583]) ).
thf(f4583,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss))) )
| ~ spl8_157 ),
inference(avatar_component_clause,[],[f4581]) ).
thf(f5510,plain,
( ! [X2: real,X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) )
| ~ spl8_206 ),
inference(avatar_component_clause,[],[f5509]) ).
thf(f17634,plain,
( ~ spl8_161
| ~ spl8_178 ),
inference(avatar_contradiction_clause,[],[f17633]) ).
thf(f17633,plain,
( $false
| ~ spl8_161
| ~ spl8_178 ),
inference(trivial_inequality_removal,[],[f17632]) ).
thf(f17632,plain,
( ( $true = $false )
| ~ spl8_161
| ~ spl8_178 ),
inference(forward_demodulation,[],[f4607,f4743]) ).
thf(f4743,plain,
( ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ~ spl8_178 ),
inference(avatar_component_clause,[],[f4741]) ).
thf(f4741,plain,
( spl8_178
<=> ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_178])]) ).
thf(f4607,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ~ spl8_161 ),
inference(avatar_component_clause,[],[f4605]) ).
thf(f4605,plain,
( spl8_161
<=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_161])]) ).
thf(f17627,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17626]) ).
thf(f17626,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17625]) ).
thf(f17625,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17624,f17089]) ).
thf(f17089,plain,
( ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_433 ),
inference(avatar_component_clause,[],[f17087]) ).
thf(f17087,plain,
( spl8_433
<=> ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_433])]) ).
thf(f17624,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f17623,f2269]) ).
thf(f2269,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) )
| ~ spl8_52 ),
inference(avatar_component_clause,[],[f2268]) ).
thf(f2268,plain,
( spl8_52
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
thf(f17623,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f17422,f5529]) ).
thf(f17422,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_161
| ~ spl8_179 ),
inference(trivial_inequality_removal,[],[f4821]) ).
thf(f4821,plain,
( ( $true != $true )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_161
| ~ spl8_179 ),
inference(superposition,[],[f4747,f4607]) ).
thf(f4747,plain,
( ! [X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) ) )
| ~ spl8_179 ),
inference(avatar_component_clause,[],[f4746]) ).
thf(f4746,plain,
( spl8_179
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_179])]) ).
thf(f17614,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17613]) ).
thf(f17613,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17612]) ).
thf(f17612,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17611,f17089]) ).
thf(f17611,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f17610,f2269]) ).
thf(f17610,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f4832,f5529]) ).
thf(f4832,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_161
| ~ spl8_179 ),
inference(trivial_inequality_removal,[],[f4821]) ).
thf(f17604,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17603]) ).
thf(f17603,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17602]) ).
thf(f17602,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17601,f17089]) ).
thf(f17601,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f4837,f5529]) ).
thf(f4837,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_52
| ~ spl8_161
| ~ spl8_179 ),
inference(forward_demodulation,[],[f4832,f2269]) ).
thf(f17575,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17574]) ).
thf(f17574,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17573]) ).
thf(f17573,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f11650,f17089]) ).
thf(f11650,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f4837,f5529]) ).
thf(f17569,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17568]) ).
thf(f17568,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17567]) ).
thf(f17567,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17566,f17089]) ).
thf(f17566,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206 ),
inference(forward_demodulation,[],[f17433,f5529]) ).
thf(f17433,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_161
| ~ spl8_189 ),
inference(trivial_inequality_removal,[],[f4995]) ).
thf(f4995,plain,
( ( $true != $true )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_161
| ~ spl8_189 ),
inference(superposition,[],[f4951,f4607]) ).
thf(f4951,plain,
( ! [X2: a,X0: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) ) )
| ~ spl8_189 ),
inference(avatar_component_clause,[],[f4950]) ).
thf(f4950,plain,
( spl8_189
<=> ! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_189])]) ).
thf(f17565,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17564]) ).
thf(f17564,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17563]) ).
thf(f17563,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17562,f17089]) ).
thf(f17562,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206 ),
inference(forward_demodulation,[],[f4998,f5529]) ).
thf(f4998,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_161
| ~ spl8_189 ),
inference(trivial_inequality_removal,[],[f4995]) ).
thf(f17556,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17555]) ).
thf(f17555,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17554]) ).
thf(f17554,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17553,f17089]) ).
thf(f17553,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f17552,f2269]) ).
thf(f17552,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f11605,f5529]) ).
thf(f11605,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_161
| ~ spl8_179 ),
inference(trivial_inequality_removal,[],[f4821]) ).
thf(f17536,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17535]) ).
thf(f17535,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17534]) ).
thf(f17534,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17533,f17089]) ).
thf(f17533,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206 ),
inference(forward_demodulation,[],[f11616,f5529]) ).
thf(f11616,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)))) )
| ~ spl8_161
| ~ spl8_189 ),
inference(trivial_inequality_removal,[],[f4995]) ).
thf(f17531,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17530]) ).
thf(f17530,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17529]) ).
thf(f17529,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f11620,f17089]) ).
thf(f11620,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206 ),
inference(forward_demodulation,[],[f4998,f5529]) ).
thf(f17525,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17524]) ).
thf(f17524,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17523]) ).
thf(f17523,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f11667,f17089]) ).
thf(f11667,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f11666,f2269]) ).
thf(f11666,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f11605,f5529]) ).
thf(f17522,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17521]) ).
thf(f17521,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17520]) ).
thf(f17520,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17519,f17089]) ).
thf(f17519,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f11656,f2269]) ).
thf(f11656,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f4832,f5529]) ).
thf(f17517,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17516]) ).
thf(f17516,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17515]) ).
thf(f17515,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f11657,f17089]) ).
thf(f11657,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f11656,f2269]) ).
thf(f17504,plain,
( ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17503]) ).
thf(f17503,plain,
( $false
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17502]) ).
thf(f17502,plain,
( ( $true = $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206
| ~ spl8_433 ),
inference(forward_demodulation,[],[f17501,f17089]) ).
thf(f17501,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_52
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_179
| ~ spl8_206 ),
inference(forward_demodulation,[],[f11666,f2269]) ).
thf(f17500,plain,
( ~ spl8_415
| ~ spl8_433 ),
inference(avatar_contradiction_clause,[],[f17499]) ).
thf(f17499,plain,
( $false
| ~ spl8_415
| ~ spl8_433 ),
inference(trivial_inequality_removal,[],[f17498]) ).
thf(f17498,plain,
( ( $true = $false )
| ~ spl8_415
| ~ spl8_433 ),
inference(forward_demodulation,[],[f16892,f17089]) ).
thf(f16892,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_415 ),
inference(avatar_component_clause,[],[f16890]) ).
thf(f16890,plain,
( spl8_415
<=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_415])]) ).
thf(f17419,plain,
( spl8_161
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_157
| ~ spl8_191 ),
inference(avatar_split_clause,[],[f5077,f5016,f4581,f2510,f2249,f1998,f4605]) ).
thf(f5016,plain,
( spl8_191
<=> ! [X2: real,X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_191])]) ).
thf(f5077,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_157
| ~ spl8_191 ),
inference(trivial_inequality_removal,[],[f5076]) ).
thf(f5076,plain,
( ( $true != $true )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_157
| ~ spl8_191 ),
inference(forward_demodulation,[],[f5051,f2512]) ).
thf(f5051,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) != $true )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_157
| ~ spl8_191 ),
inference(forward_demodulation,[],[f5045,f2284]) ).
thf(f5045,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,ss),vAPP(real,real,uminus_uminus_real,tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) != $true )
| ~ spl8_157
| ~ spl8_191 ),
inference(trivial_inequality_removal,[],[f5042]) ).
thf(f5042,plain,
( ( $true != $true )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,ss),vAPP(real,real,uminus_uminus_real,tt))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) != $true )
| ~ spl8_157
| ~ spl8_191 ),
inference(superposition,[],[f5017,f4583]) ).
thf(f5017,plain,
( ! [X2: real,X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) )
| ~ spl8_191 ),
inference(avatar_component_clause,[],[f5016]) ).
thf(f17418,plain,
( spl8_487
| ~ spl8_62
| ~ spl8_168 ),
inference(avatar_split_clause,[],[f4665,f4649,f2505,f17415]) ).
thf(f17415,plain,
( spl8_487
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),t)),x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_487])]) ).
thf(f2505,plain,
( spl8_62
<=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,t),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).
thf(f4649,plain,
( spl8_168
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_168])]) ).
thf(f4665,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),t)),x) )
| ~ spl8_62
| ~ spl8_168 ),
inference(trivial_inequality_removal,[],[f4656]) ).
thf(f4656,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),t)),x) )
| ~ spl8_62
| ~ spl8_168 ),
inference(superposition,[],[f4650,f2507]) ).
thf(f2507,plain,
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,t),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) = $true )
| ~ spl8_62 ),
inference(avatar_component_clause,[],[f2505]) ).
thf(f4650,plain,
( ! [X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),x) ) )
| ~ spl8_168 ),
inference(avatar_component_clause,[],[f4649]) ).
thf(f17413,plain,
( spl8_486
| ~ spl8_107
| ~ spl8_157 ),
inference(avatar_split_clause,[],[f4589,f4581,f3912,f17410]) ).
thf(f17410,plain,
( spl8_486
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss)),x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_486])]) ).
thf(f3912,plain,
( spl8_107
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_107])]) ).
thf(f4589,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss)),x) )
| ~ spl8_107
| ~ spl8_157 ),
inference(trivial_inequality_removal,[],[f4586]) ).
thf(f4586,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss)),x) )
| ~ spl8_107
| ~ spl8_157 ),
inference(superposition,[],[f3913,f4583]) ).
thf(f3913,plain,
( ! [X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) ) )
| ~ spl8_107 ),
inference(avatar_component_clause,[],[f3912]) ).
thf(f17406,plain,
( spl8_485
| ~ spl8_168
| ~ spl8_415 ),
inference(avatar_split_clause,[],[f17165,f16890,f4649,f17403]) ).
thf(f17403,plain,
( spl8_485
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss))),x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_485])]) ).
thf(f17165,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss))),x) )
| ~ spl8_168
| ~ spl8_415 ),
inference(trivial_inequality_removal,[],[f17132]) ).
thf(f17132,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss))),x) )
| ~ spl8_168
| ~ spl8_415 ),
inference(superposition,[],[f4650,f16892]) ).
thf(f17401,plain,
( spl8_484
| ~ spl8_51
| ~ spl8_53
| ~ spl8_98 ),
inference(avatar_split_clause,[],[f3852,f3802,f2272,f2264,f17399]) ).
thf(f17399,plain,
( spl8_484
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_484])]) ).
thf(f2264,plain,
( spl8_51
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,uminus_uminus_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
thf(f2272,plain,
( spl8_53
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
thf(f3802,plain,
( spl8_98
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_98])]) ).
thf(f3852,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ~ spl8_51
| ~ spl8_53
| ~ spl8_98 ),
inference(forward_demodulation,[],[f3851,f2265]) ).
thf(f2265,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,uminus_uminus_a,X1)) )
| ~ spl8_51 ),
inference(avatar_component_clause,[],[f2264]) ).
thf(f3851,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1))) )
| ~ spl8_51
| ~ spl8_53
| ~ spl8_98 ),
inference(forward_demodulation,[],[f3814,f2374]) ).
thf(f2374,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X1)),X0) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ~ spl8_51
| ~ spl8_53 ),
inference(superposition,[],[f2273,f2265]) ).
thf(f2273,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) )
| ~ spl8_53 ),
inference(avatar_component_clause,[],[f2272]) ).
thf(f3814,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X1)),X2)) )
| ~ spl8_51
| ~ spl8_98 ),
inference(superposition,[],[f3803,f2265]) ).
thf(f3803,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) )
| ~ spl8_98 ),
inference(avatar_component_clause,[],[f3802]) ).
thf(f17397,plain,
( spl8_483
| ~ spl8_43
| ~ spl8_98 ),
inference(avatar_split_clause,[],[f3825,f3802,f2176,f17395]) ).
thf(f17395,plain,
( spl8_483
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_483])]) ).
thf(f2176,plain,
( spl8_43
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
thf(f3825,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) = X2 )
| ~ spl8_43
| ~ spl8_98 ),
inference(superposition,[],[f2177,f3803]) ).
thf(f2177,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) = X1 )
| ~ spl8_43 ),
inference(avatar_component_clause,[],[f2176]) ).
thf(f17393,plain,
( spl8_482
| ~ spl8_43
| ~ spl8_98 ),
inference(avatar_split_clause,[],[f3807,f3802,f2176,f17391]) ).
thf(f17391,plain,
( spl8_482
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_482])]) ).
thf(f3807,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)) )
| ~ spl8_43
| ~ spl8_98 ),
inference(superposition,[],[f3803,f2177]) ).
thf(f17389,plain,
( spl8_481
| ~ spl8_41
| ~ spl8_94
| ~ spl8_95 ),
inference(avatar_split_clause,[],[f3779,f2808,f2804,f2168,f17387]) ).
thf(f17387,plain,
( spl8_481
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_481])]) ).
thf(f2168,plain,
( spl8_41
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
thf(f2804,plain,
( spl8_94
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_94])]) ).
thf(f2808,plain,
( spl8_95
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_95])]) ).
thf(f3779,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ~ spl8_41
| ~ spl8_94
| ~ spl8_95 ),
inference(forward_demodulation,[],[f3746,f2805]) ).
thf(f2805,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) )
| ~ spl8_94 ),
inference(avatar_component_clause,[],[f2804]) ).
thf(f3746,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ~ spl8_41
| ~ spl8_95 ),
inference(superposition,[],[f2809,f2169]) ).
thf(f2169,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) = X1 )
| ~ spl8_41 ),
inference(avatar_component_clause,[],[f2168]) ).
thf(f2809,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) )
| ~ spl8_95 ),
inference(avatar_component_clause,[],[f2808]) ).
thf(f17385,plain,
( spl8_480
| ~ spl8_45
| ~ spl8_95 ),
inference(avatar_split_clause,[],[f3756,f2808,f2184,f17383]) ).
thf(f17383,plain,
( spl8_480
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_480])]) ).
thf(f2184,plain,
( spl8_45
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).
thf(f3756,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))) = X0 )
| ~ spl8_45
| ~ spl8_95 ),
inference(superposition,[],[f2185,f2809]) ).
thf(f2185,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X1 )
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f2184]) ).
thf(f17381,plain,
( spl8_479
| ~ spl8_40
| ~ spl8_95 ),
inference(avatar_split_clause,[],[f3747,f2808,f2164,f17379]) ).
thf(f17379,plain,
( spl8_479
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_479])]) ).
thf(f2164,plain,
( spl8_40
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).
thf(f3747,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) = X0 )
| ~ spl8_40
| ~ spl8_95 ),
inference(superposition,[],[f2809,f2165]) ).
thf(f2165,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) = X0 )
| ~ spl8_40 ),
inference(avatar_component_clause,[],[f2164]) ).
thf(f17377,plain,
( spl8_478
| ~ spl8_48
| ~ spl8_94 ),
inference(avatar_split_clause,[],[f3695,f2804,f2249,f17375]) ).
thf(f17375,plain,
( spl8_478
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_478])]) ).
thf(f3695,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
| ~ spl8_48
| ~ spl8_94 ),
inference(forward_demodulation,[],[f3662,f2250]) ).
thf(f3662,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),vAPP(real,real,uminus_uminus_real,X1))) )
| ~ spl8_48
| ~ spl8_94 ),
inference(superposition,[],[f2805,f2250]) ).
thf(f17373,plain,
( spl8_477
| ~ spl8_41
| ~ spl8_94 ),
inference(avatar_split_clause,[],[f3673,f2804,f2168,f17371]) ).
thf(f17371,plain,
( spl8_477
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_477])]) ).
thf(f3673,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) = X2 )
| ~ spl8_41
| ~ spl8_94 ),
inference(superposition,[],[f2169,f2805]) ).
thf(f17369,plain,
( spl8_476
| ~ spl8_41
| ~ spl8_94 ),
inference(avatar_split_clause,[],[f3655,f2804,f2168,f17367]) ).
thf(f17367,plain,
( spl8_476
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_476])]) ).
thf(f3655,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ~ spl8_41
| ~ spl8_94 ),
inference(superposition,[],[f2805,f2169]) ).
thf(f17365,plain,
( spl8_475
| ~ spl8_44
| ~ spl8_93 ),
inference(avatar_split_clause,[],[f3621,f2800,f2180,f17363]) ).
thf(f17363,plain,
( spl8_475
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_475])]) ).
thf(f2180,plain,
( spl8_44
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).
thf(f2800,plain,
( spl8_93
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_93])]) ).
thf(f3621,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1))),X2) )
| ~ spl8_44
| ~ spl8_93 ),
inference(superposition,[],[f2181,f2801]) ).
thf(f2801,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ~ spl8_93 ),
inference(avatar_component_clause,[],[f2800]) ).
thf(f2181,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X1) = X0 )
| ~ spl8_44 ),
inference(avatar_component_clause,[],[f2180]) ).
thf(f17314,plain,
( spl8_474
| ~ spl8_44
| ~ spl8_92 ),
inference(avatar_split_clause,[],[f3572,f2796,f2180,f17312]) ).
thf(f17312,plain,
( spl8_474
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_474])]) ).
thf(f2796,plain,
( spl8_92
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_92])]) ).
thf(f3572,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1))),X2) )
| ~ spl8_44
| ~ spl8_92 ),
inference(superposition,[],[f2181,f2797]) ).
thf(f2797,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),X1) )
| ~ spl8_92 ),
inference(avatar_component_clause,[],[f2796]) ).
thf(f17310,plain,
( spl8_473
| ~ spl8_46
| ~ spl8_92 ),
inference(avatar_split_clause,[],[f3571,f2796,f2188,f17308]) ).
thf(f17308,plain,
( spl8_473
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_473])]) ).
thf(f2188,plain,
( spl8_46
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).
thf(f3571,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1))) )
| ~ spl8_46
| ~ spl8_92 ),
inference(superposition,[],[f2189,f2797]) ).
thf(f2189,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) = X1 )
| ~ spl8_46 ),
inference(avatar_component_clause,[],[f2188]) ).
thf(f17306,plain,
( spl8_472
| ~ spl8_91
| ~ spl8_92 ),
inference(avatar_split_clause,[],[f3565,f2796,f2792,f17304]) ).
thf(f17304,plain,
( spl8_472
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_472])]) ).
thf(f2792,plain,
( spl8_91
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_91])]) ).
thf(f3565,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ~ spl8_91
| ~ spl8_92 ),
inference(superposition,[],[f2797,f2793]) ).
thf(f2793,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) )
| ~ spl8_91 ),
inference(avatar_component_clause,[],[f2792]) ).
thf(f17302,plain,
( spl8_471
| ~ spl8_43
| ~ spl8_92 ),
inference(avatar_split_clause,[],[f3555,f2796,f2176,f17300]) ).
thf(f17300,plain,
( spl8_471
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_471])]) ).
thf(f3555,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0)) )
| ~ spl8_43
| ~ spl8_92 ),
inference(superposition,[],[f2797,f2177]) ).
thf(f17298,plain,
( spl8_470
| ~ spl8_44
| ~ spl8_91 ),
inference(avatar_split_clause,[],[f3535,f2792,f2180,f17296]) ).
thf(f17296,plain,
( spl8_470
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_470])]) ).
thf(f3535,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2))),X2) )
| ~ spl8_44
| ~ spl8_91 ),
inference(superposition,[],[f2181,f2793]) ).
thf(f17294,plain,
( spl8_469
| ~ spl8_46
| ~ spl8_91 ),
inference(avatar_split_clause,[],[f3534,f2792,f2188,f17292]) ).
thf(f17292,plain,
( spl8_469
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_469])]) ).
thf(f3534,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2))) )
| ~ spl8_46
| ~ spl8_91 ),
inference(superposition,[],[f2189,f2793]) ).
thf(f17290,plain,
( spl8_468
| ~ spl8_42
| ~ spl8_91 ),
inference(avatar_split_clause,[],[f3522,f2792,f2172,f17288]) ).
thf(f17288,plain,
( spl8_468
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_468])]) ).
thf(f2172,plain,
( spl8_42
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
thf(f3522,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) )
| ~ spl8_42
| ~ spl8_91 ),
inference(superposition,[],[f2793,f2173]) ).
thf(f2173,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) = X0 )
| ~ spl8_42 ),
inference(avatar_component_clause,[],[f2172]) ).
thf(f17286,plain,
( spl8_467
| ~ spl8_43
| ~ spl8_90 ),
inference(avatar_split_clause,[],[f3475,f2788,f2176,f17284]) ).
thf(f17284,plain,
( spl8_467
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_467])]) ).
thf(f2788,plain,
( spl8_90
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).
thf(f3475,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = X2 )
| ~ spl8_43
| ~ spl8_90 ),
inference(superposition,[],[f2177,f2789]) ).
thf(f2789,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) )
| ~ spl8_90 ),
inference(avatar_component_clause,[],[f2788]) ).
thf(f17282,plain,
( spl8_466
| ~ spl8_46
| ~ spl8_51
| ~ spl8_53
| ~ spl8_89 ),
inference(avatar_split_clause,[],[f3399,f2784,f2272,f2264,f2188,f17280]) ).
thf(f17280,plain,
( spl8_466
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_466])]) ).
thf(f2784,plain,
( spl8_89
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_89])]) ).
thf(f3399,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1))) )
| ~ spl8_46
| ~ spl8_51
| ~ spl8_53
| ~ spl8_89 ),
inference(forward_demodulation,[],[f3342,f2375]) ).
thf(f2375,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) )
| ~ spl8_51
| ~ spl8_53 ),
inference(superposition,[],[f2265,f2273]) ).
thf(f3342,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0))) )
| ~ spl8_46
| ~ spl8_89 ),
inference(superposition,[],[f2785,f2189]) ).
thf(f2785,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ~ spl8_89 ),
inference(avatar_component_clause,[],[f2784]) ).
thf(f17278,plain,
( spl8_465
| ~ spl8_43
| ~ spl8_89 ),
inference(avatar_split_clause,[],[f3374,f2784,f2176,f17276]) ).
thf(f17276,plain,
( spl8_465
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_465])]) ).
thf(f3374,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2))),X0) )
| ~ spl8_43
| ~ spl8_89 ),
inference(superposition,[],[f2177,f2785]) ).
thf(f17274,plain,
( spl8_464
| ~ spl8_11
| ~ spl8_22
| ~ spl8_400 ),
inference(avatar_split_clause,[],[f16340,f13510,f2057,f2012,f17271]) ).
thf(f17271,plain,
( spl8_464
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),i2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_464])]) ).
thf(f2012,plain,
( spl8_11
<=> ! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
thf(f2057,plain,
( spl8_22
<=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,i1),i2) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
thf(f13510,plain,
( spl8_400
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_400])]) ).
thf(f16340,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),i2) )
| ~ spl8_11
| ~ spl8_22
| ~ spl8_400 ),
inference(forward_demodulation,[],[f16308,f2013]) ).
thf(f2013,plain,
( ! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f2012]) ).
thf(f16308,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),i1)),i2) )
| ~ spl8_22
| ~ spl8_400 ),
inference(trivial_inequality_removal,[],[f16241]) ).
thf(f16241,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),i1)),i2) )
| ~ spl8_22
| ~ spl8_400 ),
inference(superposition,[],[f13511,f2059]) ).
thf(f2059,plain,
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,i1),i2) = $true )
| ~ spl8_22 ),
inference(avatar_component_clause,[],[f2057]) ).
thf(f13511,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),X1) ) )
| ~ spl8_400 ),
inference(avatar_component_clause,[],[f13510]) ).
thf(f17269,plain,
( spl8_463
| ~ spl8_42
| ~ spl8_89 ),
inference(avatar_split_clause,[],[f3373,f2784,f2172,f17267]) ).
thf(f17267,plain,
( spl8_463
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_463])]) ).
thf(f3373,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = X0 )
| ~ spl8_42
| ~ spl8_89 ),
inference(superposition,[],[f2173,f2785]) ).
thf(f17265,plain,
( spl8_462
| ~ spl8_39
| ~ spl8_87 ),
inference(avatar_split_clause,[],[f3308,f2775,f2160,f17263]) ).
thf(f17263,plain,
( spl8_462
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_462])]) ).
thf(f2160,plain,
( spl8_39
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).
thf(f2775,plain,
( spl8_87
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_87])]) ).
thf(f3308,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1))),X2) )
| ~ spl8_39
| ~ spl8_87 ),
inference(superposition,[],[f2161,f2776]) ).
thf(f2776,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),X1) )
| ~ spl8_87 ),
inference(avatar_component_clause,[],[f2775]) ).
thf(f2161,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X1) = X0 )
| ~ spl8_39 ),
inference(avatar_component_clause,[],[f2160]) ).
thf(f17261,plain,
( spl8_461
| ~ spl8_86
| ~ spl8_87 ),
inference(avatar_split_clause,[],[f3301,f2775,f2771,f17259]) ).
thf(f17259,plain,
( spl8_461
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_461])]) ).
thf(f2771,plain,
( spl8_86
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
thf(f3301,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
| ~ spl8_86
| ~ spl8_87 ),
inference(superposition,[],[f2776,f2772]) ).
thf(f2772,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) )
| ~ spl8_86 ),
inference(avatar_component_clause,[],[f2771]) ).
thf(f17257,plain,
( spl8_460
| ~ spl8_41
| ~ spl8_87 ),
inference(avatar_split_clause,[],[f3290,f2775,f2168,f17255]) ).
thf(f17255,plain,
( spl8_460
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_460])]) ).
thf(f3290,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)) )
| ~ spl8_41
| ~ spl8_87 ),
inference(superposition,[],[f2776,f2169]) ).
thf(f17253,plain,
( spl8_459
| ~ spl8_39
| ~ spl8_86 ),
inference(avatar_split_clause,[],[f3264,f2771,f2160,f17251]) ).
thf(f17251,plain,
( spl8_459
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_459])]) ).
thf(f3264,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2))),X2) )
| ~ spl8_39
| ~ spl8_86 ),
inference(superposition,[],[f2161,f2772]) ).
thf(f17249,plain,
( spl8_458
| ~ spl8_45
| ~ spl8_86 ),
inference(avatar_split_clause,[],[f3263,f2771,f2184,f17247]) ).
thf(f17247,plain,
( spl8_458
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_458])]) ).
thf(f3263,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2))) )
| ~ spl8_45
| ~ spl8_86 ),
inference(superposition,[],[f2185,f2772]) ).
thf(f17245,plain,
( spl8_457
| ~ spl8_40
| ~ spl8_86 ),
inference(avatar_split_clause,[],[f3250,f2771,f2164,f17243]) ).
thf(f17243,plain,
( spl8_457
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_457])]) ).
thf(f3250,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) )
| ~ spl8_40
| ~ spl8_86 ),
inference(superposition,[],[f2772,f2165]) ).
thf(f17241,plain,
( spl8_456
| ~ spl8_45
| ~ spl8_84
| ~ spl8_86 ),
inference(avatar_split_clause,[],[f3231,f2771,f2763,f2184,f17239]) ).
thf(f17239,plain,
( spl8_456
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_456])]) ).
thf(f2763,plain,
( spl8_84
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).
thf(f3231,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))) )
| ~ spl8_45
| ~ spl8_84
| ~ spl8_86 ),
inference(forward_demodulation,[],[f3201,f2772]) ).
thf(f3201,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),X2)) )
| ~ spl8_45
| ~ spl8_84 ),
inference(superposition,[],[f2764,f2185]) ).
thf(f2764,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ~ spl8_84 ),
inference(avatar_component_clause,[],[f2763]) ).
thf(f17237,plain,
( spl8_455
| ~ spl8_39
| ~ spl8_84 ),
inference(avatar_split_clause,[],[f3219,f2763,f2160,f17235]) ).
thf(f17235,plain,
( spl8_455
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_455])]) ).
thf(f3219,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),X2) )
| ~ spl8_39
| ~ spl8_84 ),
inference(superposition,[],[f2161,f2764]) ).
thf(f17233,plain,
( spl8_454
| ~ spl8_39
| ~ spl8_84 ),
inference(avatar_split_clause,[],[f3196,f2763,f2160,f17231]) ).
thf(f17231,plain,
( spl8_454
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_454])]) ).
thf(f3196,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ~ spl8_39
| ~ spl8_84 ),
inference(superposition,[],[f2764,f2161]) ).
thf(f17227,plain,
( spl8_453
| ~ spl8_41
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f3152,f2759,f2168,f17225]) ).
thf(f17225,plain,
( spl8_453
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2))),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_453])]) ).
thf(f2759,plain,
( spl8_83
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).
thf(f3152,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2))),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = X2 )
| ~ spl8_41
| ~ spl8_83 ),
inference(superposition,[],[f2169,f2760]) ).
thf(f2760,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) )
| ~ spl8_83 ),
inference(avatar_component_clause,[],[f2759]) ).
thf(f17222,plain,
( spl8_452
| ~ spl8_39
| ~ spl8_41
| ~ spl8_82 ),
inference(avatar_split_clause,[],[f3103,f2755,f2168,f2160,f17220]) ).
thf(f17220,plain,
( spl8_452
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_452])]) ).
thf(f2755,plain,
( spl8_82
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).
thf(f3103,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)))) = X0 )
| ~ spl8_39
| ~ spl8_41
| ~ spl8_82 ),
inference(forward_demodulation,[],[f3048,f2209]) ).
thf(f2209,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
| ~ spl8_39
| ~ spl8_41 ),
inference(superposition,[],[f2161,f2169]) ).
thf(f3048,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2))),X2)) = X0 )
| ~ spl8_39
| ~ spl8_82 ),
inference(superposition,[],[f2756,f2161]) ).
thf(f2756,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ~ spl8_82 ),
inference(avatar_component_clause,[],[f2755]) ).
thf(f17218,plain,
( spl8_451
| ~ spl8_41
| ~ spl8_82 ),
inference(avatar_split_clause,[],[f3073,f2755,f2168,f17216]) ).
thf(f17216,plain,
( spl8_451
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_451])]) ).
thf(f3073,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))),X0) )
| ~ spl8_41
| ~ spl8_82 ),
inference(superposition,[],[f2169,f2756]) ).
thf(f17214,plain,
( spl8_450
| ~ spl8_40
| ~ spl8_82 ),
inference(avatar_split_clause,[],[f3072,f2755,f2164,f17212]) ).
thf(f17212,plain,
( spl8_450
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_450])]) ).
thf(f3072,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = X0 )
| ~ spl8_40
| ~ spl8_82 ),
inference(superposition,[],[f2165,f2756]) ).
thf(f17210,plain,
( spl8_449
| ~ spl8_45
| ~ spl8_82 ),
inference(avatar_split_clause,[],[f3039,f2755,f2184,f17208]) ).
thf(f17208,plain,
( spl8_449
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_449])]) ).
thf(f3039,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))) )
| ~ spl8_45
| ~ spl8_82 ),
inference(superposition,[],[f2756,f2185]) ).
thf(f17206,plain,
( spl8_448
| ~ spl8_51
| ~ spl8_55
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f3025,f2751,f2280,f2264,f17204]) ).
thf(f17204,plain,
( spl8_448
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_448])]) ).
thf(f2280,plain,
( spl8_55
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
thf(f2751,plain,
( spl8_81
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_81])]) ).
thf(f3025,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),X1) )
| ~ spl8_51
| ~ spl8_55
| ~ spl8_81 ),
inference(forward_demodulation,[],[f2998,f2265]) ).
thf(f2998,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,uminus_uminus_a,X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),X1) )
| ~ spl8_55
| ~ spl8_81 ),
inference(superposition,[],[f2752,f2281]) ).
thf(f2281,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = X1 )
| ~ spl8_55 ),
inference(avatar_component_clause,[],[f2280]) ).
thf(f2752,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ~ spl8_81 ),
inference(avatar_component_clause,[],[f2751]) ).
thf(f17202,plain,
( spl8_447
| ~ spl8_46
| ~ spl8_51
| ~ spl8_53
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f3024,f2751,f2272,f2264,f2188,f17200]) ).
thf(f17200,plain,
( spl8_447
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_447])]) ).
thf(f3024,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1))),X1) )
| ~ spl8_46
| ~ spl8_51
| ~ spl8_53
| ~ spl8_81 ),
inference(forward_demodulation,[],[f2997,f2375]) ).
thf(f2997,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0))),X1) )
| ~ spl8_46
| ~ spl8_81 ),
inference(superposition,[],[f2752,f2189]) ).
thf(f17198,plain,
( spl8_446
| ~ spl8_50
| ~ spl8_51
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f3022,f2751,f2264,f2260,f17196]) ).
thf(f17196,plain,
( spl8_446
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_446])]) ).
thf(f2260,plain,
( spl8_50
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
thf(f3022,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) )
| ~ spl8_50
| ~ spl8_51
| ~ spl8_81 ),
inference(forward_demodulation,[],[f2994,f2265]) ).
thf(f2994,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,uminus_uminus_a,X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) )
| ~ spl8_50
| ~ spl8_81 ),
inference(superposition,[],[f2752,f2261]) ).
thf(f2261,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) )
| ~ spl8_50 ),
inference(avatar_component_clause,[],[f2260]) ).
thf(f17194,plain,
( spl8_445
| ~ spl8_46
| ~ spl8_51
| ~ spl8_53
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f3014,f2751,f2272,f2264,f2188,f17192]) ).
thf(f17192,plain,
( spl8_445
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_445])]) ).
thf(f3014,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1))) )
| ~ spl8_46
| ~ spl8_51
| ~ spl8_53
| ~ spl8_81 ),
inference(forward_demodulation,[],[f2987,f2375]) ).
thf(f2987,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0))) )
| ~ spl8_46
| ~ spl8_81 ),
inference(superposition,[],[f2752,f2189]) ).
thf(f17190,plain,
( spl8_444
| ~ spl8_44
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f3009,f2751,f2180,f17188]) ).
thf(f17188,plain,
( spl8_444
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_444])]) ).
thf(f3009,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ~ spl8_44
| ~ spl8_81 ),
inference(superposition,[],[f2181,f2752]) ).
thf(f17130,plain,
( spl8_443
| ~ spl8_46
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f3008,f2751,f2188,f17128]) ).
thf(f17128,plain,
( spl8_443
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_443])]) ).
thf(f3008,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)) )
| ~ spl8_46
| ~ spl8_81 ),
inference(superposition,[],[f2189,f2752]) ).
thf(f17126,plain,
( spl8_442
| ~ spl8_44
| ~ spl8_51
| ~ spl8_53
| ~ spl8_80
| ~ spl8_96 ),
inference(avatar_split_clause,[],[f2971,f2816,f2747,f2272,f2264,f2180,f17124]) ).
thf(f17124,plain,
( spl8_442
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_442])]) ).
thf(f2747,plain,
( spl8_80
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_80])]) ).
thf(f2816,plain,
( spl8_96
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_96])]) ).
thf(f2971,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2))),X0) )
| ~ spl8_44
| ~ spl8_51
| ~ spl8_53
| ~ spl8_80
| ~ spl8_96 ),
inference(forward_demodulation,[],[f2945,f2819]) ).
thf(f2819,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) )
| ~ spl8_51
| ~ spl8_53
| ~ spl8_96 ),
inference(forward_demodulation,[],[f2817,f2375]) ).
thf(f2817,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1)) )
| ~ spl8_96 ),
inference(avatar_component_clause,[],[f2816]) ).
thf(f2945,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2)),X0) )
| ~ spl8_44
| ~ spl8_80 ),
inference(superposition,[],[f2748,f2181]) ).
thf(f2748,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ~ spl8_80 ),
inference(avatar_component_clause,[],[f2747]) ).
thf(f17122,plain,
( spl8_441
| ~ spl8_50
| ~ spl8_55
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f2965,f2747,f2280,f2260,f17120]) ).
thf(f17120,plain,
( spl8_441
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_441])]) ).
thf(f2965,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) )
| ~ spl8_50
| ~ spl8_55
| ~ spl8_80 ),
inference(forward_demodulation,[],[f2940,f2261]) ).
thf(f2940,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X2)) )
| ~ spl8_55
| ~ spl8_80 ),
inference(superposition,[],[f2748,f2281]) ).
thf(f17118,plain,
( spl8_440
| ~ spl8_50
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f2962,f2747,f2260,f17116]) ).
thf(f17116,plain,
( spl8_440
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_440])]) ).
thf(f2962,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) )
| ~ spl8_50
| ~ spl8_80 ),
inference(forward_demodulation,[],[f2936,f2261]) ).
thf(f2936,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X2)) )
| ~ spl8_50
| ~ spl8_80 ),
inference(superposition,[],[f2748,f2261]) ).
thf(f17114,plain,
( spl8_439
| ~ spl8_44
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f2959,f2747,f2180,f17112]) ).
thf(f17112,plain,
( spl8_439
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_439])]) ).
thf(f2959,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ~ spl8_44
| ~ spl8_80 ),
inference(superposition,[],[f2181,f2748]) ).
thf(f17110,plain,
( spl8_438
| ~ spl8_46
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f2958,f2747,f2188,f17108]) ).
thf(f17108,plain,
( spl8_438
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_438])]) ).
thf(f2958,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ~ spl8_46
| ~ spl8_80 ),
inference(superposition,[],[f2189,f2748]) ).
thf(f17106,plain,
( spl8_437
| ~ spl8_49
| ~ spl8_54
| ~ spl8_79
| ~ spl8_95 ),
inference(avatar_split_clause,[],[f2914,f2808,f2743,f2276,f2256,f17104]) ).
thf(f17104,plain,
( spl8_437
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_437])]) ).
thf(f2256,plain,
( spl8_49
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
thf(f2276,plain,
( spl8_54
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
thf(f2743,plain,
( spl8_79
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_79])]) ).
thf(f2914,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)) )
| ~ spl8_49
| ~ spl8_54
| ~ spl8_79
| ~ spl8_95 ),
inference(forward_demodulation,[],[f2913,f2809]) ).
thf(f2913,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ~ spl8_49
| ~ spl8_54
| ~ spl8_79 ),
inference(forward_demodulation,[],[f2886,f2257]) ).
thf(f2257,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) )
| ~ spl8_49 ),
inference(avatar_component_clause,[],[f2256]) ).
thf(f2886,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X2)) )
| ~ spl8_54
| ~ spl8_79 ),
inference(superposition,[],[f2744,f2277]) ).
thf(f2277,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = X1 )
| ~ spl8_54 ),
inference(avatar_component_clause,[],[f2276]) ).
thf(f2744,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ~ spl8_79 ),
inference(avatar_component_clause,[],[f2743]) ).
thf(f17102,plain,
( spl8_436
| ~ spl8_49
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f2910,f2743,f2256,f17100]) ).
thf(f17100,plain,
( spl8_436
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_436])]) ).
thf(f2910,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ~ spl8_49
| ~ spl8_79 ),
inference(forward_demodulation,[],[f2882,f2257]) ).
thf(f2882,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X2)) )
| ~ spl8_49
| ~ spl8_79 ),
inference(superposition,[],[f2744,f2257]) ).
thf(f17098,plain,
( spl8_435
| ~ spl8_39
| ~ spl8_79
| ~ spl8_94 ),
inference(avatar_split_clause,[],[f2909,f2804,f2743,f2160,f17096]) ).
thf(f17096,plain,
( spl8_435
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_435])]) ).
thf(f2909,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))) )
| ~ spl8_39
| ~ spl8_79
| ~ spl8_94 ),
inference(forward_demodulation,[],[f2881,f2805]) ).
thf(f2881,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2)) )
| ~ spl8_39
| ~ spl8_79 ),
inference(superposition,[],[f2744,f2161]) ).
thf(f17094,plain,
( spl8_434
| ~ spl8_39
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f2907,f2743,f2160,f17092]) ).
thf(f17092,plain,
( spl8_434
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_434])]) ).
thf(f2907,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ~ spl8_39
| ~ spl8_79 ),
inference(superposition,[],[f2161,f2744]) ).
thf(f17090,plain,
( spl8_433
| ~ spl8_2
| spl8_415 ),
inference(avatar_split_clause,[],[f17045,f16890,f1942,f17087]) ).
thf(f1942,plain,
( spl8_2
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
thf(f17045,plain,
( ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_2
| spl8_415 ),
inference(trivial_inequality_removal,[],[f17044]) ).
thf(f17044,plain,
( ( $true != $true )
| ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_2
| spl8_415 ),
inference(superposition,[],[f16891,f1943]) ).
thf(f1943,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f1942]) ).
thf(f16891,plain,
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),ss)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| spl8_415 ),
inference(avatar_component_clause,[],[f16890]) ).
thf(f17085,plain,
( spl8_432
| ~ spl8_45
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f2906,f2743,f2184,f17083]) ).
thf(f17083,plain,
( spl8_432
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_432])]) ).
thf(f2906,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ~ spl8_45
| ~ spl8_79 ),
inference(superposition,[],[f2185,f2744]) ).
thf(f17081,plain,
( spl8_431
| ~ spl8_48
| ~ spl8_54
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f2873,f2739,f2276,f2249,f17079]) ).
thf(f17079,plain,
( spl8_431
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_431])]) ).
thf(f2739,plain,
( spl8_78
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
thf(f2873,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))),X1) )
| ~ spl8_48
| ~ spl8_54
| ~ spl8_78 ),
inference(forward_demodulation,[],[f2849,f2250]) ).
thf(f2849,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),vAPP(real,real,uminus_uminus_real,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))),X1) )
| ~ spl8_54
| ~ spl8_78 ),
inference(superposition,[],[f2740,f2277]) ).
thf(f2740,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
| ~ spl8_78 ),
inference(avatar_component_clause,[],[f2739]) ).
thf(f17077,plain,
( spl8_430
| ~ spl8_48
| ~ spl8_49
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f2871,f2739,f2256,f2249,f17075]) ).
thf(f17075,plain,
( spl8_430
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_430])]) ).
thf(f2871,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) )
| ~ spl8_48
| ~ spl8_49
| ~ spl8_78 ),
inference(forward_demodulation,[],[f2845,f2250]) ).
thf(f2845,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),vAPP(real,real,uminus_uminus_real,X0)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) )
| ~ spl8_49
| ~ spl8_78 ),
inference(superposition,[],[f2740,f2257]) ).
thf(f17073,plain,
( spl8_429
| ~ spl8_39
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f2858,f2739,f2160,f17071]) ).
thf(f17071,plain,
( spl8_429
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_429])]) ).
thf(f2858,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
| ~ spl8_39
| ~ spl8_78 ),
inference(superposition,[],[f2161,f2740]) ).
thf(f17069,plain,
( spl8_428
| ~ spl8_45
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f2857,f2739,f2184,f17067]) ).
thf(f17067,plain,
( spl8_428
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_428])]) ).
thf(f2857,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)) )
| ~ spl8_45
| ~ spl8_78 ),
inference(superposition,[],[f2185,f2740]) ).
thf(f17065,plain,
( spl8_427
| ~ spl8_45
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f2848,f2739,f2184,f17063]) ).
thf(f17063,plain,
( spl8_427
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_427])]) ).
thf(f2848,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),X1) )
| ~ spl8_45
| ~ spl8_78 ),
inference(superposition,[],[f2740,f2185]) ).
thf(f17061,plain,
( spl8_426
| ~ spl8_45
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f2838,f2739,f2184,f17059]) ).
thf(f17059,plain,
( spl8_426
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_426])]) ).
thf(f2838,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))) )
| ~ spl8_45
| ~ spl8_78 ),
inference(superposition,[],[f2740,f2185]) ).
thf(f17057,plain,
( spl8_425
| ~ spl8_2
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f2830,f2735,f1942,f17055]) ).
thf(f17055,plain,
( spl8_425
<=> ! [X0: a] :
( ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_425])]) ).
thf(f2735,plain,
( spl8_77
<=> ! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_77])]) ).
thf(f2830,plain,
( ! [X0: a] :
( ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) )
| ~ spl8_2
| ~ spl8_77 ),
inference(trivial_inequality_removal,[],[f2829]) ).
thf(f2829,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) )
| ~ spl8_2
| ~ spl8_77 ),
inference(superposition,[],[f2736,f1943]) ).
thf(f2736,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true ) )
| ~ spl8_77 ),
inference(avatar_component_clause,[],[f2735]) ).
thf(f17053,plain,
( spl8_424
| ~ spl8_2
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f2826,f2731,f1942,f17051]) ).
thf(f17051,plain,
( spl8_424
<=> ! [X0: a] :
( ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_424])]) ).
thf(f2731,plain,
( spl8_76
<=> ! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_76])]) ).
thf(f2826,plain,
( ! [X0: a] :
( ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) )
| ~ spl8_2
| ~ spl8_76 ),
inference(trivial_inequality_removal,[],[f2825]) ).
thf(f2825,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) )
| ~ spl8_2
| ~ spl8_76 ),
inference(superposition,[],[f2732,f1943]) ).
thf(f2732,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real ) )
| ~ spl8_76 ),
inference(avatar_component_clause,[],[f2731]) ).
thf(f17049,plain,
( spl8_423
| ~ spl8_2
| ~ spl8_75 ),
inference(avatar_split_clause,[],[f2822,f2727,f1942,f17047]) ).
thf(f17047,plain,
( spl8_423
<=> ! [X0: a] :
( ( vAPP(a,a,f,X0) != zero_zero_a )
| ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_423])]) ).
thf(f2727,plain,
( spl8_75
<=> ! [X0: a] :
( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_75])]) ).
thf(f2822,plain,
( ! [X0: a] :
( ( vAPP(a,a,f,X0) != zero_zero_a )
| ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) )
| ~ spl8_2
| ~ spl8_75 ),
inference(trivial_inequality_removal,[],[f2821]) ).
thf(f2821,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) )
| ~ spl8_2
| ~ spl8_75 ),
inference(superposition,[],[f2728,f1943]) ).
thf(f2728,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) ) )
| ~ spl8_75 ),
inference(avatar_component_clause,[],[f2727]) ).
thf(f17043,plain,
( spl8_422
| ~ spl8_51
| ~ spl8_53
| ~ spl8_55 ),
inference(avatar_split_clause,[],[f2421,f2280,f2272,f2264,f17041]) ).
thf(f17041,plain,
( spl8_422
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_422])]) ).
thf(f2421,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2))) = X2 )
| ~ spl8_51
| ~ spl8_53
| ~ spl8_55 ),
inference(forward_demodulation,[],[f2420,f2375]) ).
thf(f2420,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1))) = X2 )
| ~ spl8_53
| ~ spl8_55 ),
inference(forward_demodulation,[],[f2405,f1906]) ).
thf(f1906,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1)) ),
inference(forward_demodulation,[],[f1389,f1381]) ).
thf(f1381,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) ),
inference(cnf_transformation,[],[f865]) ).
thf(f865,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) ),
inference(rectify,[],[f335]) ).
thf(f335,axiom,
! [X8: a,X9: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X9),X18)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_add__diff__eq) ).
thf(f1389,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) ),
inference(cnf_transformation,[],[f873]) ).
thf(f873,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) ),
inference(rectify,[],[f331]) ).
thf(f331,axiom,
! [X8: a,X9: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9)),X18) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X18)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_diff__add__eq) ).
thf(f2405,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2)) = X2 )
| ~ spl8_53
| ~ spl8_55 ),
inference(superposition,[],[f2281,f2273]) ).
thf(f17039,plain,
( spl8_421
| ~ spl8_52
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f2398,f2276,f2268,f17037]) ).
thf(f17037,plain,
( spl8_421
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_421])]) ).
thf(f2398,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1))) = X2 )
| ~ spl8_52
| ~ spl8_54 ),
inference(forward_demodulation,[],[f2383,f1902]) ).
thf(f1902,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) ),
inference(forward_demodulation,[],[f1374,f1373]) ).
thf(f1373,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ),
inference(cnf_transformation,[],[f857]) ).
thf(f857,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ),
inference(rectify,[],[f336]) ).
thf(f336,axiom,
! [X8: real,X9: real,X18: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X9),X18)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_add__diff__eq) ).
thf(f1374,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),X1) ),
inference(cnf_transformation,[],[f858]) ).
thf(f858,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),X1) ),
inference(rectify,[],[f332]) ).
thf(f332,axiom,
! [X8: real,X9: real,X18: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9)),X18) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X18)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_diff__add__eq) ).
thf(f2383,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2)) = X2 )
| ~ spl8_52
| ~ spl8_54 ),
inference(superposition,[],[f2277,f2269]) ).
thf(f17035,plain,
( spl8_420
| ~ spl8_50
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f2376,f2272,f2260,f17033]) ).
thf(f17033,plain,
( spl8_420
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_420])]) ).
thf(f2376,plain,
( ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),X2) )
| ~ spl8_50
| ~ spl8_53 ),
inference(superposition,[],[f2261,f2273]) ).
thf(f17031,plain,
( spl8_419
| ~ spl8_51
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f2375,f2272,f2264,f17029]) ).
thf(f17029,plain,
( spl8_419
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_419])]) ).
thf(f17027,plain,
( spl8_418
| ~ spl8_49
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f2362,f2268,f2256,f17025]) ).
thf(f17025,plain,
( spl8_418
<=> ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_418])]) ).
thf(f2362,plain,
( ! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),X2) )
| ~ spl8_49
| ~ spl8_52 ),
inference(superposition,[],[f2257,f2269]) ).
thf(f16946,plain,
( spl8_417
| ~ spl8_21
| ~ spl8_156 ),
inference(avatar_split_clause,[],[f4579,f4571,f2052,f16943]) ).
thf(f16943,plain,
( spl8_417
<=> ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),xx),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_417])]) ).
thf(f2052,plain,
( spl8_21
<=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,xx),x) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
thf(f4571,plain,
( spl8_156
<=> ! [X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),zero_zero_real) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_156])]) ).
thf(f4579,plain,
( ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),xx),zero_zero_real) )
| ~ spl8_21
| ~ spl8_156 ),
inference(trivial_inequality_removal,[],[f4574]) ).
thf(f4574,plain,
( ( $true != $true )
| ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),xx),zero_zero_real) )
| ~ spl8_21
| ~ spl8_156 ),
inference(superposition,[],[f4572,f2054]) ).
thf(f2054,plain,
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,xx),x) = $true )
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f2052]) ).
thf(f4572,plain,
( ! [X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),zero_zero_real) = X1 ) )
| ~ spl8_156 ),
inference(avatar_component_clause,[],[f4571]) ).
thf(f16941,plain,
( spl8_416
| ~ spl8_21
| ~ spl8_137 ),
inference(avatar_split_clause,[],[f4380,f4368,f2052,f16938]) ).
thf(f16938,plain,
( spl8_416
<=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),xx)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_416])]) ).
thf(f4368,plain,
( spl8_137
<=> ! [X0: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_137])]) ).
thf(f4380,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),xx)) )
| ~ spl8_21
| ~ spl8_137 ),
inference(trivial_inequality_removal,[],[f4375]) ).
thf(f4375,plain,
( ( $true != $true )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),xx)) )
| ~ spl8_21
| ~ spl8_137 ),
inference(superposition,[],[f4369,f2054]) ).
thf(f4369,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ) )
| ~ spl8_137 ),
inference(avatar_component_clause,[],[f4368]) ).
thf(f16893,plain,
( spl8_415
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_161
| ~ spl8_177
| ~ spl8_189
| ~ spl8_206 ),
inference(avatar_split_clause,[],[f11620,f5509,f4950,f4737,f4605,f4581,f4550,f2515,f2510,f2249,f1998,f16890]) ).
thf(f16538,plain,
( spl8_414
| ~ spl8_29
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f4227,f3964,f2094,f16536]) ).
thf(f16536,plain,
( spl8_414
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_414])]) ).
thf(f2094,plain,
( spl8_29
<=> ! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,uminus_uminus_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
thf(f3964,plain,
( spl8_120
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_120])]) ).
thf(f4227,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ) )
| ~ spl8_29
| ~ spl8_120 ),
inference(superposition,[],[f3965,f2095]) ).
thf(f2095,plain,
( ! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,uminus_uminus_a,X0)) )
| ~ spl8_29 ),
inference(avatar_component_clause,[],[f2094]) ).
thf(f3965,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) ) )
| ~ spl8_120 ),
inference(avatar_component_clause,[],[f3964]) ).
thf(f16534,plain,
( spl8_413
| ~ spl8_29
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f4213,f3964,f2094,f16532]) ).
thf(f16532,plain,
( spl8_413
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_413])]) ).
thf(f4213,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),X1) ) )
| ~ spl8_29
| ~ spl8_120 ),
inference(superposition,[],[f3965,f2095]) ).
thf(f16530,plain,
( spl8_412
| ~ spl8_18
| ~ spl8_360 ),
inference(avatar_split_clause,[],[f13185,f13173,f2040,f16528]) ).
thf(f16528,plain,
( spl8_412
<=> ! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),xx) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_412])]) ).
thf(f2040,plain,
( spl8_18
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),zero_zero_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
thf(f13173,plain,
( spl8_360
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),xx) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_360])]) ).
thf(f13185,plain,
( ! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),xx) ) )
| ~ spl8_18
| ~ spl8_360 ),
inference(superposition,[],[f13174,f2041]) ).
thf(f2041,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),zero_zero_a) = X0 )
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f2040]) ).
thf(f13174,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),xx) ) )
| ~ spl8_360 ),
inference(avatar_component_clause,[],[f13173]) ).
thf(f16526,plain,
( spl8_411
| ~ spl8_30
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f4172,f3960,f2098,f16524]) ).
thf(f16524,plain,
( spl8_411
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_411])]) ).
thf(f2098,plain,
( spl8_30
<=> ! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
thf(f3960,plain,
( spl8_119
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_119])]) ).
thf(f4172,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ) )
| ~ spl8_30
| ~ spl8_119 ),
inference(superposition,[],[f3961,f2099]) ).
thf(f2099,plain,
( ! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X0) )
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f2098]) ).
thf(f3961,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X2) ) )
| ~ spl8_119 ),
inference(avatar_component_clause,[],[f3960]) ).
thf(f16522,plain,
( spl8_410
| ~ spl8_30
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f4158,f3960,f2098,f16520]) ).
thf(f16520,plain,
( spl8_410
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_410])]) ).
thf(f4158,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),X1) ) )
| ~ spl8_30
| ~ spl8_119 ),
inference(superposition,[],[f3961,f2099]) ).
thf(f16518,plain,
( spl8_409
| ~ spl8_32
| ~ spl8_118 ),
inference(avatar_split_clause,[],[f4133,f3956,f2106,f16516]) ).
thf(f16516,plain,
( spl8_409
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_409])]) ).
thf(f2106,plain,
( spl8_32
<=> ! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
thf(f3956,plain,
( spl8_118
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_118])]) ).
thf(f4133,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ) )
| ~ spl8_32
| ~ spl8_118 ),
inference(superposition,[],[f3957,f2107]) ).
thf(f2107,plain,
( ! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X0) )
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f2106]) ).
thf(f3957,plain,
( ! [X2: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) ) )
| ~ spl8_118 ),
inference(avatar_component_clause,[],[f3956]) ).
thf(f16514,plain,
( spl8_408
| ~ spl8_32
| ~ spl8_118 ),
inference(avatar_split_clause,[],[f4119,f3956,f2106,f16512]) ).
thf(f16512,plain,
( spl8_408
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_408])]) ).
thf(f4119,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X1) ) )
| ~ spl8_32
| ~ spl8_118 ),
inference(superposition,[],[f3957,f2107]) ).
thf(f16510,plain,
( spl8_407
| ~ spl8_31
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f4090,f3948,f2102,f16508]) ).
thf(f16508,plain,
( spl8_407
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_407])]) ).
thf(f2102,plain,
( spl8_31
<=> ! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
thf(f3948,plain,
( spl8_116
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_116])]) ).
thf(f4090,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ) )
| ~ spl8_31
| ~ spl8_116 ),
inference(superposition,[],[f3949,f2103]) ).
thf(f2103,plain,
( ! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,uminus_uminus_real,X0)) )
| ~ spl8_31 ),
inference(avatar_component_clause,[],[f2102]) ).
thf(f3949,plain,
( ! [X2: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) )
| ~ spl8_116 ),
inference(avatar_component_clause,[],[f3948]) ).
thf(f16506,plain,
( spl8_406
| ~ spl8_31
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f4076,f3948,f2102,f16504]) ).
thf(f16504,plain,
( spl8_406
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_406])]) ).
thf(f4076,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X1) ) )
| ~ spl8_31
| ~ spl8_116 ),
inference(superposition,[],[f3949,f2103]) ).
thf(f16502,plain,
( spl8_405
| ~ spl8_2
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f2721,f2717,f1942,f16500]) ).
thf(f16500,plain,
( spl8_405
<=> ! [X0: a] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK0,X0)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_405])]) ).
thf(f2717,plain,
( spl8_73
<=> ! [X0: a] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK0,X0)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).
thf(f2721,plain,
( ! [X0: a] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK0,X0)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $false ) )
| ~ spl8_2
| ~ spl8_73 ),
inference(trivial_inequality_removal,[],[f2720]) ).
thf(f2720,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK0,X0)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $false ) )
| ~ spl8_2
| ~ spl8_73 ),
inference(superposition,[],[f2718,f1943]) ).
thf(f2718,plain,
( ! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK0,X0)) ) )
| ~ spl8_73 ),
inference(avatar_component_clause,[],[f2717]) ).
thf(f16077,plain,
( spl8_404
| ~ spl8_15
| ~ spl8_349 ),
inference(avatar_split_clause,[],[f12965,f12957,f2028,f16075]) ).
thf(f16075,plain,
( spl8_404
<=> ! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_404])]) ).
thf(f2028,plain,
( spl8_15
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,zero_zero_a),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
thf(f12957,plain,
( spl8_349
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_349])]) ).
thf(f12965,plain,
( ! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),X0) ) )
| ~ spl8_15
| ~ spl8_349 ),
inference(superposition,[],[f12958,f2029]) ).
thf(f2029,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,zero_zero_a),X0) = X0 )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f2028]) ).
thf(f12958,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),X1) ) )
| ~ spl8_349 ),
inference(avatar_component_clause,[],[f12957]) ).
thf(f14235,plain,
( spl8_403
| ~ spl8_15
| ~ spl8_85
| ~ spl8_362 ),
inference(avatar_split_clause,[],[f13281,f13228,f2767,f2028,f14232]) ).
thf(f14232,plain,
( spl8_403
<=> ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),xx) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_403])]) ).
thf(f2767,plain,
( spl8_85
<=> ! [X0: a] : ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).
thf(f13228,plain,
( spl8_362
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),xx) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_362])]) ).
thf(f13281,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),xx) )
| ~ spl8_15
| ~ spl8_85
| ~ spl8_362 ),
inference(trivial_inequality_removal,[],[f13280]) ).
thf(f13280,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),xx) )
| ~ spl8_15
| ~ spl8_85
| ~ spl8_362 ),
inference(forward_demodulation,[],[f13231,f2768]) ).
thf(f2768,plain,
( ! [X0: a] : ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) )
| ~ spl8_85 ),
inference(avatar_component_clause,[],[f2767]) ).
thf(f13231,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),xx) ) )
| ~ spl8_15
| ~ spl8_362 ),
inference(superposition,[],[f13229,f2029]) ).
thf(f13229,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),xx) ) )
| ~ spl8_362 ),
inference(avatar_component_clause,[],[f13228]) ).
thf(f13729,plain,
( spl8_402
| ~ spl8_18
| ~ spl8_85
| ~ spl8_352 ),
inference(avatar_split_clause,[],[f13064,f13011,f2767,f2040,f13726]) ).
thf(f13726,plain,
( spl8_402
<=> ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),zero_zero_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_402])]) ).
thf(f13011,plain,
( spl8_352
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_352])]) ).
thf(f13064,plain,
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),zero_zero_a) )
| ~ spl8_18
| ~ spl8_85
| ~ spl8_352 ),
inference(trivial_inequality_removal,[],[f13063]) ).
thf(f13063,plain,
( ( $true = $false )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),zero_zero_a) )
| ~ spl8_18
| ~ spl8_85
| ~ spl8_352 ),
inference(forward_demodulation,[],[f13023,f2768]) ).
thf(f13023,plain,
( ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),zero_zero_a) ) )
| ~ spl8_18
| ~ spl8_352 ),
inference(superposition,[],[f13012,f2041]) ).
thf(f13012,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),X1) ) )
| ~ spl8_352 ),
inference(avatar_component_clause,[],[f13011]) ).
thf(f13516,plain,
( spl8_401
| ~ spl8_14
| ~ spl8_26
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f4533,f4420,f2077,f2024,f13514]) ).
thf(f13514,plain,
( spl8_401
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_401])]) ).
thf(f2024,plain,
( spl8_14
<=> ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
thf(f2077,plain,
( spl8_26
<=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),tt) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
thf(f4420,plain,
( spl8_146
<=> ! [X0: real,X3: real,X2: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_146])]) ).
thf(f4533,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_14
| ~ spl8_26
| ~ spl8_146 ),
inference(forward_demodulation,[],[f4526,f2025]) ).
thf(f2025,plain,
( ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real) = X0 )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f2024]) ).
thf(f4526,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),zero_zero_real)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_26
| ~ spl8_146 ),
inference(trivial_inequality_removal,[],[f4523]) ).
thf(f4523,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),zero_zero_real)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_26
| ~ spl8_146 ),
inference(superposition,[],[f4421,f2079]) ).
thf(f2079,plain,
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),tt) = $true )
| ~ spl8_26 ),
inference(avatar_component_clause,[],[f2077]) ).
thf(f4421,plain,
( ! [X2: real,X3: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_146 ),
inference(avatar_component_clause,[],[f4420]) ).
thf(f13512,plain,
( spl8_400
| ~ spl8_14
| ~ spl8_24
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f4532,f4420,f2067,f2024,f13510]) ).
thf(f2067,plain,
( spl8_24
<=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),i1) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
thf(f4532,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_14
| ~ spl8_24
| ~ spl8_146 ),
inference(forward_demodulation,[],[f4528,f2025]) ).
thf(f4528,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),zero_zero_real)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_24
| ~ spl8_146 ),
inference(trivial_inequality_removal,[],[f4521]) ).
thf(f4521,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),zero_zero_real)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_24
| ~ spl8_146 ),
inference(superposition,[],[f4421,f2069]) ).
thf(f2069,plain,
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),i1) = $true )
| ~ spl8_24 ),
inference(avatar_component_clause,[],[f2067]) ).
thf(f13508,plain,
( spl8_399
| ~ spl8_14
| ~ spl8_25
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f4531,f4420,f2072,f2024,f13506]) ).
thf(f13506,plain,
( spl8_399
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_399])]) ).
thf(f2072,plain,
( spl8_25
<=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),d) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
thf(f4531,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),X1) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_14
| ~ spl8_25
| ~ spl8_146 ),
inference(forward_demodulation,[],[f4529,f2025]) ).
thf(f4529,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),zero_zero_real)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_25
| ~ spl8_146 ),
inference(trivial_inequality_removal,[],[f4520]) ).
thf(f4520,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),zero_zero_real)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_25
| ~ spl8_146 ),
inference(superposition,[],[f4421,f2074]) ).
thf(f2074,plain,
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),d) = $true )
| ~ spl8_25 ),
inference(avatar_component_clause,[],[f2072]) ).
thf(f13504,plain,
( spl8_398
| ~ spl8_13
| ~ spl8_26
| ~ spl8_144 ),
inference(avatar_split_clause,[],[f4514,f4412,f2077,f2020,f13502]) ).
thf(f13502,plain,
( spl8_398
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),tt)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_398])]) ).
thf(f2020,plain,
( spl8_13
<=> ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
thf(f4412,plain,
( spl8_144
<=> ! [X0: real,X3: real,X2: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_144])]) ).
thf(f4514,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),tt)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_13
| ~ spl8_26
| ~ spl8_144 ),
inference(forward_demodulation,[],[f4507,f2021]) ).
thf(f2021,plain,
( ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real) = X0 )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f2020]) ).
thf(f4507,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),tt)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_26
| ~ spl8_144 ),
inference(trivial_inequality_removal,[],[f4504]) ).
thf(f4504,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),tt)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_26
| ~ spl8_144 ),
inference(superposition,[],[f4413,f2079]) ).
thf(f4413,plain,
( ! [X2: real,X3: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_144 ),
inference(avatar_component_clause,[],[f4412]) ).
thf(f13500,plain,
( spl8_397
| ~ spl8_13
| ~ spl8_24
| ~ spl8_144 ),
inference(avatar_split_clause,[],[f4513,f4412,f2067,f2020,f13498]) ).
thf(f13498,plain,
( spl8_397
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),i1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_397])]) ).
thf(f4513,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),i1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_13
| ~ spl8_24
| ~ spl8_144 ),
inference(forward_demodulation,[],[f4509,f2021]) ).
thf(f4509,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),i1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_24
| ~ spl8_144 ),
inference(trivial_inequality_removal,[],[f4502]) ).
thf(f4502,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),i1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_24
| ~ spl8_144 ),
inference(superposition,[],[f4413,f2069]) ).
thf(f13496,plain,
( spl8_396
| ~ spl8_13
| ~ spl8_25
| ~ spl8_144 ),
inference(avatar_split_clause,[],[f4512,f4412,f2072,f2020,f13494]) ).
thf(f13494,plain,
( spl8_396
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),d)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_396])]) ).
thf(f4512,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),d)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_13
| ~ spl8_25
| ~ spl8_144 ),
inference(forward_demodulation,[],[f4510,f2021]) ).
thf(f4510,plain,
( ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),d)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_25
| ~ spl8_144 ),
inference(trivial_inequality_removal,[],[f4501]) ).
thf(f4501,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),d)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_25
| ~ spl8_144 ),
inference(superposition,[],[f4413,f2074]) ).
thf(f13492,plain,
( spl8_395
| ~ spl8_25
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f4333,f4312,f2072,f13490]) ).
thf(f13490,plain,
( spl8_395
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_395])]) ).
thf(f4312,plain,
( spl8_130
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_130])]) ).
thf(f4333,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X1)) ) )
| ~ spl8_25
| ~ spl8_130 ),
inference(trivial_inequality_removal,[],[f4326]) ).
thf(f4326,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X1)) ) )
| ~ spl8_25
| ~ spl8_130 ),
inference(superposition,[],[f4313,f2074]) ).
thf(f4313,plain,
( ! [X2: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) )
| ~ spl8_130 ),
inference(avatar_component_clause,[],[f4312]) ).
thf(f13488,plain,
( spl8_394
| ~ spl8_24
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f4332,f4312,f2067,f13486]) ).
thf(f13486,plain,
( spl8_394
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_394])]) ).
thf(f4332,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X1)) ) )
| ~ spl8_24
| ~ spl8_130 ),
inference(trivial_inequality_removal,[],[f4327]) ).
thf(f4327,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X1)) ) )
| ~ spl8_24
| ~ spl8_130 ),
inference(superposition,[],[f4313,f2069]) ).
thf(f13484,plain,
( spl8_393
| ~ spl8_26
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f4331,f4312,f2077,f13482]) ).
thf(f13482,plain,
( spl8_393
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_393])]) ).
thf(f4331,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X1)) ) )
| ~ spl8_26
| ~ spl8_130 ),
inference(trivial_inequality_removal,[],[f4328]) ).
thf(f4328,plain,
( ! [X0: real,X1: real] :
( ( $true != $true )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X1)) ) )
| ~ spl8_26
| ~ spl8_130 ),
inference(superposition,[],[f4313,f2079]) ).
thf(f13480,plain,
( spl8_392
| ~ spl8_121 ),
inference(avatar_split_clause,[],[f4273,f3968,f13478]) ).
thf(f13478,plain,
( spl8_392
<=> ! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_392])]) ).
thf(f3968,plain,
( spl8_121
<=> ! [X0: real] : ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_121])]) ).
thf(f4273,plain,
( ! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) )
| ~ spl8_121 ),
inference(trivial_inequality_removal,[],[f4272]) ).
thf(f4272,plain,
( ! [X0: a] :
( ( $true = $false )
| ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false ) )
| ~ spl8_121 ),
inference(forward_demodulation,[],[f1800,f3969]) ).
thf(f3969,plain,
( ! [X0: real] : ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ~ spl8_121 ),
inference(avatar_component_clause,[],[f3968]) ).
thf(f1800,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $false ) ),
inference(not_proxy_clausification,[],[f1799]) ).
thf(f1799,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $false )
| ( $true = vAPP($o,$o,vNOT,vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real)) ) ),
inference(not_proxy_clausification,[],[f1798]) ).
thf(f1798,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( $true = vAPP($o,$o,vNOT,vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)) )
| ( $true = vAPP($o,$o,vNOT,vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real)) ) ),
inference(binary_proxy_clausification,[],[f1797]) ).
thf(f1797,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($o,$o,vNOT,vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real))),vAPP($o,$o,vNOT,vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x))) ) ),
inference(equality_proxy_clausification,[],[f1796]) ).
thf(f1796,plain,
! [X0: a] :
( ( $false = vAPP(set_real,$o,vAPP(set_real,sTfun(set_real,$o),vEQ(set_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)),bot_bot_set_real) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($o,$o,vNOT,vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real))),vAPP($o,$o,vNOT,vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x))) ) ),
inference(binary_proxy_clausification,[],[f1200]) ).
thf(f1200,plain,
! [X0: a] : ( vAPP(set_real,$o,vAPP(set_real,sTfun(set_real,$o),vEQ(set_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)),bot_bot_set_real) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($o,$o,vNOT,vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real))),vAPP($o,$o,vNOT,vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x))) ),
inference(cnf_transformation,[],[f374]) ).
thf(f374,plain,
! [X0: a] : ( vAPP(set_real,$o,vAPP(set_real,sTfun(set_real,$o),vEQ(set_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)),bot_bot_set_real) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP($o,$o,vNOT,vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real))),vAPP($o,$o,vNOT,vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x))) ),
inference(fool_elimination,[],[f373]) ).
thf(f373,plain,
! [X0: a] :
( ( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = bot_bot_set_real )
= ~ vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) )
| ~ vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) ),
inference(rectify,[],[f245]) ).
thf(f245,axiom,
! [X3: a] :
( ( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3) = bot_bot_set_real )
= ~ vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x) )
| ~ vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_local_Oexistence__ivl__empty__iff) ).
thf(f13476,plain,
( spl8_391
| ~ spl8_18
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f4226,f3964,f2040,f13474]) ).
thf(f13474,plain,
( spl8_391
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_391])]) ).
thf(f4226,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) ) )
| ~ spl8_18
| ~ spl8_120 ),
inference(superposition,[],[f3965,f2041]) ).
thf(f13472,plain,
( spl8_390
| ~ spl8_18
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f4212,f3964,f2040,f13470]) ).
thf(f13470,plain,
( spl8_390
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_390])]) ).
thf(f4212,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) ) )
| ~ spl8_18
| ~ spl8_120 ),
inference(superposition,[],[f3965,f2041]) ).
thf(f13468,plain,
( spl8_389
| ~ spl8_9
| ~ spl8_29
| ~ spl8_51
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f4194,f3960,f2264,f2094,f2002,f13466]) ).
thf(f13466,plain,
( spl8_389
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_389])]) ).
thf(f2002,plain,
( spl8_9
<=> ! [X0: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,uminus_uminus_a,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
thf(f4194,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ) )
| ~ spl8_9
| ~ spl8_29
| ~ spl8_51
| ~ spl8_119 ),
inference(forward_demodulation,[],[f4178,f2338]) ).
thf(f2338,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,uminus_uminus_a,X0)) )
| ~ spl8_9
| ~ spl8_51 ),
inference(superposition,[],[f2265,f2003]) ).
thf(f2003,plain,
( ! [X0: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,uminus_uminus_a,X0)) = X0 )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f2002]) ).
thf(f4178,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,uminus_uminus_a,X0))),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ) )
| ~ spl8_29
| ~ spl8_119 ),
inference(superposition,[],[f3961,f2095]) ).
thf(f13464,plain,
( spl8_388
| ~ spl8_9
| ~ spl8_29
| ~ spl8_51
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f4189,f3960,f2264,f2094,f2002,f13462]) ).
thf(f13462,plain,
( spl8_388
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_388])]) ).
thf(f4189,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) )
| ~ spl8_9
| ~ spl8_29
| ~ spl8_51
| ~ spl8_119 ),
inference(forward_demodulation,[],[f4164,f2338]) ).
thf(f4164,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,uminus_uminus_a,X0))) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) )
| ~ spl8_29
| ~ spl8_119 ),
inference(superposition,[],[f3961,f2095]) ).
thf(f13460,plain,
( spl8_387
| ~ spl8_15
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f4171,f3960,f2028,f13458]) ).
thf(f13458,plain,
( spl8_387
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_387])]) ).
thf(f4171,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) ) )
| ~ spl8_15
| ~ spl8_119 ),
inference(superposition,[],[f3961,f2029]) ).
thf(f13456,plain,
( spl8_386
| ~ spl8_15
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f4157,f3960,f2028,f13454]) ).
thf(f13454,plain,
( spl8_386
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_386])]) ).
thf(f4157,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) ) )
| ~ spl8_15
| ~ spl8_119 ),
inference(superposition,[],[f3961,f2029]) ).
thf(f13452,plain,
( spl8_385
| ~ spl8_106
| ~ spl8_343 ),
inference(avatar_split_clause,[],[f13110,f12318,f3908,f13450]) ).
thf(f13450,plain,
( spl8_385
<=> ! [X0: a] :
( ( xx != vAPP(a,a,uminus_uminus_a,X0) )
| ( xx = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_385])]) ).
thf(f3908,plain,
( spl8_106
<=> ! [X0: a,X1: a] :
( ( X0 = X1 )
| ( vAPP(a,a,uminus_uminus_a,X0) != vAPP(a,a,uminus_uminus_a,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_106])]) ).
thf(f12318,plain,
( spl8_343
<=> ( xx = vAPP(a,a,uminus_uminus_a,xx) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_343])]) ).
thf(f13110,plain,
( ! [X0: a] :
( ( xx != vAPP(a,a,uminus_uminus_a,X0) )
| ( xx = X0 ) )
| ~ spl8_106
| ~ spl8_343 ),
inference(superposition,[],[f3909,f12320]) ).
thf(f12320,plain,
( ( xx = vAPP(a,a,uminus_uminus_a,xx) )
| ~ spl8_343 ),
inference(avatar_component_clause,[],[f12318]) ).
thf(f3909,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,uminus_uminus_a,X0) != vAPP(a,a,uminus_uminus_a,X1) )
| ( X0 = X1 ) )
| ~ spl8_106 ),
inference(avatar_component_clause,[],[f3908]) ).
thf(f13448,plain,
( spl8_384
| ~ spl8_12
| ~ spl8_118 ),
inference(avatar_split_clause,[],[f4132,f3956,f2016,f13446]) ).
thf(f13446,plain,
( spl8_384
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_384])]) ).
thf(f2016,plain,
( spl8_12
<=> ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
thf(f4132,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) )
| ~ spl8_12
| ~ spl8_118 ),
inference(superposition,[],[f3957,f2017]) ).
thf(f2017,plain,
( ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0) = X0 )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f2016]) ).
thf(f13444,plain,
( spl8_383
| ~ spl8_12
| ~ spl8_118 ),
inference(avatar_split_clause,[],[f4118,f3956,f2016,f13442]) ).
thf(f13442,plain,
( spl8_383
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_383])]) ).
thf(f4118,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) )
| ~ spl8_12
| ~ spl8_118 ),
inference(superposition,[],[f3957,f2017]) ).
thf(f13440,plain,
( spl8_382
| ~ spl8_32
| ~ spl8_49
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f4110,f3948,f2256,f2106,f13438]) ).
thf(f13438,plain,
( spl8_382
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_382])]) ).
thf(f4110,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) )
| ~ spl8_32
| ~ spl8_49
| ~ spl8_116 ),
inference(forward_demodulation,[],[f4084,f2257]) ).
thf(f4084,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X1)),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) )
| ~ spl8_32
| ~ spl8_116 ),
inference(superposition,[],[f3949,f2107]) ).
thf(f13436,plain,
( spl8_381
| ~ spl8_32
| ~ spl8_49
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f4101,f3948,f2256,f2106,f13434]) ).
thf(f13434,plain,
( spl8_381
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_381])]) ).
thf(f4101,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_32
| ~ spl8_49
| ~ spl8_116 ),
inference(forward_demodulation,[],[f4070,f2257]) ).
thf(f4070,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
| ~ spl8_32
| ~ spl8_116 ),
inference(superposition,[],[f3949,f2107]) ).
thf(f13432,plain,
( spl8_380
| ~ spl8_13
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f4089,f3948,f2020,f13430]) ).
thf(f13430,plain,
( spl8_380
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_380])]) ).
thf(f4089,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) ) )
| ~ spl8_13
| ~ spl8_116 ),
inference(superposition,[],[f3949,f2021]) ).
thf(f13428,plain,
( spl8_379
| ~ spl8_13
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f4075,f3948,f2020,f13426]) ).
thf(f13426,plain,
( spl8_379
<=> ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_379])]) ).
thf(f4075,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) )
| ~ spl8_13
| ~ spl8_116 ),
inference(superposition,[],[f3949,f2021]) ).
thf(f13424,plain,
( spl8_378
| ~ spl8_2
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f2715,f2711,f1942,f13422]) ).
thf(f13422,plain,
( spl8_378
<=> ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_378])]) ).
thf(f2711,plain,
( spl8_72
<=> ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).
thf(f2715,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $false ) )
| ~ spl8_2
| ~ spl8_72 ),
inference(trivial_inequality_removal,[],[f2714]) ).
thf(f2714,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $false ) )
| ~ spl8_2
| ~ spl8_72 ),
inference(superposition,[],[f2712,f1943]) ).
thf(f2712,plain,
( ! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true ) )
| ~ spl8_72 ),
inference(avatar_component_clause,[],[f2711]) ).
thf(f13359,plain,
( spl8_377
| ~ spl8_33
| ~ spl8_162 ),
inference(avatar_split_clause,[],[f11676,f4609,f2110,f13357]) ).
thf(f13357,plain,
( spl8_377
<=> ! [X0: a] :
( ( xx != X0 )
| ( xx = vAPP(a,a,uminus_uminus_a,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_377])]) ).
thf(f2110,plain,
( spl8_33
<=> ! [X0: a] :
( ( zero_zero_a != X0 )
| ( zero_zero_a = vAPP(a,a,uminus_uminus_a,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
thf(f4609,plain,
( spl8_162
<=> ( xx = zero_zero_a ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_162])]) ).
thf(f11676,plain,
( ! [X0: a] :
( ( xx != X0 )
| ( xx = vAPP(a,a,uminus_uminus_a,X0) ) )
| ~ spl8_33
| ~ spl8_162 ),
inference(superposition,[],[f2111,f4610]) ).
thf(f4610,plain,
( ( xx = zero_zero_a )
| ~ spl8_162 ),
inference(avatar_component_clause,[],[f4609]) ).
thf(f2111,plain,
( ! [X0: a] :
( ( zero_zero_a != X0 )
| ( zero_zero_a = vAPP(a,a,uminus_uminus_a,X0) ) )
| ~ spl8_33 ),
inference(avatar_component_clause,[],[f2110]) ).
thf(f13355,plain,
spl8_376,
inference(avatar_split_clause,[],[f1859,f13353]) ).
thf(f13353,plain,
( spl8_376
<=> ! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_376])]) ).
thf(f1859,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ) ),
inference(binary_proxy_clausification,[],[f1187]) ).
thf(f1187,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ),
inference(cnf_transformation,[],[f786]) ).
thf(f786,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ),
inference(rectify,[],[f232]) ).
thf(f232,axiom,
! [X8: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X8) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_linordered__ab__group__add__class_Ozero__less__double__add__iff__zero__less__single__add) ).
thf(f13351,plain,
spl8_375,
inference(avatar_split_clause,[],[f1858,f13349]) ).
thf(f13349,plain,
( spl8_375
<=> ! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_375])]) ).
thf(f1858,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ) ),
inference(binary_proxy_clausification,[],[f1187]) ).
thf(f13347,plain,
spl8_374,
inference(avatar_split_clause,[],[f1857,f13345]) ).
thf(f13345,plain,
( spl8_374
<=> ! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_374])]) ).
thf(f1857,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1188]) ).
thf(f1188,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real) ),
inference(cnf_transformation,[],[f787]) ).
thf(f787,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real) ),
inference(rectify,[],[f231]) ).
thf(f231,axiom,
! [X8: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X8)),zero_zero_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_double__add__less__zero__iff__single__add__less__zero) ).
thf(f13343,plain,
spl8_373,
inference(avatar_split_clause,[],[f1856,f13341]) ).
thf(f13341,plain,
( spl8_373
<=> ! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_373])]) ).
thf(f1856,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1188]) ).
thf(f13339,plain,
spl8_372,
inference(avatar_split_clause,[],[f1738,f13337]) ).
thf(f13337,plain,
( spl8_372
<=> ! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_372])]) ).
thf(f1738,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1282]) ).
thf(f1282,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) ),
inference(cnf_transformation,[],[f822]) ).
thf(f822,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) ),
inference(rectify,[],[f230]) ).
thf(f230,axiom,
! [X8: real,X9: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X9) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_less__add__same__cancel2) ).
thf(f13335,plain,
spl8_371,
inference(avatar_split_clause,[],[f1737,f13333]) ).
thf(f13333,plain,
( spl8_371
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_371])]) ).
thf(f1737,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1282]) ).
thf(f13331,plain,
spl8_370,
inference(avatar_split_clause,[],[f1736,f13329]) ).
thf(f13329,plain,
( spl8_370
<=> ! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_370])]) ).
thf(f1736,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) ) ),
inference(binary_proxy_clausification,[],[f1283]) ).
thf(f1283,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) ),
inference(cnf_transformation,[],[f823]) ).
thf(f823,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) ),
inference(rectify,[],[f226]) ).
thf(f226,axiom,
! [X8: real,X9: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_add__less__same__cancel2) ).
thf(f13327,plain,
spl8_369,
inference(avatar_split_clause,[],[f1735,f13325]) ).
thf(f13325,plain,
( spl8_369
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_369])]) ).
thf(f1735,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) ) ),
inference(binary_proxy_clausification,[],[f1283]) ).
thf(f13323,plain,
spl8_368,
inference(avatar_split_clause,[],[f1734,f13321]) ).
thf(f13321,plain,
( spl8_368
<=> ! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_368])]) ).
thf(f1734,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1284]) ).
thf(f1284,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ),
inference(cnf_transformation,[],[f824]) ).
thf(f824,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ),
inference(rectify,[],[f224]) ).
thf(f224,axiom,
! [X9: real,X8: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X8)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_add__less__same__cancel1) ).
thf(f13319,plain,
spl8_367,
inference(avatar_split_clause,[],[f1733,f13317]) ).
thf(f13317,plain,
( spl8_367
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_367])]) ).
thf(f1733,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1284]) ).
thf(f13314,plain,
spl8_366,
inference(avatar_split_clause,[],[f1732,f13312]) ).
thf(f13312,plain,
( spl8_366
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_366])]) ).
thf(f1732,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1285]) ).
thf(f1285,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) ),
inference(cnf_transformation,[],[f825]) ).
thf(f825,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) ),
inference(rectify,[],[f229]) ).
thf(f229,axiom,
! [X8: a,X9: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X9) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_less__add__same__cancel2) ).
thf(f13309,plain,
spl8_365,
inference(avatar_split_clause,[],[f1731,f13307]) ).
thf(f13307,plain,
( spl8_365
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_365])]) ).
thf(f1731,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1285]) ).
thf(f13304,plain,
spl8_364,
inference(avatar_split_clause,[],[f1730,f13302]) ).
thf(f13302,plain,
( spl8_364
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_364])]) ).
thf(f1730,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1286]) ).
thf(f1286,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ),
inference(cnf_transformation,[],[f826]) ).
thf(f826,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ),
inference(rectify,[],[f223]) ).
thf(f223,axiom,
! [X9: a,X8: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X8)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add__less__same__cancel1) ).
thf(f13299,plain,
spl8_363,
inference(avatar_split_clause,[],[f1729,f13297]) ).
thf(f13297,plain,
( spl8_363
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_363])]) ).
thf(f1729,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1286]) ).
thf(f13230,plain,
( spl8_362
| ~ spl8_162
| ~ spl8_361 ),
inference(avatar_split_clause,[],[f13226,f13223,f4609,f13228]) ).
thf(f13223,plain,
( spl8_361
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_361])]) ).
thf(f13226,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),xx) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ) )
| ~ spl8_162
| ~ spl8_361 ),
inference(forward_demodulation,[],[f13224,f4610]) ).
thf(f13224,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) ) )
| ~ spl8_361 ),
inference(avatar_component_clause,[],[f13223]) ).
thf(f13225,plain,
spl8_361,
inference(avatar_split_clause,[],[f1728,f13223]) ).
thf(f1728,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ) ),
inference(binary_proxy_clausification,[],[f1287]) ).
thf(f1287,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ),
inference(cnf_transformation,[],[f827]) ).
thf(f827,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ),
inference(rectify,[],[f225]) ).
thf(f225,axiom,
! [X8: a,X9: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_add__less__same__cancel2) ).
thf(f13175,plain,
( spl8_360
| ~ spl8_162
| ~ spl8_359 ),
inference(avatar_split_clause,[],[f13171,f13168,f4609,f13173]) ).
thf(f13168,plain,
( spl8_359
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_359])]) ).
thf(f13171,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),xx) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ) )
| ~ spl8_162
| ~ spl8_359 ),
inference(forward_demodulation,[],[f13169,f4610]) ).
thf(f13169,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) ) )
| ~ spl8_359 ),
inference(avatar_component_clause,[],[f13168]) ).
thf(f13170,plain,
spl8_359,
inference(avatar_split_clause,[],[f1727,f13168]) ).
thf(f1727,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) ) ),
inference(binary_proxy_clausification,[],[f1287]) ).
thf(f13097,plain,
spl8_358,
inference(avatar_split_clause,[],[f1726,f13095]) ).
thf(f13095,plain,
( spl8_358
<=> ! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_358])]) ).
thf(f1726,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1288]) ).
thf(f1288,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ),
inference(cnf_transformation,[],[f828]) ).
thf(f828,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ),
inference(rectify,[],[f234]) ).
thf(f234,axiom,
! [X8: real,X9: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_diff__gt__0__iff__gt) ).
thf(f13093,plain,
spl8_357,
inference(avatar_split_clause,[],[f1725,f13091]) ).
thf(f13091,plain,
( spl8_357
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_357])]) ).
thf(f1725,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1288]) ).
thf(f13088,plain,
spl8_356,
inference(avatar_split_clause,[],[f1724,f13086]) ).
thf(f13086,plain,
( spl8_356
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_356])]) ).
thf(f1724,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1289]) ).
thf(f1289,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ),
inference(cnf_transformation,[],[f829]) ).
thf(f829,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ),
inference(rectify,[],[f233]) ).
thf(f233,axiom,
! [X8: a,X9: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_diff__gt__0__iff__gt) ).
thf(f13083,plain,
spl8_355,
inference(avatar_split_clause,[],[f1723,f13081]) ).
thf(f13081,plain,
( spl8_355
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_355])]) ).
thf(f1723,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1289]) ).
thf(f13079,plain,
spl8_354,
inference(avatar_split_clause,[],[f1722,f13077]) ).
thf(f13077,plain,
( spl8_354
<=> ! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_354])]) ).
thf(f1722,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1290]) ).
thf(f1290,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ),
inference(cnf_transformation,[],[f830]) ).
thf(f830,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ),
inference(rectify,[],[f228]) ).
thf(f228,axiom,
! [X8: real,X9: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_less__add__same__cancel1) ).
thf(f13075,plain,
spl8_353,
inference(avatar_split_clause,[],[f1721,f13073]) ).
thf(f13073,plain,
( spl8_353
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_353])]) ).
thf(f1721,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1290]) ).
thf(f13013,plain,
( spl8_352
| ~ spl8_162
| ~ spl8_351 ),
inference(avatar_split_clause,[],[f13009,f13006,f4609,f13011]) ).
thf(f13006,plain,
( spl8_351
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_351])]) ).
thf(f13009,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) )
| ~ spl8_162
| ~ spl8_351 ),
inference(forward_demodulation,[],[f13007,f4610]) ).
thf(f13007,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) ) )
| ~ spl8_351 ),
inference(avatar_component_clause,[],[f13006]) ).
thf(f13008,plain,
spl8_351,
inference(avatar_split_clause,[],[f1720,f13006]) ).
thf(f1720,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1291]) ).
thf(f1291,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ),
inference(cnf_transformation,[],[f831]) ).
thf(f831,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ),
inference(rectify,[],[f227]) ).
thf(f227,axiom,
! [X8: a,X9: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_less__add__same__cancel1) ).
thf(f12964,plain,
( ~ spl8_350
| ~ spl8_162
| spl8_304 ),
inference(avatar_split_clause,[],[f11690,f8659,f4609,f12961]) ).
thf(f12961,plain,
( spl8_350
<=> ( xx = vAPP(a,a,f,xx) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_350])]) ).
thf(f8659,plain,
( spl8_304
<=> ( zero_zero_a = vAPP(a,a,f,zero_zero_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_304])]) ).
thf(f11690,plain,
( ( xx != vAPP(a,a,f,xx) )
| ~ spl8_162
| spl8_304 ),
inference(superposition,[],[f8661,f4610]) ).
thf(f8661,plain,
( ( zero_zero_a != vAPP(a,a,f,zero_zero_a) )
| spl8_304 ),
inference(avatar_component_clause,[],[f8659]) ).
thf(f12959,plain,
( spl8_349
| ~ spl8_162
| ~ spl8_348 ),
inference(avatar_split_clause,[],[f12955,f12952,f4609,f12957]) ).
thf(f12952,plain,
( spl8_348
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_348])]) ).
thf(f12955,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,xx),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) )
| ~ spl8_162
| ~ spl8_348 ),
inference(forward_demodulation,[],[f12953,f4610]) ).
thf(f12953,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) ) )
| ~ spl8_348 ),
inference(avatar_component_clause,[],[f12952]) ).
thf(f12954,plain,
spl8_348,
inference(avatar_split_clause,[],[f1719,f12952]) ).
thf(f1719,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ),
inference(binary_proxy_clausification,[],[f1291]) ).
thf(f12337,plain,
( spl8_347
| ~ spl8_42
| ~ spl8_70 ),
inference(avatar_split_clause,[],[f2652,f2558,f2172,f12335]) ).
thf(f12335,plain,
( spl8_347
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),vAPP(a,a,uminus_uminus_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_347])]) ).
thf(f2558,plain,
( spl8_70
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
thf(f2652,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),vAPP(a,a,uminus_uminus_a,X1)) )
| ~ spl8_42
| ~ spl8_70 ),
inference(superposition,[],[f2173,f2559]) ).
thf(f2559,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) )
| ~ spl8_70 ),
inference(avatar_component_clause,[],[f2558]) ).
thf(f12333,plain,
( spl8_346
| ~ spl8_43
| ~ spl8_70 ),
inference(avatar_split_clause,[],[f2651,f2558,f2176,f12331]) ).
thf(f12331,plain,
( spl8_346
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),vAPP(a,a,uminus_uminus_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_346])]) ).
thf(f2651,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),vAPP(a,a,uminus_uminus_a,X0)) )
| ~ spl8_43
| ~ spl8_70 ),
inference(superposition,[],[f2177,f2559]) ).
thf(f12329,plain,
( spl8_345
| ~ spl8_40
| ~ spl8_68 ),
inference(avatar_split_clause,[],[f2582,f2550,f2164,f12327]) ).
thf(f12327,plain,
( spl8_345
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_345])]) ).
thf(f2550,plain,
( spl8_68
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
thf(f2582,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X1)) )
| ~ spl8_40
| ~ spl8_68 ),
inference(superposition,[],[f2165,f2551]) ).
thf(f2551,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) )
| ~ spl8_68 ),
inference(avatar_component_clause,[],[f2550]) ).
thf(f12325,plain,
( spl8_344
| ~ spl8_41
| ~ spl8_68 ),
inference(avatar_split_clause,[],[f2581,f2550,f2168,f12323]) ).
thf(f12323,plain,
( spl8_344
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_344])]) ).
thf(f2581,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X0)) )
| ~ spl8_41
| ~ spl8_68 ),
inference(superposition,[],[f2169,f2551]) ).
thf(f12321,plain,
( spl8_343
| ~ spl8_3
| ~ spl8_162 ),
inference(avatar_split_clause,[],[f11672,f4609,f1974,f12318]) ).
thf(f1974,plain,
( spl8_3
<=> ( zero_zero_a = vAPP(a,a,uminus_uminus_a,zero_zero_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
thf(f11672,plain,
( ( xx = vAPP(a,a,uminus_uminus_a,xx) )
| ~ spl8_3
| ~ spl8_162 ),
inference(superposition,[],[f1976,f4610]) ).
thf(f1976,plain,
( ( zero_zero_a = vAPP(a,a,uminus_uminus_a,zero_zero_a) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f1974]) ).
thf(f11696,plain,
spl8_342,
inference(avatar_split_clause,[],[f1749,f11694]) ).
thf(f11694,plain,
( spl8_342
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X1)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_342])]) ).
thf(f1749,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X1)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1274]) ).
thf(f1274,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X1)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(cnf_transformation,[],[f814]) ).
thf(f814,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X1)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(rectify,[],[f310]) ).
thf(f310,axiom,
! [X8: real,X9: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),vAPP(real,real,uminus_uminus_real,X9)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X9),vAPP(real,real,uminus_uminus_real,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_less__minus__iff) ).
thf(f11602,plain,
( spl8_162
| ~ spl8_122
| ~ spl8_334 ),
inference(avatar_split_clause,[],[f11534,f10501,f3971,f4609]) ).
thf(f3971,plain,
( spl8_122
<=> ! [X1: a] : ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_122])]) ).
thf(f10501,plain,
( spl8_334
<=> ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_334])]) ).
thf(f11534,plain,
( ( xx = zero_zero_a )
| ~ spl8_122
| ~ spl8_334 ),
inference(superposition,[],[f10503,f3972]) ).
thf(f3972,plain,
( ! [X1: a] : ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),zero_zero_real) )
| ~ spl8_122 ),
inference(avatar_component_clause,[],[f3971]) ).
thf(f10503,plain,
( ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),zero_zero_real) )
| ~ spl8_334 ),
inference(avatar_component_clause,[],[f10501]) ).
thf(f11601,plain,
spl8_341,
inference(avatar_split_clause,[],[f1747,f11599]) ).
thf(f11599,plain,
( spl8_341
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_341])]) ).
thf(f1747,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1275]) ).
thf(f1275,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),X0) ),
inference(cnf_transformation,[],[f815]) ).
thf(f815,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),X0) ),
inference(rectify,[],[f312]) ).
thf(f312,axiom,
! [X8: real,X9: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X8)),X9) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X9)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_minus__less__iff) ).
thf(f11597,plain,
spl8_340,
inference(avatar_split_clause,[],[f1745,f11595]) ).
thf(f11595,plain,
( spl8_340
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,uminus_uminus_a,X1)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_340])]) ).
thf(f1745,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,uminus_uminus_a,X1)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ) ),
inference(binary_proxy_clausification,[],[f1277]) ).
thf(f1277,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,uminus_uminus_a,X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(cnf_transformation,[],[f817]) ).
thf(f817,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),vAPP(a,a,uminus_uminus_a,X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(rectify,[],[f309]) ).
thf(f309,axiom,
! [X8: a,X9: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),vAPP(a,a,uminus_uminus_a,X9)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X9),vAPP(a,a,uminus_uminus_a,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_less__minus__iff) ).
thf(f11593,plain,
spl8_339,
inference(avatar_split_clause,[],[f1743,f11591]) ).
thf(f11591,plain,
( spl8_339
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_339])]) ).
thf(f1743,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1278]) ).
thf(f1278,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),X0) ),
inference(cnf_transformation,[],[f818]) ).
thf(f818,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),X0) ),
inference(rectify,[],[f311]) ).
thf(f311,axiom,
! [X8: a,X9: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X8)),X9) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X9)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_minus__less__iff) ).
thf(f11589,plain,
spl8_338,
inference(avatar_split_clause,[],[f1742,f11587]) ).
thf(f11587,plain,
( spl8_338
<=> ! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_338])]) ).
thf(f1742,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ),
inference(binary_proxy_clausification,[],[f1280]) ).
thf(f1280,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ),
inference(cnf_transformation,[],[f820]) ).
thf(f820,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ),
inference(rectify,[],[f188]) ).
thf(f188,axiom,
! [X9: real,X8: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X9)),vAPP(real,real,uminus_uminus_real,X8)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_neg__less__iff__less) ).
thf(f11585,plain,
spl8_337,
inference(avatar_split_clause,[],[f1741,f11583]) ).
thf(f11583,plain,
( spl8_337
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_337])]) ).
thf(f1741,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X0) ) ),
inference(binary_proxy_clausification,[],[f1280]) ).
thf(f11581,plain,
spl8_336,
inference(avatar_split_clause,[],[f1740,f11579]) ).
thf(f11579,plain,
( spl8_336
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_336])]) ).
thf(f1740,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ) ),
inference(binary_proxy_clausification,[],[f1281]) ).
thf(f1281,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ),
inference(cnf_transformation,[],[f821]) ).
thf(f821,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ),
inference(rectify,[],[f187]) ).
thf(f187,axiom,
! [X9: a,X8: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X9)),vAPP(a,a,uminus_uminus_a,X8)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_neg__less__iff__less) ).
thf(f11577,plain,
spl8_335,
inference(avatar_split_clause,[],[f1739,f11575]) ).
thf(f11575,plain,
( spl8_335
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_335])]) ).
thf(f1739,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X0) ) ),
inference(binary_proxy_clausification,[],[f1281]) ).
thf(f10504,plain,
( spl8_334
| ~ spl8_21
| ~ spl8_149 ),
inference(avatar_split_clause,[],[f4486,f4431,f2052,f10501]) ).
thf(f4431,plain,
( spl8_149
<=> ! [X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),zero_zero_real) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_149])]) ).
thf(f4486,plain,
( ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),zero_zero_real) )
| ~ spl8_21
| ~ spl8_149 ),
inference(trivial_inequality_removal,[],[f4481]) ).
thf(f4481,plain,
( ( $true != $true )
| ( xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),zero_zero_real) )
| ~ spl8_21
| ~ spl8_149 ),
inference(superposition,[],[f4432,f2054]) ).
thf(f4432,plain,
( ! [X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),zero_zero_real) = X1 ) )
| ~ spl8_149 ),
inference(avatar_component_clause,[],[f4431]) ).
thf(f10499,plain,
( spl8_333
| ~ spl8_23
| ~ spl8_111 ),
inference(avatar_split_clause,[],[f4053,f3928,f2062,f10497]) ).
thf(f10497,plain,
( spl8_333
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,d),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_333])]) ).
thf(f2062,plain,
( spl8_23
<=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,tt),d) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
thf(f3928,plain,
( spl8_111
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_111])]) ).
thf(f4053,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,d),X0)) )
| ~ spl8_23
| ~ spl8_111 ),
inference(trivial_inequality_removal,[],[f4042]) ).
thf(f4042,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,d),X0)) ) )
| ~ spl8_23
| ~ spl8_111 ),
inference(superposition,[],[f3929,f2064]) ).
thf(f2064,plain,
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,tt),d) = $true )
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f2062]) ).
thf(f3929,plain,
( ! [X2: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ) )
| ~ spl8_111 ),
inference(avatar_component_clause,[],[f3928]) ).
thf(f10495,plain,
( spl8_332
| ~ spl8_22
| ~ spl8_111 ),
inference(avatar_split_clause,[],[f4050,f3928,f2057,f10493]) ).
thf(f10493,plain,
( spl8_332
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_332])]) ).
thf(f4050,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i2),X0)) )
| ~ spl8_22
| ~ spl8_111 ),
inference(trivial_inequality_removal,[],[f4045]) ).
thf(f4045,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i2),X0)) ) )
| ~ spl8_22
| ~ spl8_111 ),
inference(superposition,[],[f3929,f2059]) ).
thf(f10491,plain,
( spl8_331
| ~ spl8_23
| ~ spl8_110 ),
inference(avatar_split_clause,[],[f4037,f3924,f2062,f10489]) ).
thf(f10489,plain,
( spl8_331
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_331])]) ).
thf(f3924,plain,
( spl8_110
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_110])]) ).
thf(f4037,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)) )
| ~ spl8_23
| ~ spl8_110 ),
inference(trivial_inequality_removal,[],[f4026]) ).
thf(f4026,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)) ) )
| ~ spl8_23
| ~ spl8_110 ),
inference(superposition,[],[f3925,f2064]) ).
thf(f3925,plain,
( ! [X2: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) ) )
| ~ spl8_110 ),
inference(avatar_component_clause,[],[f3924]) ).
thf(f10487,plain,
( spl8_330
| ~ spl8_22
| ~ spl8_110 ),
inference(avatar_split_clause,[],[f4034,f3924,f2057,f10485]) ).
thf(f10485,plain,
( spl8_330
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_330])]) ).
thf(f4034,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)) )
| ~ spl8_22
| ~ spl8_110 ),
inference(trivial_inequality_removal,[],[f4029]) ).
thf(f4029,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)) ) )
| ~ spl8_22
| ~ spl8_110 ),
inference(superposition,[],[f3925,f2059]) ).
thf(f10483,plain,
( spl8_329
| ~ spl8_23
| ~ spl8_109 ),
inference(avatar_split_clause,[],[f4021,f3920,f2062,f10481]) ).
thf(f10481,plain,
( spl8_329
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),tt)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),d)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_329])]) ).
thf(f3920,plain,
( spl8_109
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_109])]) ).
thf(f4021,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),tt)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),d)) )
| ~ spl8_23
| ~ spl8_109 ),
inference(trivial_inequality_removal,[],[f4010]) ).
thf(f4010,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),tt)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),d)) ) )
| ~ spl8_23
| ~ spl8_109 ),
inference(superposition,[],[f3921,f2064]) ).
thf(f3921,plain,
( ! [X2: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) )
| ~ spl8_109 ),
inference(avatar_component_clause,[],[f3920]) ).
thf(f10479,plain,
( spl8_328
| ~ spl8_22
| ~ spl8_109 ),
inference(avatar_split_clause,[],[f4018,f3920,f2057,f10477]) ).
thf(f10477,plain,
( spl8_328
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_328])]) ).
thf(f4018,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i2)) )
| ~ spl8_22
| ~ spl8_109 ),
inference(trivial_inequality_removal,[],[f4013]) ).
thf(f4013,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i2)) ) )
| ~ spl8_22
| ~ spl8_109 ),
inference(superposition,[],[f3921,f2059]) ).
thf(f10475,plain,
( spl8_327
| ~ spl8_23
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f4000,f3916,f2062,f10473]) ).
thf(f10473,plain,
( spl8_327
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_327])]) ).
thf(f3916,plain,
( spl8_108
<=> ! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_108])]) ).
thf(f4000,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X0)) )
| ~ spl8_23
| ~ spl8_108 ),
inference(trivial_inequality_removal,[],[f3989]) ).
thf(f3989,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X0)) ) )
| ~ spl8_23
| ~ spl8_108 ),
inference(superposition,[],[f3917,f2064]) ).
thf(f3917,plain,
( ! [X2: real,X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) ) )
| ~ spl8_108 ),
inference(avatar_component_clause,[],[f3916]) ).
thf(f10471,plain,
( spl8_326
| ~ spl8_22
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f3997,f3916,f2057,f10469]) ).
thf(f10469,plain,
( spl8_326
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_326])]) ).
thf(f3997,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i2),X0)) )
| ~ spl8_22
| ~ spl8_108 ),
inference(trivial_inequality_removal,[],[f3992]) ).
thf(f3992,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i2),X0)) ) )
| ~ spl8_22
| ~ spl8_108 ),
inference(superposition,[],[f3917,f2059]) ).
thf(f10467,plain,
( spl8_325
| ~ spl8_29
| ~ spl8_273 ),
inference(avatar_split_clause,[],[f9861,f7061,f2094,f10465]) ).
thf(f10465,plain,
( spl8_325
<=> ! [X0: a] :
( ( zero_zero_a != X0 )
| ( vAPP(a,a,uminus_uminus_a,zero_zero_a) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_325])]) ).
thf(f7061,plain,
( spl8_273
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,zero_zero_a),X1) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_273])]) ).
thf(f9861,plain,
( ! [X0: a] :
( ( zero_zero_a != X0 )
| ( vAPP(a,a,uminus_uminus_a,zero_zero_a) = X0 ) )
| ~ spl8_29
| ~ spl8_273 ),
inference(superposition,[],[f7062,f2095]) ).
thf(f7062,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,zero_zero_a),X1) != X0 )
| ( X0 = X1 ) )
| ~ spl8_273 ),
inference(avatar_component_clause,[],[f7061]) ).
thf(f10463,plain,
( spl8_324
| ~ spl8_21
| ~ spl8_101 ),
inference(avatar_split_clause,[],[f3977,f3888,f2052,f10460]) ).
thf(f10460,plain,
( spl8_324
<=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_324])]) ).
thf(f3888,plain,
( spl8_101
<=> ! [X0: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_101])]) ).
thf(f3977,plain,
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_21
| ~ spl8_101 ),
inference(trivial_inequality_removal,[],[f3974]) ).
thf(f3974,plain,
( ( $true != $true )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) )
| ~ spl8_21
| ~ spl8_101 ),
inference(superposition,[],[f3889,f2054]) ).
thf(f3889,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) ) )
| ~ spl8_101 ),
inference(avatar_component_clause,[],[f3888]) ).
thf(f10458,plain,
( spl8_323
| ~ spl8_30
| ~ spl8_50
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f2960,f2747,f2260,f2098,f10456]) ).
thf(f10456,plain,
( spl8_323
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_323])]) ).
thf(f2960,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) )
| ~ spl8_30
| ~ spl8_50
| ~ spl8_80 ),
inference(forward_demodulation,[],[f2934,f2261]) ).
thf(f2934,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X1)) )
| ~ spl8_30
| ~ spl8_80 ),
inference(superposition,[],[f2748,f2099]) ).
thf(f10454,plain,
( spl8_322
| ~ spl8_8
| ~ spl8_31
| ~ spl8_48
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f2862,f2739,f2249,f2102,f1998,f10452]) ).
thf(f10452,plain,
( spl8_322
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_322])]) ).
thf(f2862,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) )
| ~ spl8_8
| ~ spl8_31
| ~ spl8_48
| ~ spl8_78 ),
inference(forward_demodulation,[],[f2837,f2284]) ).
thf(f2837,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,uminus_uminus_real,X0))) )
| ~ spl8_31
| ~ spl8_78 ),
inference(superposition,[],[f2740,f2103]) ).
thf(f10450,plain,
( spl8_321
| ~ spl8_30
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f2377,f2272,f2098,f10448]) ).
thf(f10448,plain,
( spl8_321
<=> ! [X0: a,X1: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_321])]) ).
thf(f2377,plain,
( ! [X0: a,X1: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) )
| ~ spl8_30
| ~ spl8_53 ),
inference(superposition,[],[f2099,f2273]) ).
thf(f10446,plain,
( spl8_320
| ~ spl8_32
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f2365,f2268,f2106,f10444]) ).
thf(f10444,plain,
( spl8_320
<=> ! [X0: real,X1: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_320])]) ).
thf(f2365,plain,
( ! [X0: real,X1: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) )
| ~ spl8_32
| ~ spl8_52 ),
inference(superposition,[],[f2107,f2269]) ).
thf(f9040,plain,
( spl8_319
| ~ spl8_30
| ~ spl8_35
| ~ spl8_93 ),
inference(avatar_split_clause,[],[f3626,f2800,f2118,f2098,f9038]) ).
thf(f9038,plain,
( spl8_319
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_319])]) ).
thf(f2118,plain,
( spl8_35
<=> ! [X0: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
thf(f3626,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) )
| ~ spl8_30
| ~ spl8_35
| ~ spl8_93 ),
inference(forward_demodulation,[],[f3595,f2119]) ).
thf(f2119,plain,
( ! [X0: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),X0) )
| ~ spl8_35 ),
inference(avatar_component_clause,[],[f2118]) ).
thf(f3595,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) )
| ~ spl8_30
| ~ spl8_93 ),
inference(superposition,[],[f2801,f2099]) ).
thf(f9036,plain,
( spl8_318
| ~ spl8_32
| ~ spl8_34
| ~ spl8_84 ),
inference(avatar_split_clause,[],[f3224,f2763,f2114,f2106,f9034]) ).
thf(f9034,plain,
( spl8_318
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_318])]) ).
thf(f2114,plain,
( spl8_34
<=> ! [X0: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
thf(f3224,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) )
| ~ spl8_32
| ~ spl8_34
| ~ spl8_84 ),
inference(forward_demodulation,[],[f3195,f2115]) ).
thf(f2115,plain,
( ! [X0: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0) )
| ~ spl8_34 ),
inference(avatar_component_clause,[],[f2114]) ).
thf(f3195,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) )
| ~ spl8_32
| ~ spl8_84 ),
inference(superposition,[],[f2764,f2107]) ).
thf(f9032,plain,
( spl8_317
| ~ spl8_70
| ~ spl8_71 ),
inference(avatar_split_clause,[],[f2679,f2565,f2558,f9030]) ).
thf(f9030,plain,
( spl8_317
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_317])]) ).
thf(f2565,plain,
( spl8_71
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
thf(f2679,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)) )
| ~ spl8_70
| ~ spl8_71 ),
inference(superposition,[],[f2566,f2559]) ).
thf(f2566,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) )
| ~ spl8_71 ),
inference(avatar_component_clause,[],[f2565]) ).
thf(f9028,plain,
( spl8_316
| ~ spl8_13
| ~ spl8_258 ),
inference(avatar_split_clause,[],[f6980,f6767,f2020,f9026]) ).
thf(f9026,plain,
( spl8_316
<=> ! [X0: real,X1: real] :
( ( X0 != X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),zero_zero_real) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_316])]) ).
thf(f6767,plain,
( spl8_258
<=> ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = X2 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_258])]) ).
thf(f6980,plain,
( ! [X0: real,X1: real] :
( ( X0 != X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),zero_zero_real) = X0 ) )
| ~ spl8_13
| ~ spl8_258 ),
inference(superposition,[],[f6768,f2021]) ).
thf(f6768,plain,
( ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) != X0 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = X2 ) )
| ~ spl8_258 ),
inference(avatar_component_clause,[],[f6767]) ).
thf(f9024,plain,
( spl8_315
| ~ spl8_9
| ~ spl8_55
| ~ spl8_70 ),
inference(avatar_split_clause,[],[f2672,f2558,f2280,f2002,f9022]) ).
thf(f9022,plain,
( spl8_315
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_315])]) ).
thf(f2672,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))) )
| ~ spl8_9
| ~ spl8_55
| ~ spl8_70 ),
inference(forward_demodulation,[],[f2650,f2003]) ).
thf(f2650,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,vAPP(a,a,uminus_uminus_a,X0))),vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))) )
| ~ spl8_55
| ~ spl8_70 ),
inference(superposition,[],[f2281,f2559]) ).
thf(f9020,plain,
( spl8_314
| ~ spl8_8
| ~ spl8_54
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f2637,f2554,f2276,f1998,f9018]) ).
thf(f9018,plain,
( spl8_314
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_314])]) ).
thf(f2554,plain,
( spl8_69
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
thf(f2637,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))) )
| ~ spl8_8
| ~ spl8_54
| ~ spl8_69 ),
inference(forward_demodulation,[],[f2616,f1999]) ).
thf(f2616,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,uminus_uminus_real,X0))),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))) )
| ~ spl8_54
| ~ spl8_69 ),
inference(superposition,[],[f2277,f2555]) ).
thf(f2555,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) )
| ~ spl8_69 ),
inference(avatar_component_clause,[],[f2554]) ).
thf(f9016,plain,
( spl8_313
| ~ spl8_68
| ~ spl8_69 ),
inference(avatar_split_clause,[],[f2608,f2554,f2550,f9014]) ).
thf(f9014,plain,
( spl8_313
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_313])]) ).
thf(f2608,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)) )
| ~ spl8_68
| ~ spl8_69 ),
inference(superposition,[],[f2555,f2551]) ).
thf(f9012,plain,
( spl8_312
| ~ spl8_44
| ~ spl8_61 ),
inference(avatar_split_clause,[],[f2489,f2454,f2180,f9010]) ).
thf(f9010,plain,
( spl8_312
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_312])]) ).
thf(f2454,plain,
( spl8_61
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).
thf(f2489,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))),X1) )
| ~ spl8_44
| ~ spl8_61 ),
inference(superposition,[],[f2181,f2455]) ).
thf(f2455,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ~ spl8_61 ),
inference(avatar_component_clause,[],[f2454]) ).
thf(f9008,plain,
( spl8_311
| ~ spl8_46
| ~ spl8_61 ),
inference(avatar_split_clause,[],[f2488,f2454,f2188,f9006]) ).
thf(f9006,plain,
( spl8_311
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_311])]) ).
thf(f2488,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1))) )
| ~ spl8_46
| ~ spl8_61 ),
inference(superposition,[],[f2189,f2455]) ).
thf(f9004,plain,
( spl8_310
| ~ spl8_39
| ~ spl8_60 ),
inference(avatar_split_clause,[],[f2466,f2450,f2160,f9002]) ).
thf(f9002,plain,
( spl8_310
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_310])]) ).
thf(f2450,plain,
( spl8_60
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
thf(f2466,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))),X1) )
| ~ spl8_39
| ~ spl8_60 ),
inference(superposition,[],[f2161,f2451]) ).
thf(f2451,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ~ spl8_60 ),
inference(avatar_component_clause,[],[f2450]) ).
thf(f9000,plain,
( spl8_309
| ~ spl8_45
| ~ spl8_60 ),
inference(avatar_split_clause,[],[f2465,f2450,f2184,f8998]) ).
thf(f8998,plain,
( spl8_309
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_309])]) ).
thf(f2465,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1))) )
| ~ spl8_45
| ~ spl8_60 ),
inference(superposition,[],[f2185,f2451]) ).
thf(f8996,plain,
( spl8_308
| ~ spl8_51
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f2374,f2272,f2264,f8994]) ).
thf(f8994,plain,
( spl8_308
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X1)),X0) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_308])]) ).
thf(f8992,plain,
( spl8_307
| ~ spl8_48
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f2361,f2268,f2249,f8990]) ).
thf(f8990,plain,
( spl8_307
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X1)),X0) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_307])]) ).
thf(f2361,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X1)),X0) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ~ spl8_48
| ~ spl8_52 ),
inference(superposition,[],[f2269,f2250]) ).
thf(f8946,plain,
( spl8_306
| ~ spl8_14
| ~ spl8_257 ),
inference(avatar_split_clause,[],[f6964,f6763,f2024,f8944]) ).
thf(f8944,plain,
( spl8_306
<=> ! [X0: real,X1: real] :
( ( X0 != X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),zero_zero_real) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_306])]) ).
thf(f6763,plain,
( spl8_257
<=> ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) != X2 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_257])]) ).
thf(f6964,plain,
( ! [X0: real,X1: real] :
( ( X0 != X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),zero_zero_real) = X0 ) )
| ~ spl8_14
| ~ spl8_257 ),
inference(superposition,[],[f6764,f2025]) ).
thf(f6764,plain,
( ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) != X2 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = X0 ) )
| ~ spl8_257 ),
inference(avatar_component_clause,[],[f6763]) ).
thf(f8679,plain,
( spl8_305
| ~ spl8_18
| ~ spl8_256 ),
inference(avatar_split_clause,[],[f6947,f6759,f2040,f8677]) ).
thf(f8677,plain,
( spl8_305
<=> ! [X0: a,X1: a] :
( ( X0 != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),zero_zero_a) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_305])]) ).
thf(f6759,plain,
( spl8_256
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_256])]) ).
thf(f6947,plain,
( ! [X0: a,X1: a] :
( ( X0 != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),zero_zero_a) = X0 ) )
| ~ spl8_18
| ~ spl8_256 ),
inference(superposition,[],[f6760,f2041]) ).
thf(f6760,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) != X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = X2 ) )
| ~ spl8_256 ),
inference(avatar_component_clause,[],[f6759]) ).
thf(f8662,plain,
( spl8_303
| ~ spl8_304
| ~ spl8_122
| ~ spl8_152 ),
inference(avatar_split_clause,[],[f4541,f4538,f3971,f8659,f8656]) ).
thf(f8656,plain,
( spl8_303
<=> ! [X0: a] : ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_303])]) ).
thf(f4538,plain,
( spl8_152
<=> ! [X0: a,X1: real] :
( ( zero_zero_a != vAPP(a,a,f,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_152])]) ).
thf(f4541,plain,
( ! [X0: a] :
( ( zero_zero_a != vAPP(a,a,f,zero_zero_a) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) )
| ~ spl8_122
| ~ spl8_152 ),
inference(superposition,[],[f4539,f3972]) ).
thf(f4539,plain,
( ! [X0: a,X1: real] :
( ( zero_zero_a != vAPP(a,a,f,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) )
| ~ spl8_152 ),
inference(avatar_component_clause,[],[f4538]) ).
thf(f8654,plain,
( spl8_301
| ~ spl8_302
| ~ spl8_21
| ~ spl8_75 ),
inference(avatar_split_clause,[],[f2823,f2727,f2052,f8651,f8647]) ).
thf(f8647,plain,
( spl8_301
<=> ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),xx) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_301])]) ).
thf(f8651,plain,
( spl8_302
<=> ( zero_zero_a = vAPP(a,a,f,xx) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_302])]) ).
thf(f2823,plain,
( ( zero_zero_a != vAPP(a,a,f,xx) )
| ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),xx) )
| ~ spl8_21
| ~ spl8_75 ),
inference(trivial_inequality_removal,[],[f2820]) ).
thf(f2820,plain,
( ( $true != $true )
| ( zero_zero_a != vAPP(a,a,f,xx) )
| ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),xx) )
| ~ spl8_21
| ~ spl8_75 ),
inference(superposition,[],[f2728,f2054]) ).
thf(f8645,plain,
spl8_300,
inference(avatar_split_clause,[],[f1871,f8643]) ).
thf(f8643,plain,
( spl8_300
<=> ! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_300])]) ).
thf(f1871,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1181]) ).
thf(f1181,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),zero_zero_real) ),
inference(cnf_transformation,[],[f780]) ).
thf(f780,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),zero_zero_real) ),
inference(rectify,[],[f222]) ).
thf(f222,axiom,
! [X8: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X8) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X8)),zero_zero_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_neg__less__0__iff__less) ).
thf(f8641,plain,
spl8_299,
inference(avatar_split_clause,[],[f1870,f8639]) ).
thf(f8639,plain,
( spl8_299
<=> ! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_299])]) ).
thf(f1870,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),zero_zero_real) ) ),
inference(binary_proxy_clausification,[],[f1181]) ).
thf(f8637,plain,
spl8_298,
inference(avatar_split_clause,[],[f1869,f8635]) ).
thf(f8635,plain,
( spl8_298
<=> ! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_298])]) ).
thf(f1869,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1182]) ).
thf(f1182,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(cnf_transformation,[],[f781]) ).
thf(f781,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(rectify,[],[f220]) ).
thf(f220,axiom,
! [X8: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_neg__0__less__iff__less) ).
thf(f8633,plain,
spl8_297,
inference(avatar_split_clause,[],[f1868,f8631]) ).
thf(f8631,plain,
( spl8_297
<=> ! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_297])]) ).
thf(f1868,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1182]) ).
thf(f8629,plain,
( spl8_296
| ~ spl8_17
| ~ spl8_255 ),
inference(avatar_split_clause,[],[f6932,f6755,f2036,f8627]) ).
thf(f8627,plain,
( spl8_296
<=> ! [X0: a,X1: a] :
( ( X0 != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),zero_zero_a) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_296])]) ).
thf(f2036,plain,
( spl8_17
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),zero_zero_a) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
thf(f6755,plain,
( spl8_255
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_255])]) ).
thf(f6932,plain,
( ! [X0: a,X1: a] :
( ( X0 != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),zero_zero_a) = X0 ) )
| ~ spl8_17
| ~ spl8_255 ),
inference(superposition,[],[f6756,f2037]) ).
thf(f2037,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),zero_zero_a) = X0 )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f2036]) ).
thf(f6756,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) = X0 ) )
| ~ spl8_255 ),
inference(avatar_component_clause,[],[f6755]) ).
thf(f8625,plain,
spl8_295,
inference(avatar_split_clause,[],[f1867,f8623]) ).
thf(f8623,plain,
( spl8_295
<=> ! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_295])]) ).
thf(f1867,plain,
! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ) ),
inference(binary_proxy_clausification,[],[f1183]) ).
thf(f1183,plain,
! [X0: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(cnf_transformation,[],[f782]) ).
thf(f782,plain,
! [X0: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(rectify,[],[f219]) ).
thf(f219,axiom,
! [X8: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X8)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),zero_zero_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_neg__0__less__iff__less) ).
thf(f8621,plain,
spl8_294,
inference(avatar_split_clause,[],[f1866,f8619]) ).
thf(f8619,plain,
( spl8_294
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_294])]) ).
thf(f1866,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ) ),
inference(binary_proxy_clausification,[],[f1183]) ).
thf(f8617,plain,
spl8_293,
inference(avatar_split_clause,[],[f1865,f8615]) ).
thf(f8615,plain,
( spl8_293
<=> ! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),zero_zero_a) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_293])]) ).
thf(f1865,plain,
! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),zero_zero_a) ) ),
inference(binary_proxy_clausification,[],[f1184]) ).
thf(f1184,plain,
! [X0: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),zero_zero_a) ),
inference(cnf_transformation,[],[f783]) ).
thf(f783,plain,
! [X0: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),zero_zero_a) ),
inference(rectify,[],[f221]) ).
thf(f221,axiom,
! [X8: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X8)),zero_zero_a) = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_neg__less__0__iff__less) ).
thf(f8613,plain,
spl8_292,
inference(avatar_split_clause,[],[f1864,f8611]) ).
thf(f8611,plain,
( spl8_292
<=> ! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),zero_zero_a) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_292])]) ).
thf(f1864,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X0)),zero_zero_a) ) ),
inference(binary_proxy_clausification,[],[f1184]) ).
thf(f8609,plain,
spl8_291,
inference(avatar_split_clause,[],[f1863,f8607]) ).
thf(f8607,plain,
( spl8_291
<=> ! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_291])]) ).
thf(f1863,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1185]) ).
thf(f1185,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(cnf_transformation,[],[f784]) ).
thf(f784,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(rectify,[],[f217]) ).
thf(f217,axiom,
! [X8: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),vAPP(real,real,uminus_uminus_real,X8)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),zero_zero_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_less__neg__neg) ).
thf(f8605,plain,
spl8_290,
inference(avatar_split_clause,[],[f1862,f8603]) ).
thf(f8603,plain,
( spl8_290
<=> ! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_290])]) ).
thf(f1862,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1185]) ).
thf(f8601,plain,
spl8_289,
inference(avatar_split_clause,[],[f1861,f8599]) ).
thf(f8599,plain,
( spl8_289
<=> ! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_289])]) ).
thf(f1861,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ) ),
inference(binary_proxy_clausification,[],[f1186]) ).
thf(f1186,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ),
inference(cnf_transformation,[],[f785]) ).
thf(f785,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ),
inference(rectify,[],[f218]) ).
thf(f218,axiom,
! [X8: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X8)),X8) = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_neg__less__pos) ).
thf(f8597,plain,
spl8_288,
inference(avatar_split_clause,[],[f1860,f8595]) ).
thf(f8595,plain,
( spl8_288
<=> ! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_288])]) ).
thf(f1860,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ) ),
inference(binary_proxy_clausification,[],[f1186]) ).
thf(f8511,plain,
( spl8_287
| ~ spl8_13
| ~ spl8_253 ),
inference(avatar_split_clause,[],[f6898,f6747,f2020,f8509]) ).
thf(f8509,plain,
( spl8_287
<=> ! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),zero_zero_real) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_287])]) ).
thf(f6747,plain,
( spl8_253
<=> ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_253])]) ).
thf(f6898,plain,
( ! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),zero_zero_real) != X0 )
| ( X0 = X1 ) )
| ~ spl8_13
| ~ spl8_253 ),
inference(superposition,[],[f6748,f2021]) ).
thf(f6748,plain,
( ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
| ( X0 = X2 ) )
| ~ spl8_253 ),
inference(avatar_component_clause,[],[f6747]) ).
thf(f8507,plain,
spl8_286,
inference(avatar_split_clause,[],[f1530,f8505]) ).
thf(f8505,plain,
( spl8_286
<=> ! [X0: real,X3: real,X2: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) != vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) )
| ( X2 != X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_286])]) ).
thf(f1530,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) != vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[],[f1529]) ).
thf(f1529,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) != vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X2),X3) ) ),
inference(equality_proxy_clausification,[],[f1525]) ).
thf(f1525,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) != vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X2),X3) ) ),
inference(binary_proxy_clausification,[],[f1465]) ).
thf(f1465,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X2),X3) )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) != vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1085]) ).
thf(f1085,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X2),X3) )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) != vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) ) ),
inference(ennf_transformation,[],[f690]) ).
thf(f690,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X2),X3) ) ),
inference(fool_elimination,[],[f689]) ).
thf(f689,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) )
=> ( ( X0 = X1 )
= ( X2 = X3 ) ) ),
inference(rectify,[],[f138]) ).
thf(f138,axiom,
! [X8: real,X9: real,X18: real,X19: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X18),X19) )
=> ( ( X8 = X9 )
= ( X18 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_diff__eq__diff__eq) ).
thf(f8503,plain,
spl8_285,
inference(avatar_split_clause,[],[f1522,f8501]) ).
thf(f8501,plain,
( spl8_285
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( X0 = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) )
| ( X2 != X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_285])]) ).
thf(f1522,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( X0 = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[],[f1521]) ).
thf(f1521,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( X0 = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) ) ),
inference(equality_proxy_clausification,[],[f1517]) ).
thf(f1517,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) ) ),
inference(binary_proxy_clausification,[],[f1467]) ).
thf(f1467,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) ) ),
inference(cnf_transformation,[],[f1087]) ).
thf(f1087,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) ) ),
inference(ennf_transformation,[],[f692]) ).
thf(f692,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) ) ),
inference(fool_elimination,[],[f691]) ).
thf(f691,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) )
=> ( ( X0 = X1 )
= ( X2 = X3 ) ) ),
inference(rectify,[],[f137]) ).
thf(f137,axiom,
! [X8: a,X9: a,X18: a,X19: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X18),X19) )
=> ( ( X8 = X9 )
= ( X18 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_diff__eq__diff__eq) ).
thf(f7939,plain,
( spl8_284
| ~ spl8_12
| ~ spl8_251 ),
inference(avatar_split_clause,[],[f6855,f6739,f2016,f7937]) ).
thf(f7937,plain,
( spl8_284
<=> ! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X1) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_284])]) ).
thf(f6739,plain,
( spl8_251
<=> ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_251])]) ).
thf(f6855,plain,
( ! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X1) != X0 )
| ( X0 = X1 ) )
| ~ spl8_12
| ~ spl8_251 ),
inference(superposition,[],[f6740,f2017]) ).
thf(f6740,plain,
( ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2) )
| ( X1 = X2 ) )
| ~ spl8_251 ),
inference(avatar_component_clause,[],[f6739]) ).
thf(f7180,plain,
( spl8_283
| ~ spl8_18
| ~ spl8_249 ),
inference(avatar_split_clause,[],[f6829,f6731,f2040,f7178]) ).
thf(f7178,plain,
( spl8_283
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),zero_zero_a) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_283])]) ).
thf(f6731,plain,
( spl8_249
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_249])]) ).
thf(f6829,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),zero_zero_a) != X0 )
| ( X0 = X1 ) )
| ~ spl8_18
| ~ spl8_249 ),
inference(superposition,[],[f6732,f2041]) ).
thf(f6732,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) )
| ( X0 = X2 ) )
| ~ spl8_249 ),
inference(avatar_component_clause,[],[f6731]) ).
thf(f7099,plain,
( spl8_282
| ~ spl8_26
| ~ spl8_34
| ~ spl8_111 ),
inference(avatar_split_clause,[],[f4056,f3928,f2114,f2077,f7097]) ).
thf(f7097,plain,
( spl8_282
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_282])]) ).
thf(f4056,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),X0)) )
| ~ spl8_26
| ~ spl8_34
| ~ spl8_111 ),
inference(forward_demodulation,[],[f4049,f2115]) ).
thf(f4049,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),X0)) )
| ~ spl8_26
| ~ spl8_111 ),
inference(trivial_inequality_removal,[],[f4046]) ).
thf(f4046,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,tt),X0)) ) )
| ~ spl8_26
| ~ spl8_111 ),
inference(superposition,[],[f3929,f2079]) ).
thf(f7095,plain,
( spl8_281
| ~ spl8_24
| ~ spl8_34
| ~ spl8_111 ),
inference(avatar_split_clause,[],[f4055,f3928,f2114,f2067,f7093]) ).
thf(f7093,plain,
( spl8_281
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_281])]) ).
thf(f4055,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),X0)) )
| ~ spl8_24
| ~ spl8_34
| ~ spl8_111 ),
inference(forward_demodulation,[],[f4051,f2115]) ).
thf(f4051,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),X0)) )
| ~ spl8_24
| ~ spl8_111 ),
inference(trivial_inequality_removal,[],[f4044]) ).
thf(f4044,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,i1),X0)) ) )
| ~ spl8_24
| ~ spl8_111 ),
inference(superposition,[],[f3929,f2069]) ).
thf(f7091,plain,
( spl8_280
| ~ spl8_25
| ~ spl8_34
| ~ spl8_111 ),
inference(avatar_split_clause,[],[f4054,f3928,f2114,f2072,f7089]) ).
thf(f7089,plain,
( spl8_280
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,d),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_280])]) ).
thf(f4054,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,d),X0)) )
| ~ spl8_25
| ~ spl8_34
| ~ spl8_111 ),
inference(forward_demodulation,[],[f4052,f2115]) ).
thf(f4052,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,d),X0)) )
| ~ spl8_25
| ~ spl8_111 ),
inference(trivial_inequality_removal,[],[f4043]) ).
thf(f4043,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,d),X0)) ) )
| ~ spl8_25
| ~ spl8_111 ),
inference(superposition,[],[f3929,f2074]) ).
thf(f7087,plain,
( spl8_279
| ~ spl8_42
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f2372,f2272,f2172,f7085]) ).
thf(f7085,plain,
( spl8_279
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_279])]) ).
thf(f2372,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ~ spl8_42
| ~ spl8_53 ),
inference(superposition,[],[f2273,f2173]) ).
thf(f7083,plain,
( spl8_278
| ~ spl8_43
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f2371,f2272,f2176,f7081]) ).
thf(f7081,plain,
( spl8_278
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_278])]) ).
thf(f2371,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ~ spl8_43
| ~ spl8_53 ),
inference(superposition,[],[f2273,f2177]) ).
thf(f7079,plain,
( spl8_277
| ~ spl8_40
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f2359,f2268,f2164,f7077]) ).
thf(f7077,plain,
( spl8_277
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_277])]) ).
thf(f2359,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ~ spl8_40
| ~ spl8_52 ),
inference(superposition,[],[f2269,f2165]) ).
thf(f7075,plain,
( spl8_276
| ~ spl8_41
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f2358,f2268,f2168,f7073]) ).
thf(f7073,plain,
( spl8_276
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_276])]) ).
thf(f2358,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ~ spl8_41
| ~ spl8_52 ),
inference(superposition,[],[f2269,f2169]) ).
thf(f7071,plain,
( spl8_275
| ~ spl8_44
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f2348,f2264,f2180,f7069]) ).
thf(f7069,plain,
( spl8_275
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,uminus_uminus_a,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_275])]) ).
thf(f2348,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,uminus_uminus_a,X1)) = X0 )
| ~ spl8_44
| ~ spl8_51 ),
inference(superposition,[],[f2181,f2265]) ).
thf(f7067,plain,
( spl8_274
| ~ spl8_46
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f2347,f2264,f2188,f7065]) ).
thf(f7065,plain,
( spl8_274
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_274])]) ).
thf(f2347,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = X0 )
| ~ spl8_46
| ~ spl8_51 ),
inference(superposition,[],[f2189,f2265]) ).
thf(f7063,plain,
( spl8_273
| ~ spl8_15
| ~ spl8_247 ),
inference(avatar_split_clause,[],[f6787,f6709,f2028,f7061]) ).
thf(f6709,plain,
( spl8_247
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_247])]) ).
thf(f6787,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,zero_zero_a),X1) != X0 )
| ( X0 = X1 ) )
| ~ spl8_15
| ~ spl8_247 ),
inference(superposition,[],[f6710,f2029]) ).
thf(f6710,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2) )
| ( X1 = X2 ) )
| ~ spl8_247 ),
inference(avatar_component_clause,[],[f6709]) ).
thf(f7059,plain,
( spl8_272
| ~ spl8_9
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f2338,f2264,f2002,f7057]) ).
thf(f7057,plain,
( spl8_272
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_272])]) ).
thf(f7055,plain,
( spl8_271
| ~ spl8_42
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f2328,f2260,f2172,f7053]) ).
thf(f7053,plain,
( spl8_271
<=> ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_271])]) ).
thf(f2328,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),X1) )
| ~ spl8_42
| ~ spl8_50 ),
inference(superposition,[],[f2173,f2261]) ).
thf(f7051,plain,
( spl8_270
| ~ spl8_43
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f2327,f2260,f2176,f7049]) ).
thf(f7049,plain,
( spl8_270
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,uminus_uminus_a,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_270])]) ).
thf(f2327,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)),vAPP(a,a,uminus_uminus_a,X0)) = X1 )
| ~ spl8_43
| ~ spl8_50 ),
inference(superposition,[],[f2177,f2261]) ).
thf(f7047,plain,
( spl8_269
| ~ spl8_9
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f2321,f2260,f2002,f7045]) ).
thf(f7045,plain,
( spl8_269
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,uminus_uminus_a,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_269])]) ).
thf(f2321,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),vAPP(a,a,uminus_uminus_a,X0)) )
| ~ spl8_9
| ~ spl8_50 ),
inference(superposition,[],[f2261,f2003]) ).
thf(f7043,plain,
( spl8_268
| ~ spl8_40
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f2310,f2256,f2164,f7041]) ).
thf(f7041,plain,
( spl8_268
<=> ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_268])]) ).
thf(f2310,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),X1) )
| ~ spl8_40
| ~ spl8_49 ),
inference(superposition,[],[f2165,f2257]) ).
thf(f7039,plain,
( spl8_267
| ~ spl8_41
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f2309,f2256,f2168,f7037]) ).
thf(f7037,plain,
( spl8_267
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,uminus_uminus_real,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_267])]) ).
thf(f2309,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ~ spl8_41
| ~ spl8_49 ),
inference(superposition,[],[f2169,f2257]) ).
thf(f7035,plain,
( spl8_266
| ~ spl8_8
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f2303,f2256,f1998,f7033]) ).
thf(f7033,plain,
( spl8_266
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_266])]) ).
thf(f2303,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,uminus_uminus_real,X0)) )
| ~ spl8_8
| ~ spl8_49 ),
inference(superposition,[],[f2257,f1999]) ).
thf(f7031,plain,
( spl8_265
| ~ spl8_39
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f2293,f2249,f2160,f7029]) ).
thf(f7029,plain,
( spl8_265
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,uminus_uminus_real,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_265])]) ).
thf(f2293,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,uminus_uminus_real,X1)) = X0 )
| ~ spl8_39
| ~ spl8_48 ),
inference(superposition,[],[f2161,f2250]) ).
thf(f7027,plain,
( spl8_264
| ~ spl8_45
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f2292,f2249,f2184,f7025]) ).
thf(f7025,plain,
( spl8_264
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_264])]) ).
thf(f2292,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = X0 )
| ~ spl8_45
| ~ spl8_48 ),
inference(superposition,[],[f2185,f2250]) ).
thf(f7023,plain,
( spl8_263
| ~ spl8_8
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f2284,f2249,f1998,f7021]) ).
thf(f7021,plain,
( spl8_263
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,uminus_uminus_real,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_263])]) ).
thf(f6786,plain,
spl8_262,
inference(avatar_split_clause,[],[f1754,f6784]) ).
thf(f6784,plain,
( spl8_262
<=> ! [X0: real,X1: real > $o] :
( ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(sTfun(real,$o),set_real,collect_real,X1)) )
| ( $true = vAPP(real,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_262])]) ).
thf(f1754,plain,
! [X0: real,X1: real > $o] :
( ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(sTfun(real,$o),set_real,collect_real,X1)) )
| ( $true = vAPP(real,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1254]) ).
thf(f1254,plain,
! [X0: real,X1: real > $o] : ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(sTfun(real,$o),set_real,collect_real,X1)) = vAPP(real,$o,X1,X0) ),
inference(cnf_transformation,[],[f794]) ).
thf(f794,plain,
! [X0: real,X1: real > $o] : ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(sTfun(real,$o),set_real,collect_real,X1)) = vAPP(real,$o,X1,X0) ),
inference(rectify,[],[f48]) ).
thf(f48,axiom,
! [X8: real,X11: real > $o] : ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X8),vAPP(sTfun(real,$o),set_real,collect_real,X11)) = vAPP(real,$o,X11,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_mem__Collect__eq) ).
thf(f6782,plain,
spl8_261,
inference(avatar_split_clause,[],[f1753,f6780]) ).
thf(f6780,plain,
( spl8_261
<=> ! [X0: real,X1: real > $o] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(sTfun(real,$o),set_real,collect_real,X1)) )
| ( $false = vAPP(real,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_261])]) ).
thf(f1753,plain,
! [X0: real,X1: real > $o] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(sTfun(real,$o),set_real,collect_real,X1)) )
| ( $false = vAPP(real,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1254]) ).
thf(f6778,plain,
spl8_260,
inference(avatar_split_clause,[],[f1752,f6776]) ).
thf(f6776,plain,
( spl8_260
<=> ! [X0: a,X1: a > $o] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) )
| ( $true = vAPP(a,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_260])]) ).
thf(f1752,plain,
! [X0: a,X1: a > $o] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) )
| ( $true = vAPP(a,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1255]) ).
thf(f1255,plain,
! [X0: a,X1: a > $o] : ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) = vAPP(a,$o,X1,X0) ),
inference(cnf_transformation,[],[f795]) ).
thf(f795,plain,
! [X0: a,X1: a > $o] : ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) = vAPP(a,$o,X1,X0) ),
inference(rectify,[],[f47]) ).
thf(f47,axiom,
! [X8: a,X11: a > $o] : ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(sTfun(a,$o),set_a,collect_a,X11)) = vAPP(a,$o,X11,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mem__Collect__eq) ).
thf(f6774,plain,
spl8_259,
inference(avatar_split_clause,[],[f1751,f6772]) ).
thf(f6772,plain,
( spl8_259
<=> ! [X0: a,X1: a > $o] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) )
| ( $false = vAPP(a,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_259])]) ).
thf(f1751,plain,
! [X0: a,X1: a > $o] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) )
| ( $false = vAPP(a,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1255]) ).
thf(f6769,plain,
spl8_258,
inference(avatar_split_clause,[],[f1604,f6767]) ).
thf(f1604,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = X2 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) != X0 ) ),
inference(equality_proxy_clausification,[],[f1603]) ).
thf(f1603,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = X2 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1599]) ).
thf(f1599,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1390]) ).
thf(f1390,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),X0) ),
inference(cnf_transformation,[],[f578]) ).
thf(f578,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),X0) ),
inference(fool_elimination,[],[f577]) ).
thf(f577,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) = X2 )
= ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = X0 ) ),
inference(rectify,[],[f340]) ).
thf(f340,axiom,
! [X8: real,X9: real,X18: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9) = X18 )
= ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X18),X9) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_diff__eq__eq) ).
thf(f6765,plain,
spl8_257,
inference(avatar_split_clause,[],[f1602,f6763]) ).
thf(f1602,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) != X2 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = X0 ) ),
inference(equality_proxy_clausification,[],[f1601]) ).
thf(f1601,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) != X2 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1600]) ).
thf(f1600,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1390]) ).
thf(f6761,plain,
spl8_256,
inference(avatar_split_clause,[],[f1592,f6759]) ).
thf(f1592,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) != X0 ) ),
inference(equality_proxy_clausification,[],[f1591]) ).
thf(f1591,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = X2 )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1587]) ).
thf(f1587,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1392]) ).
thf(f1392,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),X0) ),
inference(cnf_transformation,[],[f582]) ).
thf(f582,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),X0) ),
inference(fool_elimination,[],[f581]) ).
thf(f581,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) = X2 )
= ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) = X0 ) ),
inference(rectify,[],[f339]) ).
thf(f339,axiom,
! [X8: a,X9: a,X18: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9) = X18 )
= ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X18),X9) = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_diff__eq__eq) ).
thf(f6757,plain,
spl8_255,
inference(avatar_split_clause,[],[f1590,f6755]) ).
thf(f1590,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) = X0 ) ),
inference(equality_proxy_clausification,[],[f1589]) ).
thf(f1589,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) != X2 )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1588]) ).
thf(f1588,plain,
! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1392]) ).
thf(f6753,plain,
spl8_254,
inference(avatar_split_clause,[],[f1580,f6751]) ).
thf(f6751,plain,
( spl8_254
<=> ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_254])]) ).
thf(f1580,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f1579]) ).
thf(f1579,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f1575]) ).
thf(f1575,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1394]) ).
thf(f1394,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2) ),
inference(cnf_transformation,[],[f586]) ).
thf(f586,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2) ),
inference(fool_elimination,[],[f585]) ).
thf(f585,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
= ( X0 = X2 ) ),
inference(rectify,[],[f156]) ).
thf(f156,axiom,
! [X9: real,X8: real,X18: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X8) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X18),X8) )
= ( X9 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_add__right__cancel) ).
thf(f6749,plain,
spl8_253,
inference(avatar_split_clause,[],[f1578,f6747]) ).
thf(f1578,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
| ( X0 = X2 ) ),
inference(equality_proxy_clausification,[],[f1577]) ).
thf(f1577,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f1576]) ).
thf(f1576,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1394]) ).
thf(f6745,plain,
spl8_252,
inference(avatar_split_clause,[],[f1574,f6743]) ).
thf(f6743,plain,
( spl8_252
<=> ! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2) )
| ( X1 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_252])]) ).
thf(f1574,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1573]) ).
thf(f1573,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1569]) ).
thf(f1569,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1395]) ).
thf(f1395,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2) ),
inference(cnf_transformation,[],[f588]) ).
thf(f588,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2) ),
inference(fool_elimination,[],[f587]) ).
thf(f587,plain,
! [X0: real,X1: real,X2: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2) )
= ( X1 = X2 ) ),
inference(rectify,[],[f158]) ).
thf(f158,axiom,
! [X8: real,X9: real,X18: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X18) )
= ( X9 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add__left__cancel) ).
thf(f6741,plain,
spl8_251,
inference(avatar_split_clause,[],[f1572,f6739]) ).
thf(f1572,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f1571]) ).
thf(f1571,plain,
! [X2: real,X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1570]) ).
thf(f1570,plain,
! [X2: real,X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1395]) ).
thf(f6737,plain,
spl8_250,
inference(avatar_split_clause,[],[f1556,f6735]) ).
thf(f6735,plain,
( spl8_250
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_250])]) ).
thf(f1556,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f1555]) ).
thf(f1555,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f1551]) ).
thf(f1551,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1398]) ).
thf(f1398,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) ),
inference(cnf_transformation,[],[f594]) ).
thf(f594,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) ),
inference(fool_elimination,[],[f593]) ).
thf(f593,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) )
= ( X0 = X2 ) ),
inference(rectify,[],[f277]) ).
thf(f277,axiom,
! [X9: a,X8: a,X18: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X18),X8) )
= ( X9 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_add_Oright__cancel) ).
thf(f6733,plain,
spl8_249,
inference(avatar_split_clause,[],[f1554,f6731]) ).
thf(f1554,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) )
| ( X0 = X2 ) ),
inference(equality_proxy_clausification,[],[f1553]) ).
thf(f1553,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f1552]) ).
thf(f1552,plain,
! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1398]) ).
thf(f6715,plain,
spl8_248,
inference(avatar_split_clause,[],[f1550,f6713]) ).
thf(f6713,plain,
( spl8_248
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2) )
| ( X1 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_248])]) ).
thf(f1550,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1549]) ).
thf(f1549,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1545]) ).
thf(f1545,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1399]) ).
thf(f1399,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ),
inference(cnf_transformation,[],[f596]) ).
thf(f596,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ),
inference(fool_elimination,[],[f595]) ).
thf(f595,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2) )
= ( X1 = X2 ) ),
inference(rectify,[],[f157]) ).
thf(f157,axiom,
! [X8: a,X9: a,X18: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X18) )
= ( X9 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_add__left__cancel) ).
thf(f6711,plain,
spl8_247,
inference(avatar_split_clause,[],[f1548,f6709]) ).
thf(f1548,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f1547]) ).
thf(f1547,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1546]) ).
thf(f1546,plain,
! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1399]) ).
thf(f6463,plain,
( spl8_246
| ~ spl8_45
| ~ spl8_218 ),
inference(avatar_split_clause,[],[f5777,f5717,f2184,f6461]) ).
thf(f6461,plain,
( spl8_246
<=> ! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) != X1 )
| ( zero_zero_real = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_246])]) ).
thf(f5717,plain,
( spl8_218
<=> ! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_218])]) ).
thf(f5777,plain,
( ! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) != X1 )
| ( zero_zero_real = X0 ) )
| ~ spl8_45
| ~ spl8_218 ),
inference(superposition,[],[f5718,f2185]) ).
thf(f5718,plain,
( ! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) != X0 )
| ( zero_zero_real = X1 ) )
| ~ spl8_218 ),
inference(avatar_component_clause,[],[f5717]) ).
thf(f6115,plain,
( spl8_245
| ~ spl8_14
| ~ spl8_26
| ~ spl8_110 ),
inference(avatar_split_clause,[],[f4040,f3924,f2077,f2024,f6113]) ).
thf(f6113,plain,
( spl8_245
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_245])]) ).
thf(f4040,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)),X0) )
| ~ spl8_14
| ~ spl8_26
| ~ spl8_110 ),
inference(forward_demodulation,[],[f4033,f2025]) ).
thf(f4033,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real)) )
| ~ spl8_26
| ~ spl8_110 ),
inference(trivial_inequality_removal,[],[f4030]) ).
thf(f4030,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),tt)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real)) ) )
| ~ spl8_26
| ~ spl8_110 ),
inference(superposition,[],[f3925,f2079]) ).
thf(f6111,plain,
( spl8_244
| ~ spl8_14
| ~ spl8_24
| ~ spl8_110 ),
inference(avatar_split_clause,[],[f4039,f3924,f2067,f2024,f6109]) ).
thf(f6109,plain,
( spl8_244
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_244])]) ).
thf(f4039,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),X0) )
| ~ spl8_14
| ~ spl8_24
| ~ spl8_110 ),
inference(forward_demodulation,[],[f4035,f2025]) ).
thf(f4035,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real)) )
| ~ spl8_24
| ~ spl8_110 ),
inference(trivial_inequality_removal,[],[f4028]) ).
thf(f4028,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),i1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real)) ) )
| ~ spl8_24
| ~ spl8_110 ),
inference(superposition,[],[f3925,f2069]) ).
thf(f6107,plain,
( spl8_243
| ~ spl8_14
| ~ spl8_25
| ~ spl8_110 ),
inference(avatar_split_clause,[],[f4038,f3924,f2072,f2024,f6105]) ).
thf(f6105,plain,
( spl8_243
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_243])]) ).
thf(f4038,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),X0) )
| ~ spl8_14
| ~ spl8_25
| ~ spl8_110 ),
inference(forward_demodulation,[],[f4036,f2025]) ).
thf(f4036,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real)) )
| ~ spl8_25
| ~ spl8_110 ),
inference(trivial_inequality_removal,[],[f4027]) ).
thf(f4027,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),d)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real)) ) )
| ~ spl8_25
| ~ spl8_110 ),
inference(superposition,[],[f3925,f2074]) ).
thf(f6103,plain,
( spl8_242
| ~ spl8_13
| ~ spl8_26
| ~ spl8_109 ),
inference(avatar_split_clause,[],[f4024,f3920,f2077,f2020,f6101]) ).
thf(f6101,plain,
( spl8_242
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),tt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_242])]) ).
thf(f4024,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),tt)) )
| ~ spl8_13
| ~ spl8_26
| ~ spl8_109 ),
inference(forward_demodulation,[],[f4017,f2021]) ).
thf(f4017,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),tt)) )
| ~ spl8_26
| ~ spl8_109 ),
inference(trivial_inequality_removal,[],[f4014]) ).
thf(f4014,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),tt)) ) )
| ~ spl8_26
| ~ spl8_109 ),
inference(superposition,[],[f3921,f2079]) ).
thf(f6099,plain,
( spl8_241
| ~ spl8_13
| ~ spl8_24
| ~ spl8_109 ),
inference(avatar_split_clause,[],[f4023,f3920,f2067,f2020,f6097]) ).
thf(f6097,plain,
( spl8_241
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_241])]) ).
thf(f4023,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i1)) )
| ~ spl8_13
| ~ spl8_24
| ~ spl8_109 ),
inference(forward_demodulation,[],[f4019,f2021]) ).
thf(f4019,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i1)) )
| ~ spl8_24
| ~ spl8_109 ),
inference(trivial_inequality_removal,[],[f4012]) ).
thf(f4012,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),i1)) ) )
| ~ spl8_24
| ~ spl8_109 ),
inference(superposition,[],[f3921,f2069]) ).
thf(f6095,plain,
( spl8_240
| ~ spl8_39
| ~ spl8_218 ),
inference(avatar_split_clause,[],[f5771,f5717,f2160,f6093]) ).
thf(f6093,plain,
( spl8_240
<=> ! [X0: real,X1: real] :
( ( X0 != X1 )
| ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_240])]) ).
thf(f5771,plain,
( ! [X0: real,X1: real] :
( ( X0 != X1 )
| ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1) ) )
| ~ spl8_39
| ~ spl8_218 ),
inference(superposition,[],[f5718,f2161]) ).
thf(f6091,plain,
( spl8_239
| ~ spl8_13
| ~ spl8_25
| ~ spl8_109 ),
inference(avatar_split_clause,[],[f4022,f3920,f2072,f2020,f6089]) ).
thf(f6089,plain,
( spl8_239
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),d)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_239])]) ).
thf(f4022,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),d)) )
| ~ spl8_13
| ~ spl8_25
| ~ spl8_109 ),
inference(forward_demodulation,[],[f4020,f2021]) ).
thf(f4020,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),d)) )
| ~ spl8_25
| ~ spl8_109 ),
inference(trivial_inequality_removal,[],[f4011]) ).
thf(f4011,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),d)) ) )
| ~ spl8_25
| ~ spl8_109 ),
inference(superposition,[],[f3921,f2074]) ).
thf(f6087,plain,
( spl8_238
| ~ spl8_12
| ~ spl8_26
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f4003,f3916,f2077,f2016,f6085]) ).
thf(f6085,plain,
( spl8_238
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_238])]) ).
thf(f4003,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X0)) )
| ~ spl8_12
| ~ spl8_26
| ~ spl8_108 ),
inference(forward_demodulation,[],[f3996,f2017]) ).
thf(f3996,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X0)) )
| ~ spl8_26
| ~ spl8_108 ),
inference(trivial_inequality_removal,[],[f3993]) ).
thf(f3993,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,tt),X0)) ) )
| ~ spl8_26
| ~ spl8_108 ),
inference(superposition,[],[f3917,f2079]) ).
thf(f6083,plain,
( spl8_237
| ~ spl8_12
| ~ spl8_24
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f4002,f3916,f2067,f2016,f6081]) ).
thf(f6081,plain,
( spl8_237
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_237])]) ).
thf(f4002,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X0)) )
| ~ spl8_12
| ~ spl8_24
| ~ spl8_108 ),
inference(forward_demodulation,[],[f3998,f2017]) ).
thf(f3998,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X0)) )
| ~ spl8_24
| ~ spl8_108 ),
inference(trivial_inequality_removal,[],[f3991]) ).
thf(f3991,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,i1),X0)) ) )
| ~ spl8_24
| ~ spl8_108 ),
inference(superposition,[],[f3917,f2069]) ).
thf(f6079,plain,
( spl8_236
| ~ spl8_12
| ~ spl8_25
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f4001,f3916,f2072,f2016,f6077]) ).
thf(f6077,plain,
( spl8_236
<=> ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_236])]) ).
thf(f4001,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X0)) )
| ~ spl8_12
| ~ spl8_25
| ~ spl8_108 ),
inference(forward_demodulation,[],[f3999,f2017]) ).
thf(f3999,plain,
( ! [X0: real] : ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X0)) )
| ~ spl8_25
| ~ spl8_108 ),
inference(trivial_inequality_removal,[],[f3990]) ).
thf(f3990,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,d),X0)) ) )
| ~ spl8_25
| ~ spl8_108 ),
inference(superposition,[],[f3917,f2074]) ).
thf(f6075,plain,
( spl8_235
| ~ spl8_43
| ~ spl8_44 ),
inference(avatar_split_clause,[],[f2228,f2180,f2176,f6073]) ).
thf(f6073,plain,
( spl8_235
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_235])]) ).
thf(f2228,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) = X1 )
| ~ spl8_43
| ~ spl8_44 ),
inference(superposition,[],[f2177,f2181]) ).
thf(f6071,plain,
( spl8_234
| ~ spl8_43
| ~ spl8_44 ),
inference(avatar_split_clause,[],[f2225,f2180,f2176,f6069]) ).
thf(f6069,plain,
( spl8_234
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_234])]) ).
thf(f2225,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) )
| ~ spl8_43
| ~ spl8_44 ),
inference(superposition,[],[f2181,f2177]) ).
thf(f6067,plain,
( spl8_233
| ~ spl8_39
| ~ spl8_41 ),
inference(avatar_split_clause,[],[f2209,f2168,f2160,f6065]) ).
thf(f6065,plain,
( spl8_233
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_233])]) ).
thf(f6063,plain,
( spl8_232
| ~ spl8_39
| ~ spl8_41 ),
inference(avatar_split_clause,[],[f2205,f2168,f2160,f6061]) ).
thf(f6061,plain,
( spl8_232
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_232])]) ).
thf(f2205,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) = X1 )
| ~ spl8_39
| ~ spl8_41 ),
inference(superposition,[],[f2169,f2161]) ).
thf(f6003,plain,
( spl8_231
| ~ spl8_46
| ~ spl8_213 ),
inference(avatar_split_clause,[],[f5745,f5696,f2188,f6001]) ).
thf(f6001,plain,
( spl8_231
<=> ! [X0: a,X1: a] :
( ( X0 != X1 )
| ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_231])]) ).
thf(f5696,plain,
( spl8_213
<=> ! [X0: a,X1: a] :
( ( zero_zero_a = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_213])]) ).
thf(f5745,plain,
( ! [X0: a,X1: a] :
( ( X0 != X1 )
| ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) ) )
| ~ spl8_46
| ~ spl8_213 ),
inference(superposition,[],[f5697,f2189]) ).
thf(f5697,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != X0 )
| ( zero_zero_a = X1 ) )
| ~ spl8_213 ),
inference(avatar_component_clause,[],[f5696]) ).
thf(f5999,plain,
( spl8_230
| ~ spl8_23
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f2539,f2521,f2062,f5996]) ).
thf(f5996,plain,
( spl8_230
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,d)),vAPP(real,real,uminus_uminus_real,tt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_230])]) ).
thf(f2521,plain,
( spl8_65
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
thf(f2539,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,d)),vAPP(real,real,uminus_uminus_real,tt)) )
| ~ spl8_23
| ~ spl8_65 ),
inference(trivial_inequality_removal,[],[f2528]) ).
thf(f2528,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,d)),vAPP(real,real,uminus_uminus_real,tt)) )
| ~ spl8_23
| ~ spl8_65 ),
inference(superposition,[],[f2522,f2064]) ).
thf(f2522,plain,
( ! [X0: real,X1: real] :
( ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ) )
| ~ spl8_65 ),
inference(avatar_component_clause,[],[f2521]) ).
thf(f5994,plain,
( spl8_229
| ~ spl8_22
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f2536,f2521,f2057,f5991]) ).
thf(f5991,plain,
( spl8_229
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,i2)),vAPP(real,real,uminus_uminus_real,i1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_229])]) ).
thf(f2536,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,i2)),vAPP(real,real,uminus_uminus_real,i1)) )
| ~ spl8_22
| ~ spl8_65 ),
inference(trivial_inequality_removal,[],[f2531]) ).
thf(f2531,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,i2)),vAPP(real,real,uminus_uminus_real,i1)) )
| ~ spl8_22
| ~ spl8_65 ),
inference(superposition,[],[f2522,f2059]) ).
thf(f5837,plain,
( spl8_228
| ~ spl8_4
| ~ spl8_26
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f2542,f2521,f2077,f1979,f5834]) ).
thf(f5834,plain,
( spl8_228
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,tt)),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_228])]) ).
thf(f1979,plain,
( spl8_4
<=> ( zero_zero_real = vAPP(real,real,uminus_uminus_real,zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
thf(f2542,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,tt)),zero_zero_real) )
| ~ spl8_4
| ~ spl8_26
| ~ spl8_65 ),
inference(forward_demodulation,[],[f2535,f1981]) ).
thf(f1981,plain,
( ( zero_zero_real = vAPP(real,real,uminus_uminus_real,zero_zero_real) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f1979]) ).
thf(f2535,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(real,real,uminus_uminus_real,zero_zero_real)) )
| ~ spl8_26
| ~ spl8_65 ),
inference(trivial_inequality_removal,[],[f2532]) ).
thf(f2532,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(real,real,uminus_uminus_real,zero_zero_real)) )
| ~ spl8_26
| ~ spl8_65 ),
inference(superposition,[],[f2522,f2079]) ).
thf(f5832,plain,
( spl8_227
| ~ spl8_4
| ~ spl8_24
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f2541,f2521,f2067,f1979,f5829]) ).
thf(f5829,plain,
( spl8_227
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,i1)),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_227])]) ).
thf(f2541,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,i1)),zero_zero_real) )
| ~ spl8_4
| ~ spl8_24
| ~ spl8_65 ),
inference(forward_demodulation,[],[f2537,f1981]) ).
thf(f2537,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,i1)),vAPP(real,real,uminus_uminus_real,zero_zero_real)) )
| ~ spl8_24
| ~ spl8_65 ),
inference(trivial_inequality_removal,[],[f2530]) ).
thf(f2530,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,i1)),vAPP(real,real,uminus_uminus_real,zero_zero_real)) )
| ~ spl8_24
| ~ spl8_65 ),
inference(superposition,[],[f2522,f2069]) ).
thf(f5827,plain,
( spl8_226
| ~ spl8_4
| ~ spl8_25
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f2540,f2521,f2072,f1979,f5824]) ).
thf(f5824,plain,
( spl8_226
<=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,d)),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_226])]) ).
thf(f2540,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,d)),zero_zero_real) )
| ~ spl8_4
| ~ spl8_25
| ~ spl8_65 ),
inference(forward_demodulation,[],[f2538,f1981]) ).
thf(f2538,plain,
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,d)),vAPP(real,real,uminus_uminus_real,zero_zero_real)) )
| ~ spl8_25
| ~ spl8_65 ),
inference(trivial_inequality_removal,[],[f2529]) ).
thf(f2529,plain,
( ( $true != $true )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,d)),vAPP(real,real,uminus_uminus_real,zero_zero_real)) )
| ~ spl8_25
| ~ spl8_65 ),
inference(superposition,[],[f2522,f2074]) ).
thf(f5822,plain,
( spl8_225
| ~ spl8_44
| ~ spl8_213 ),
inference(avatar_split_clause,[],[f5739,f5696,f2180,f5820]) ).
thf(f5820,plain,
( spl8_225
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) != X0 )
| ( zero_zero_a = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_225])]) ).
thf(f5739,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1) != X0 )
| ( zero_zero_a = X1 ) )
| ~ spl8_44
| ~ spl8_213 ),
inference(superposition,[],[f5697,f2181]) ).
thf(f5818,plain,
( spl8_224
| ~ spl8_29
| ~ spl8_42 ),
inference(avatar_split_clause,[],[f2214,f2172,f2094,f5816]) ).
thf(f5816,plain,
( spl8_224
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_224])]) ).
thf(f2214,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) = X0 )
| ~ spl8_29
| ~ spl8_42 ),
inference(superposition,[],[f2173,f2095]) ).
thf(f5814,plain,
( spl8_223
| ~ spl8_31
| ~ spl8_40 ),
inference(avatar_split_clause,[],[f2200,f2164,f2102,f5812]) ).
thf(f5812,plain,
( spl8_223
<=> ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_223])]) ).
thf(f2200,plain,
( ! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) = X0 )
| ~ spl8_31
| ~ spl8_40 ),
inference(superposition,[],[f2165,f2103]) ).
thf(f5735,plain,
spl8_222,
inference(avatar_split_clause,[],[f1817,f5733]) ).
thf(f5733,plain,
( spl8_222
<=> ! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_222])]) ).
thf(f1817,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) ) ),
inference(equality_proxy_clausification,[],[f1816]) ).
thf(f1816,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ) ),
inference(equality_proxy_clausification,[],[f1812]) ).
thf(f1812,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ) ),
inference(binary_proxy_clausification,[],[f1198]) ).
thf(f1198,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ),
inference(cnf_transformation,[],[f370]) ).
thf(f370,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ),
inference(fool_elimination,[],[f369]) ).
thf(f369,plain,
! [X0: real] :
( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) )
= ( zero_zero_real = X0 ) ),
inference(rectify,[],[f178]) ).
thf(f178,axiom,
! [X8: real] :
( ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X8) )
= ( zero_zero_real = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_double__zero__sym) ).
thf(f5731,plain,
spl8_221,
inference(avatar_split_clause,[],[f1815,f5729]) ).
thf(f5729,plain,
( spl8_221
<=> ! [X0: real] :
( ( zero_zero_real != X0 )
| ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_221])]) ).
thf(f1815,plain,
! [X0: real] :
( ( zero_zero_real != X0 )
| ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0) ) ),
inference(equality_proxy_clausification,[],[f1814]) ).
thf(f1814,plain,
! [X0: real] :
( ( zero_zero_real != X0 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ) ),
inference(equality_proxy_clausification,[],[f1813]) ).
thf(f1813,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X0)) ) ),
inference(binary_proxy_clausification,[],[f1198]) ).
thf(f5727,plain,
spl8_220,
inference(avatar_split_clause,[],[f1682,f5725]) ).
thf(f5725,plain,
( spl8_220
<=> ! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_220])]) ).
thf(f1682,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) != X0 ) ),
inference(equality_proxy_clausification,[],[f1681]) ).
thf(f1681,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1677]) ).
thf(f1677,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1304]) ).
thf(f1304,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ),
inference(cnf_transformation,[],[f482]) ).
thf(f482,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ),
inference(fool_elimination,[],[f481]) ).
thf(f481,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = X0 )
= ( zero_zero_real = X1 ) ),
inference(rectify,[],[f186]) ).
thf(f186,axiom,
! [X8: real,X9: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9) = X8 )
= ( zero_zero_real = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_add__cancel__right__right) ).
thf(f5723,plain,
spl8_219,
inference(avatar_split_clause,[],[f1680,f5721]) ).
thf(f5721,plain,
( spl8_219
<=> ! [X0: real,X1: real] :
( ( zero_zero_real != X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_219])]) ).
thf(f1680,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = X0 ) ),
inference(equality_proxy_clausification,[],[f1679]) ).
thf(f1679,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != X1 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1678]) ).
thf(f1678,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1304]) ).
thf(f5719,plain,
spl8_218,
inference(avatar_split_clause,[],[f1676,f5717]) ).
thf(f1676,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) != X0 ) ),
inference(equality_proxy_clausification,[],[f1675]) ).
thf(f1675,plain,
! [X0: real,X1: real] :
( ( zero_zero_real = X1 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),X0) ) ),
inference(equality_proxy_clausification,[],[f1671]) ).
thf(f1671,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),X0) ) ),
inference(binary_proxy_clausification,[],[f1305]) ).
thf(f1305,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),X0) ),
inference(cnf_transformation,[],[f484]) ).
thf(f484,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),X0) ),
inference(fool_elimination,[],[f483]) ).
thf(f483,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) = X0 )
= ( zero_zero_real = X1 ) ),
inference(rectify,[],[f184]) ).
thf(f184,axiom,
! [X8: real,X9: real] :
( ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X8) = X8 )
= ( zero_zero_real = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_add__cancel__right__left) ).
thf(f5715,plain,
spl8_217,
inference(avatar_split_clause,[],[f1674,f5713]) ).
thf(f5713,plain,
( spl8_217
<=> ! [X0: real,X1: real] :
( ( zero_zero_real != X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_217])]) ).
thf(f1674,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != X1 )
| ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) = X0 ) ),
inference(equality_proxy_clausification,[],[f1673]) ).
thf(f1673,plain,
! [X0: real,X1: real] :
( ( zero_zero_real != X1 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),X0) ) ),
inference(equality_proxy_clausification,[],[f1672]) ).
thf(f1672,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0)),X0) ) ),
inference(binary_proxy_clausification,[],[f1305]) ).
thf(f5711,plain,
spl8_216,
inference(avatar_split_clause,[],[f1658,f5709]) ).
thf(f5709,plain,
( spl8_216
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) = X0 )
| ( zero_zero_a != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_216])]) ).
thf(f1658,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) = X0 )
| ( zero_zero_a != X1 ) ),
inference(equality_proxy_clausification,[],[f1657]) ).
thf(f1657,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) = X0 )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) ) ),
inference(equality_proxy_clausification,[],[f1653]) ).
thf(f1653,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) ) ),
inference(binary_proxy_clausification,[],[f1308]) ).
thf(f1308,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) ),
inference(cnf_transformation,[],[f490]) ).
thf(f490,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) ),
inference(fool_elimination,[],[f489]) ).
thf(f489,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) = X0 )
= ( zero_zero_a = X1 ) ),
inference(rectify,[],[f183]) ).
thf(f183,axiom,
! [X8: a,X9: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X8) = X8 )
= ( zero_zero_a = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_add__cancel__right__left) ).
thf(f5707,plain,
spl8_215,
inference(avatar_split_clause,[],[f1656,f5705]) ).
thf(f5705,plain,
( spl8_215
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) != X0 )
| ( zero_zero_a = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_215])]) ).
thf(f1656,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) != X0 )
| ( zero_zero_a = X1 ) ),
inference(equality_proxy_clausification,[],[f1655]) ).
thf(f1655,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) != X0 )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) ) ),
inference(equality_proxy_clausification,[],[f1654]) ).
thf(f1654,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0)),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) ) ),
inference(binary_proxy_clausification,[],[f1308]) ).
thf(f5703,plain,
( ~ spl8_214
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_177
| ~ spl8_206
| spl8_209 ),
inference(avatar_split_clause,[],[f5580,f5576,f5509,f4737,f4581,f4550,f2515,f2510,f2249,f1998,f5700]) ).
thf(f5700,plain,
( spl8_214
<=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,xx),x) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_214])]) ).
thf(f5576,plain,
( spl8_209
<=> ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_209])]) ).
thf(f5580,plain,
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,xx),x) != $false )
| ~ spl8_8
| ~ spl8_48
| ~ spl8_63
| ~ spl8_64
| ~ spl8_154
| ~ spl8_157
| ~ spl8_177
| ~ spl8_206
| spl8_209 ),
inference(forward_demodulation,[],[f5577,f5529]) ).
thf(f5577,plain,
( ( $false != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),x) )
| spl8_209 ),
inference(avatar_component_clause,[],[f5576]) ).
thf(f5698,plain,
spl8_213,
inference(avatar_split_clause,[],[f1652,f5696]) ).
thf(f1652,plain,
! [X0: a,X1: a] :
( ( zero_zero_a = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) != X0 ) ),
inference(equality_proxy_clausification,[],[f1651]) ).
thf(f1651,plain,
! [X0: a,X1: a] :
( ( zero_zero_a = X1 )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1647]) ).
thf(f1647,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1309]) ).
thf(f1309,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ),
inference(cnf_transformation,[],[f492]) ).
thf(f492,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ),
inference(fool_elimination,[],[f491]) ).
thf(f491,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = X0 )
= ( zero_zero_a = X1 ) ),
inference(rectify,[],[f181]) ).
thf(f181,axiom,
! [X8: a,X9: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9) = X8 )
= ( zero_zero_a = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_add__cancel__left__right) ).
thf(f5694,plain,
spl8_212,
inference(avatar_split_clause,[],[f1650,f5692]) ).
thf(f5692,plain,
( spl8_212
<=> ! [X0: a,X1: a] :
( ( zero_zero_a != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_212])]) ).
thf(f1650,plain,
! [X0: a,X1: a] :
( ( zero_zero_a != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = X0 ) ),
inference(equality_proxy_clausification,[],[f1649]) ).
thf(f1649,plain,
! [X0: a,X1: a] :
( ( zero_zero_a != X1 )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1648]) ).
thf(f1648,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1309]) ).
thf(f5624,plain,
spl8_211,
inference(avatar_split_clause,[],[f1927,f5622]) ).
thf(f5622,plain,
( spl8_211
<=> ! [X0: real,X3: real,X2: a,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)))) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X3)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_211])]) ).
thf(f1927,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)))) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X3)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1926,f1268]) ).
thf(f1268,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ),
inference(cnf_transformation,[],[f808]) ).
thf(f808,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)) ),
inference(rectify,[],[f114]) ).
thf(f114,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_minus__diff__eq) ).
thf(f1926,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))))) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X3)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1925,f1297]) ).
thf(f1297,plain,
! [X0: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X1)) ),
inference(cnf_transformation,[],[f837]) ).
thf(f837,plain,
! [X0: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X1)) ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X6: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X6),vAPP(real,real,uminus_uminus_real,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_rev__eq__flow) ).
thf(f1925,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X3)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1924,f1268]) ).
thf(f1924,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X3)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1923,f1297]) ).
thf(f1923,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),vAPP(real,real,uminus_uminus_real,X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1922,f1268]) ).
thf(f1922,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))),vAPP(real,real,uminus_uminus_real,X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1921,f1297]) ).
thf(f1921,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))),X3) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1482,f1297]) ).
thf(f1482,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(cnf_transformation,[],[f1117]) ).
thf(f1117,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(flattening,[],[f1116]) ).
thf(f1116,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(ennf_transformation,[],[f718]) ).
thf(f718,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) ) ) ),
inference(fool_elimination,[],[f717]) ).
thf(f717,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) ) ) ),
inference(rectify,[],[f171]) ).
thf(f171,axiom,
! [X15: real,X2: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2))))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X1)),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2))),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_rev_Ogeneral_Oflow__trans) ).
thf(f5585,plain,
spl8_210,
inference(avatar_split_clause,[],[f1919,f5583]) ).
thf(f5583,plain,
( spl8_210
<=> ! [X0: real,X3: real,X2: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X3),X1))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_210])]) ).
thf(f1919,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X3),X1))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(forward_demodulation,[],[f1480,f1373]) ).
thf(f1480,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(cnf_transformation,[],[f1113]) ).
thf(f1113,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(flattening,[],[f1112]) ).
thf(f1112,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(ennf_transformation,[],[f714]) ).
thf(f714,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) ) ) ),
inference(fool_elimination,[],[f713]) ).
thf(f713,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),X3) ) ) ),
inference(rectify,[],[f167]) ).
thf(f167,axiom,
! [X15: real,X2: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2))))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X1)),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2))),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_general_Oflow__trans) ).
thf(f5579,plain,
( spl8_209
| ~ spl8_2
| spl8_193 ),
inference(avatar_split_clause,[],[f5380,f5071,f1942,f5576]) ).
thf(f5071,plain,
( spl8_193
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_193])]) ).
thf(f5380,plain,
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),x) )
| ~ spl8_2
| spl8_193 ),
inference(trivial_inequality_removal,[],[f5379]) ).
thf(f5379,plain,
( ( $true != $true )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),x) )
| ~ spl8_2
| spl8_193 ),
inference(superposition,[],[f5072,f1943]) ).
thf(f5072,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),x) )
| spl8_193 ),
inference(avatar_component_clause,[],[f5071]) ).
thf(f5557,plain,
spl8_208,
inference(avatar_split_clause,[],[f1911,f5555]) ).
thf(f5555,plain,
( spl8_208
<=> ! [X2: real,X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),vAPP(real,real,uminus_uminus_real,X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_208])]) ).
thf(f1911,plain,
! [X2: real,X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),vAPP(real,real,uminus_uminus_real,X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1910,f1297]) ).
thf(f1910,plain,
! [X2: real,X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),vAPP(real,real,uminus_uminus_real,X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1909,f1297]) ).
thf(f1909,plain,
! [X2: real,X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),vAPP(real,real,uminus_uminus_real,X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1908,f1297]) ).
thf(f1908,plain,
! [X2: real,X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1434,f1297]) ).
thf(f1434,plain,
! [X2: real,X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f1051]) ).
thf(f1051,plain,
! [X0: real,X1: a,X2: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(flattening,[],[f1050]) ).
thf(f1050,plain,
! [X0: real,X1: a,X2: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f650]) ).
thf(f650,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),X2) ) ) ),
inference(fool_elimination,[],[f649]) ).
thf(f649,plain,
! [X0: real,X1: a,X2: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),X2) ) ) ),
inference(rectify,[],[f164]) ).
thf(f164,axiom,
! [X15: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X15),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),X15)))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),X15)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_local_Orev_Oflow__trans) ).
thf(f5533,plain,
spl8_207,
inference(avatar_split_clause,[],[f1404,f5531]) ).
thf(f5531,plain,
( spl8_207
<=> ! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) )
| ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_207])]) ).
thf(f1404,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) )
| ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f1013]) ).
thf(f1013,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) )
| ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( X0 = X1 ) ),
inference(flattening,[],[f1012]) ).
thf(f1012,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) )
| ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f606]) ).
thf(f606,plain,
! [X0: real,X1: real,X2: a] :
( ( X0 != X1 )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
=> ( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X2) )
=> ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) ) ) ) ) ) ),
inference(fool_elimination,[],[f605]) ).
thf(f605,plain,
! [X0: real,X1: real,X2: a] :
( ( X0 != X1 )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
=> ( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X2) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) ) ) ) ) ),
inference(rectify,[],[f96]) ).
thf(f96,axiom,
! [X1: real,X5: real,X6: a] :
( ( X1 != X5 )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X5),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6),X5) )
=> ( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X6) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rev_Operiodic__orbitI) ).
thf(f5511,plain,
spl8_206,
inference(avatar_split_clause,[],[f1427,f5509]) ).
thf(f1427,plain,
! [X2: real,X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f1041]) ).
thf(f1041,plain,
! [X0: real,X1: a,X2: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(flattening,[],[f1040]) ).
thf(f1040,plain,
! [X0: real,X1: a,X2: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),X2) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f636]) ).
thf(f636,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),X2) ) ) ),
inference(fool_elimination,[],[f635]) ).
thf(f635,plain,
! [X0: real,X1: a,X2: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),X2) ) ) ),
inference(rectify,[],[f160]) ).
thf(f160,axiom,
! [X15: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X15),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),X15)))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),X15)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_local_Oflow__trans) ).
thf(f5487,plain,
spl8_205,
inference(avatar_split_clause,[],[f1405,f5485]) ).
thf(f5485,plain,
( spl8_205
<=> ! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_205])]) ).
thf(f1405,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f1015]) ).
thf(f1015,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( X0 = X1 ) ),
inference(flattening,[],[f1014]) ).
thf(f1014,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f608]) ).
thf(f608,plain,
! [X0: real,X1: real,X2: a] :
( ( X0 != X1 )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
=> ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) ) ) ) ) ),
inference(fool_elimination,[],[f607]) ).
thf(f607,plain,
! [X0: real,X1: real,X2: a] :
( ( X0 != X1 )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X1) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2) ) ) ) ),
inference(rectify,[],[f84]) ).
thf(f84,axiom,
! [X1: real,X5: real,X6: a] :
( ( X1 != X5 )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X5),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6),X5) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rev_Oclosed__orbitI) ).
thf(f5376,plain,
spl8_204,
inference(avatar_split_clause,[],[f1934,f5374]) ).
thf(f5374,plain,
( spl8_204
<=> ! [X0: real,X3: a,X2: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_204])]) ).
thf(f1934,plain,
! [X2: real,X3: a,X0: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ),
inference(forward_demodulation,[],[f1933,f1373]) ).
thf(f1933,plain,
! [X2: real,X3: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ),
inference(forward_demodulation,[],[f1932,f1268]) ).
thf(f1932,plain,
! [X2: real,X3: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2))))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ),
inference(forward_demodulation,[],[f1485,f1297]) ).
thf(f1485,plain,
! [X2: real,X3: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ),
inference(cnf_transformation,[],[f1123]) ).
thf(f1123,plain,
! [X0: real,X1: real,X2: real,X3: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ),
inference(flattening,[],[f1122]) ).
thf(f1122,plain,
! [X0: real,X1: real,X2: real,X3: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ),
inference(ennf_transformation,[],[f724]) ).
thf(f724,plain,
! [X0: real,X1: real,X2: real,X3: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) ) ) ),
inference(fool_elimination,[],[f723]) ).
thf(f723,plain,
! [X0: real,X1: real,X2: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) ) ),
inference(rectify,[],[f172]) ).
thf(f172,axiom,
! [X1: real,X15: real,X2: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X15)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X15),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rev_Ogeneral_Oexistence__ivl__trans_H) ).
thf(f5372,plain,
spl8_203,
inference(avatar_split_clause,[],[f1930,f5370]) ).
thf(f5370,plain,
( spl8_203
<=> ! [X0: real,X3: real,X2: a,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)))) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X3),X1))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_203])]) ).
thf(f1930,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)))) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X3),X1))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1929,f1268]) ).
thf(f1929,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))))) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X3),X1))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1928,f1297]) ).
thf(f1928,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X3),X1))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1483,f1373]) ).
thf(f1483,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(cnf_transformation,[],[f1119]) ).
thf(f1119,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(flattening,[],[f1118]) ).
thf(f1118,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(ennf_transformation,[],[f720]) ).
thf(f720,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ) ),
inference(fool_elimination,[],[f719]) ).
thf(f719,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(rectify,[],[f153]) ).
thf(f153,axiom,
! [X15: real,X2: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2))))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rev_Ogeneral_Oexistence__ivl__trans) ).
thf(f5275,plain,
spl8_202,
inference(avatar_split_clause,[],[f1931,f5273]) ).
thf(f5273,plain,
( spl8_202
<=> ! [X0: real,X3: a,X2: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_202])]) ).
thf(f1931,plain,
! [X2: real,X3: a,X0: real,X1: real] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) ) ),
inference(forward_demodulation,[],[f1484,f1373]) ).
thf(f1484,plain,
! [X2: real,X3: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) ) ),
inference(cnf_transformation,[],[f1121]) ).
thf(f1121,plain,
! [X0: real,X1: real,X2: real,X3: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) ) ),
inference(flattening,[],[f1120]) ).
thf(f1120,plain,
! [X0: real,X1: real,X2: real,X3: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) ) ),
inference(ennf_transformation,[],[f722]) ).
thf(f722,plain,
! [X0: real,X1: real,X2: real,X3: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) ) ) ),
inference(fool_elimination,[],[f721]) ).
thf(f721,plain,
! [X0: real,X1: real,X2: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)))) ) ),
inference(rectify,[],[f168]) ).
thf(f168,axiom,
! [X1: real,X15: real,X2: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X15)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X15),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_general_Oexistence__ivl__trans_H) ).
thf(f5271,plain,
spl8_201,
inference(avatar_split_clause,[],[f1920,f5269]) ).
thf(f5269,plain,
( spl8_201
<=> ! [X0: real,X3: real,X2: a,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X3),X1))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_201])]) ).
thf(f1920,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X3),X1))),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(forward_demodulation,[],[f1481,f1373]) ).
thf(f1481,plain,
! [X2: a,X3: real,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(cnf_transformation,[],[f1115]) ).
thf(f1115,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(flattening,[],[f1114]) ).
thf(f1114,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(ennf_transformation,[],[f716]) ).
thf(f716,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ) ),
inference(fool_elimination,[],[f715]) ).
thf(f715,plain,
! [X0: real,X1: real,X2: a,X3: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X3),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X3)),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(rectify,[],[f169]) ).
thf(f169,axiom,
! [X15: real,X2: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X15),X2))))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X1)),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_general_Oexistence__ivl__trans) ).
thf(f5211,plain,
spl8_200,
inference(avatar_split_clause,[],[f1913,f5209]) ).
thf(f5209,plain,
( spl8_200
<=> ! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_200])]) ).
thf(f1913,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1447,f1297]) ).
thf(f1447,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(cnf_transformation,[],[f1067]) ).
thf(f1067,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(flattening,[],[f1066]) ).
thf(f1066,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(ennf_transformation,[],[f672]) ).
thf(f672,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0))) ) ) ),
inference(fool_elimination,[],[f671]) ).
thf(f671,plain,
! [X0: real,X1: real,X2: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),X0))) ) ),
inference(rectify,[],[f165]) ).
thf(f165,axiom,
! [X1: real,X15: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X15)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X15),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_local_Orev_Oexistence__ivl__trans_H) ).
thf(f5188,plain,
spl8_199,
inference(avatar_split_clause,[],[f1912,f5186]) ).
thf(f5186,plain,
( spl8_199
<=> ! [X2: real,X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_199])]) ).
thf(f1912,plain,
! [X2: real,X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1435,f1297]) ).
thf(f1435,plain,
! [X2: real,X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f1053]) ).
thf(f1053,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(flattening,[],[f1052]) ).
thf(f1052,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f652]) ).
thf(f652,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
inference(fool_elimination,[],[f651]) ).
thf(f651,plain,
! [X0: real,X1: a,X2: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(rectify,[],[f166]) ).
thf(f166,axiom,
! [X15: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X15),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),X15)))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_local_Orev_Oexistence__ivl__trans) ).
thf(f5184,plain,
spl8_198,
inference(avatar_split_clause,[],[f1907,f5182]) ).
thf(f5182,plain,
( spl8_198
<=> ! [X2: real,X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_198])]) ).
thf(f1907,plain,
! [X2: real,X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1433,f1297]) ).
thf(f1433,plain,
! [X2: real,X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f1049]) ).
thf(f1049,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(flattening,[],[f1048]) ).
thf(f1048,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f648]) ).
thf(f648,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) ) ) ),
inference(fool_elimination,[],[f647]) ).
thf(f647,plain,
! [X0: real,X1: a,X2: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) ) ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X2: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rev_Odiff__existence__ivl__trans) ).
thf(f5164,plain,
spl8_197,
inference(avatar_split_clause,[],[f1402,f5162]) ).
thf(f5162,plain,
( spl8_197
<=> ! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X2) )
| ( zero_zero_a = vAPP(a,a,f,X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_197])]) ).
thf(f1402,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X2) )
| ( zero_zero_a = vAPP(a,a,f,X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f1009]) ).
thf(f1009,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X2) )
| ( zero_zero_a = vAPP(a,a,f,X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( X0 = X1 ) ),
inference(flattening,[],[f1008]) ).
thf(f1008,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X2) )
| ( zero_zero_a = vAPP(a,a,f,X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f602]) ).
thf(f602,plain,
! [X0: real,X1: real,X2: a] :
( ( X0 != X1 )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
=> ( ( zero_zero_a != vAPP(a,a,f,X2) )
=> ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X2) ) ) ) ) ) ),
inference(fool_elimination,[],[f601]) ).
thf(f601,plain,
! [X0: real,X1: real,X2: a] :
( ( X0 != X1 )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
=> ( ( zero_zero_a != vAPP(a,a,f,X2) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X2) ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f26,axiom,
! [X1: real,X5: real,X6: a] :
( ( X1 != X5 )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X6))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X5),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X6))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X6),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X6),X5) )
=> ( ( zero_zero_a != vAPP(a,a,f,X6) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X6) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_periodic__orbitI) ).
thf(f5144,plain,
spl8_196,
inference(avatar_split_clause,[],[f1403,f5142]) ).
thf(f5142,plain,
( spl8_196
<=> ! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_196])]) ).
thf(f1403,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f1011]) ).
thf(f1011,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( X0 = X1 ) ),
inference(flattening,[],[f1010]) ).
thf(f1010,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X2) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f604]) ).
thf(f604,plain,
! [X0: real,X1: real,X2: a] :
( ( X0 != X1 )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
=> ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X2) ) ) ) ) ),
inference(fool_elimination,[],[f603]) ).
thf(f603,plain,
! [X0: real,X1: real,X2: a] :
( ( X0 != X1 )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X1) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X2) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X1: real,X5: real,X6: a] :
( ( X1 != X5 )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X6))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X5),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X6))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X6),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X6),X5) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_closed__orbitI) ).
thf(f5086,plain,
spl8_195,
inference(avatar_split_clause,[],[f1918,f5084]) ).
thf(f5084,plain,
( spl8_195
<=> ! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_195])]) ).
thf(f1918,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1917,f1268]) ).
thf(f1917,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1457,f1297]) ).
thf(f1457,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(cnf_transformation,[],[f1077]) ).
thf(f1077,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(ennf_transformation,[],[f688]) ).
thf(f688,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) ) ),
inference(fool_elimination,[],[f687]) ).
thf(f687,plain,
! [X0: real,X1: real,X2: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) ),
inference(rectify,[],[f74]) ).
thf(f74,axiom,
! [X1: real,X2: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rev_Ogeneral_Oexistence__ivl__reverse) ).
thf(f5082,plain,
spl8_194,
inference(avatar_split_clause,[],[f1915,f5080]) ).
thf(f5080,plain,
( spl8_194
<=> ! [X2: a,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_194])]) ).
thf(f1915,plain,
! [X2: a,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1914,f1268]) ).
thf(f1914,plain,
! [X2: a,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(forward_demodulation,[],[f1448,f1297]) ).
thf(f1448,plain,
! [X2: a,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(cnf_transformation,[],[f1068]) ).
thf(f1068,plain,
! [X0: real,X1: real,X2: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) ) ),
inference(ennf_transformation,[],[f674]) ).
thf(f674,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2)) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 ) ),
inference(fool_elimination,[],[f673]) ).
thf(f673,plain,
! [X0: real,X1: real,X2: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 ) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
! [X1: real,X2: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rev_Ogeneral_Oflows__reverse) ).
thf(f5074,plain,
( spl8_193
| ~ spl8_161
| ~ spl8_168 ),
inference(avatar_split_clause,[],[f4830,f4649,f4605,f5071]) ).
thf(f4830,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),x) )
| ~ spl8_161
| ~ spl8_168 ),
inference(trivial_inequality_removal,[],[f4823]) ).
thf(f4823,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt))),x) )
| ~ spl8_161
| ~ spl8_168 ),
inference(superposition,[],[f4650,f4607]) ).
thf(f5022,plain,
spl8_192,
inference(avatar_split_clause,[],[f1436,f5020]) ).
thf(f5020,plain,
( spl8_192
<=> ! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_192])]) ).
thf(f1436,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(cnf_transformation,[],[f1055]) ).
thf(f1055,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(flattening,[],[f1054]) ).
thf(f1054,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(ennf_transformation,[],[f654]) ).
thf(f654,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0))) ) ) ),
inference(fool_elimination,[],[f653]) ).
thf(f653,plain,
! [X0: real,X1: real,X2: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),X0))) ) ),
inference(rectify,[],[f161]) ).
thf(f161,axiom,
! [X1: real,X15: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X15)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X15),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_local_Oexistence__ivl__trans_H) ).
thf(f5018,plain,
spl8_191,
inference(avatar_split_clause,[],[f1428,f5016]) ).
thf(f1428,plain,
! [X2: real,X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f1043]) ).
thf(f1043,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(flattening,[],[f1042]) ).
thf(f1042,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f638]) ).
thf(f638,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
inference(fool_elimination,[],[f637]) ).
thf(f637,plain,
! [X0: real,X1: a,X2: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(rectify,[],[f162]) ).
thf(f162,axiom,
! [X15: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X15),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),X15)))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X15),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_local_Oexistence__ivl__trans) ).
thf(f5014,plain,
spl8_190,
inference(avatar_split_clause,[],[f1426,f5012]) ).
thf(f5012,plain,
( spl8_190
<=> ! [X2: real,X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_190])]) ).
thf(f1426,plain,
! [X2: real,X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f1039]) ).
thf(f1039,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(flattening,[],[f1038]) ).
thf(f1038,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f634]) ).
thf(f634,plain,
! [X0: real,X1: a,X2: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) ) ) ),
inference(fool_elimination,[],[f633]) ).
thf(f633,plain,
! [X0: real,X1: a,X2: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) ) ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X2: real,X3: a,X1: real] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_diff__existence__ivl__trans) ).
thf(f4952,plain,
spl8_189,
inference(avatar_split_clause,[],[f1446,f4950]) ).
thf(f1446,plain,
! [X2: a,X0: real,X1: real] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(cnf_transformation,[],[f1065]) ).
thf(f1065,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(ennf_transformation,[],[f670]) ).
thf(f670,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) ) ),
inference(fool_elimination,[],[f669]) ).
thf(f669,plain,
! [X0: real,X1: real,X2: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)))) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X1: real,X2: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_general_Oexistence__ivl__reverse) ).
thf(f4948,plain,
spl8_188,
inference(avatar_split_clause,[],[f1437,f4946]) ).
thf(f4946,plain,
( spl8_188
<=> ! [X2: a,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_188])]) ).
thf(f1437,plain,
! [X2: a,X0: real,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(cnf_transformation,[],[f1056]) ).
thf(f1056,plain,
! [X0: real,X1: real,X2: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) ) ),
inference(ennf_transformation,[],[f656]) ).
thf(f656,plain,
! [X0: real,X1: real,X2: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2)) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 ) ),
inference(fool_elimination,[],[f655]) ).
thf(f655,plain,
! [X0: real,X1: real,X2: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X2))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X2 ) ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X1: real,X2: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2))),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_general_Oflows__reverse) ).
thf(f4940,plain,
( spl8_187
| ~ spl8_165
| ~ spl8_186 ),
inference(avatar_split_clause,[],[f4936,f4933,f4624,f4938]) ).
thf(f4938,plain,
( spl8_187
<=> ! [X2: real,X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK1,X0))) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X2)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_187])]) ).
thf(f4624,plain,
( spl8_165
<=> ! [X0: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_165])]) ).
thf(f4933,plain,
( spl8_186
<=> ! [X2: real,X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK1,X0))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_186])]) ).
thf(f4936,plain,
( ! [X2: real,X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK1,X0))) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X2)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) )
| ~ spl8_165
| ~ spl8_186 ),
inference(forward_demodulation,[],[f4934,f4625]) ).
thf(f4625,plain,
( ! [X0: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X1)) )
| ~ spl8_165 ),
inference(avatar_component_clause,[],[f4624]) ).
thf(f4934,plain,
( ! [X2: real,X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK1,X0))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) )
| ~ spl8_186 ),
inference(avatar_component_clause,[],[f4933]) ).
thf(f4935,plain,
spl8_186,
inference(avatar_split_clause,[],[f1248,f4933]) ).
thf(f1248,plain,
! [X2: real,X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK1,X0))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f1127]) ).
thf(f1127,plain,
! [X0: a] :
( ( ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK1,X0))) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK1,X0)) ) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f948,f1126]) ).
thf(f1126,plain,
! [X0: a] :
( ? [X1: real] :
( ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) )
=> ( ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK1,X0))) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK1,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f948,plain,
! [X0: a] :
( ? [X1: real] :
( ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f458]) ).
thf(f458,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ~ ! [X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
=> ~ ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) ) ) ),
inference(fool_elimination,[],[f457]) ).
thf(f457,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ~ ! [X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ~ ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X2) ) ) ),
inference(rectify,[],[f215]) ).
thf(f215,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ~ ! [X24: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X24)
=> ~ ! [X25: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X25),X24)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_rev_Oclosed__orbitE) ).
thf(f4889,plain,
spl8_185,
inference(avatar_split_clause,[],[f1897,f4887]) ).
thf(f4887,plain,
( spl8_185
<=> ! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) != X1 )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_185])]) ).
thf(f1897,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) != X1 )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1353,f1297]) ).
thf(f1353,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f1001]) ).
thf(f1001,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(flattening,[],[f1000]) ).
thf(f1000,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f564]) ).
thf(f564,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) = X1 )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
inference(fool_elimination,[],[f563]) ).
thf(f563,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) = X1 )
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(rectify,[],[f78]) ).
thf(f78,axiom,
! [X4: real,X0: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X4),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X4) = X0 )
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X4)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rev_Orecurrence__time__flip__sign_I1_J) ).
thf(f4885,plain,
spl8_184,
inference(avatar_split_clause,[],[f1896,f4883]) ).
thf(f4883,plain,
( spl8_184
<=> ! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) != X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_184])]) ).
thf(f1896,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) != X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1352,f1297]) ).
thf(f1352,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f999]) ).
thf(f999,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(flattening,[],[f998]) ).
thf(f998,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f562]) ).
thf(f562,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) = X1 )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 ) ) ),
inference(fool_elimination,[],[f561]) ).
thf(f561,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) = X1 )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 ) ) ),
inference(rectify,[],[f77]) ).
thf(f77,axiom,
! [X4: real,X0: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X4),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X4) = X0 )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,uminus_uminus_real,X4)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_rev_Orecurrence__time__flip__sign_I2_J) ).
thf(f4843,plain,
spl8_183,
inference(avatar_split_clause,[],[f1901,f4841]) ).
thf(f4841,plain,
( spl8_183
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_183])]) ).
thf(f1901,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1900,f1177]) ).
thf(f1177,plain,
! [X0: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0) ),
inference(cnf_transformation,[],[f776]) ).
thf(f776,plain,
! [X0: real] : ( vAPP(real,real,uminus_uminus_real,X0) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X9) = vAPP(real,real,uminus_uminus_real,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_verit__minus__simplify_I3_J) ).
thf(f1900,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1359,f1297]) ).
thf(f1359,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f1007]) ).
thf(f1007,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f576]) ).
thf(f576,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) ) ),
inference(fool_elimination,[],[f575]) ).
thf(f575,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0))) ),
inference(rectify,[],[f87]) ).
thf(f87,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_local_Orev_Oexistence__ivl__reverse) ).
thf(f4818,plain,
spl8_182,
inference(avatar_split_clause,[],[f1895,f4816]) ).
thf(f4816,plain,
( spl8_182
<=> ! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_182])]) ).
thf(f1895,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1894,f1297]) ).
thf(f1894,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1351,f1177]) ).
thf(f1351,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f997]) ).
thf(f997,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f560]) ).
thf(f560,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)) = X1 ) ),
inference(fool_elimination,[],[f559]) ).
thf(f559,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)) = X1 ) ),
inference(rectify,[],[f88]) ).
thf(f88,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X1)) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_local_Orev_Oflows__reverse) ).
thf(f4786,plain,
spl8_181,
inference(avatar_split_clause,[],[f1344,f4784]) ).
thf(f4784,plain,
( spl8_181
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_181])]) ).
thf(f1344,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f990]) ).
thf(f990,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(flattening,[],[f989]) ).
thf(f989,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f546]) ).
thf(f546,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) = X1 )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
inference(fool_elimination,[],[f545]) ).
thf(f545,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) = X1 )
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X4: real,X0: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X4),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X4) = X0 )
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X4)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_recurrence__time__flip__sign_I1_J) ).
thf(f4782,plain,
spl8_180,
inference(avatar_split_clause,[],[f1343,f4780]) ).
thf(f4780,plain,
( spl8_180
<=> ! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_180])]) ).
thf(f1343,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f988]) ).
thf(f988,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(flattening,[],[f987]) ).
thf(f987,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) != X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f544]) ).
thf(f544,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) = X1 )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 ) ) ),
inference(fool_elimination,[],[f543]) ).
thf(f543,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) = X1 )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0)) = X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
! [X4: real,X0: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X4),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0))
=> ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X4) = X0 )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X4)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_recurrence__time__flip__sign_I2_J) ).
thf(f4748,plain,
spl8_179,
inference(avatar_split_clause,[],[f1893,f4746]) ).
thf(f1893,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(forward_demodulation,[],[f1350,f1177]) ).
thf(f1350,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f996]) ).
thf(f996,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f558]) ).
thf(f558,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) ) ),
inference(fool_elimination,[],[f557]) ).
thf(f557,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0))) ),
inference(rectify,[],[f35]) ).
thf(f35,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X1)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_local_Oexistence__ivl__reverse) ).
thf(f4744,plain,
( spl8_178
| ~ spl8_2
| spl8_161 ),
inference(avatar_split_clause,[],[f4684,f4605,f1942,f4741]) ).
thf(f4684,plain,
( ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ~ spl8_2
| spl8_161 ),
inference(trivial_inequality_removal,[],[f4683]) ).
thf(f4683,plain,
( ( $true != $true )
| ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| ~ spl8_2
| spl8_161 ),
inference(superposition,[],[f4606,f1943]) ).
thf(f4606,plain,
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| spl8_161 ),
inference(avatar_component_clause,[],[f4605]) ).
thf(f4739,plain,
spl8_177,
inference(avatar_split_clause,[],[f1892,f4737]) ).
thf(f1892,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),vAPP(real,real,uminus_uminus_real,X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(forward_demodulation,[],[f1342,f1177]) ).
thf(f1342,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f986]) ).
thf(f986,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)) = X1 )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f542]) ).
thf(f542,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)) = X1 ) ),
inference(fool_elimination,[],[f541]) ).
thf(f541,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X0)) = X1 ) ),
inference(rectify,[],[f34]) ).
thf(f34,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,zero_zero_real),X1)) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_local_Oflows__reverse) ).
thf(f4735,plain,
spl8_176,
inference(avatar_split_clause,[],[f1242,f4733]) ).
thf(f4733,plain,
( spl8_176
<=> ! [X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = X0 )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_176])]) ).
thf(f1242,plain,
! [X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = X0 )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f941]) ).
thf(f941,plain,
! [X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = X0 )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f448]) ).
thf(f448,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = X0 ) ),
inference(fool_elimination,[],[f447]) ).
thf(f447,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = X0 ) ),
inference(rectify,[],[f147]) ).
thf(f147,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_rev_Operiodic__orbit__period_I2_J) ).
thf(f4731,plain,
spl8_175,
inference(avatar_split_clause,[],[f1240,f4729]) ).
thf(f4729,plain,
( spl8_175
<=> ! [X2: real,X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK0,X0))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_175])]) ).
thf(f1240,plain,
! [X2: real,X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK0,X0))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f1125]) ).
thf(f1125,plain,
! [X0: a] :
( ( ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK0,X0))) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK0,X0)) ) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f939,f1124]) ).
thf(f1124,plain,
! [X0: a] :
( ? [X1: real] :
( ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X2) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) )
=> ( ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X2) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),vAPP(a,real,sK0,X0))) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK0,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f939,plain,
! [X0: a] :
( ? [X1: real] :
( ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X2) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) ) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f444]) ).
thf(f444,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
=> ~ ! [X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1) )
=> ~ ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X2) ) ) ),
inference(fool_elimination,[],[f443]) ).
thf(f443,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> ~ ! [X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X1)
=> ~ ! [X2: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X2) ) ) ),
inference(rectify,[],[f189]) ).
thf(f189,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> ~ ! [X24: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X24)
=> ~ ! [X25: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X25),X24)) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X25) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_closed__orbitE) ).
thf(f4725,plain,
spl8_174,
inference(avatar_split_clause,[],[f1891,f4723]) ).
thf(f4723,plain,
( spl8_174
<=> ! [X0: a,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X1))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_174])]) ).
thf(f1891,plain,
! [X0: a,X1: real] :
( ( $true = vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X1))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(forward_demodulation,[],[f1341,f1297]) ).
thf(f1341,plain,
! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f985]) ).
thf(f985,plain,
! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f540]) ).
thf(f540,plain,
! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) = $true ) ),
inference(fool_elimination,[],[f539]) ).
thf(f539,plain,
! [X0: a,X1: real] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) ),
inference(rectify,[],[f60]) ).
thf(f60,axiom,
! [X0: a,X1: real] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rev_Oclosed__orbit__flow0) ).
thf(f4710,plain,
spl8_173,
inference(avatar_split_clause,[],[f1898,f4708]) ).
thf(f4708,plain,
( spl8_173
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_173])]) ).
thf(f1898,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,uminus_uminus_real,X0))),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(forward_demodulation,[],[f1357,f1297]) ).
thf(f1357,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f1005]) ).
thf(f1005,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f572]) ).
thf(f572,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),x) ) ),
inference(fool_elimination,[],[f571]) ).
thf(f571,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0)),x) ),
inference(rectify,[],[f118]) ).
thf(f118,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),X1)),x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_local_Orev_Oflow__in__domain) ).
thf(f4694,plain,
spl8_172,
inference(avatar_split_clause,[],[f1323,f4692]) ).
thf(f4692,plain,
( spl8_172
<=> ! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_172])]) ).
thf(f1323,plain,
! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f957]) ).
thf(f957,plain,
! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f841]) ).
thf(f841,plain,
! [X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) ) ),
inference(flattening,[],[f508]) ).
thf(f508,plain,
! [X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) ) ),
inference(fool_elimination,[],[f507]) ).
thf(f507,plain,
! [X0: real,X1: a] :
( ~ vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),X0) ) ),
inference(rectify,[],[f81]) ).
thf(f81,axiom,
! [X1: real,X0: a] :
( ~ vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0))
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_local_Orev_Oflow__undefined0) ).
thf(f4682,plain,
spl8_171,
inference(avatar_split_clause,[],[f1890,f4680]) ).
thf(f4680,plain,
( spl8_171
<=> ! [X0: a,X1: real] :
( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X1))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_171])]) ).
thf(f1890,plain,
! [X0: a,X1: real] :
( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(real,real,uminus_uminus_real,X1))) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(forward_demodulation,[],[f1340,f1297]) ).
thf(f1340,plain,
! [X0: a,X1: real] :
( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f984]) ).
thf(f984,plain,
! [X0: a,X1: real] :
( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f538]) ).
thf(f538,plain,
! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) ) ),
inference(fool_elimination,[],[f537]) ).
thf(f537,plain,
! [X0: a,X1: real] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) ) ),
inference(rectify,[],[f85]) ).
thf(f85,axiom,
! [X0: a,X1: real] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_rev_Operiodic__orbit__imp__flow0__regular) ).
thf(f4674,plain,
spl8_170,
inference(avatar_split_clause,[],[f1246,f4672]) ).
thf(f4672,plain,
( spl8_170
<=> ! [X0: a] :
( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( zero_zero_real != vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_170])]) ).
thf(f1246,plain,
! [X0: a] :
( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( zero_zero_real != vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f947]) ).
thf(f947,plain,
! [X0: a] :
( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( zero_zero_real != vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(flattening,[],[f946]) ).
thf(f946,plain,
! [X0: a] :
( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( zero_zero_real != vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f456]) ).
thf(f456,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
=> ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) ) ) ),
inference(fool_elimination,[],[f455]) ).
thf(f455,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
=> ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) ) ) ),
inference(rectify,[],[f145]) ).
thf(f145,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
=> ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_rev_Oclosed__orbit__period__zero__fixed__point) ).
thf(f4670,plain,
spl8_169,
inference(avatar_split_clause,[],[f1245,f4668]) ).
thf(f4668,plain,
( spl8_169
<=> ! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
| ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_169])]) ).
thf(f1245,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
| ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f945]) ).
thf(f945,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
| ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(flattening,[],[f944]) ).
thf(f944,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
| ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f454]) ).
thf(f454,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true ) ) ),
inference(fool_elimination,[],[f453]) ).
thf(f453,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ),
inference(rectify,[],[f86]) ).
thf(f86,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_rev_Oclosed__orbit__periodic) ).
thf(f4651,plain,
spl8_168,
inference(avatar_split_clause,[],[f1348,f4649]) ).
thf(f1348,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f994]) ).
thf(f994,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f554]) ).
thf(f554,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),x) ) ),
inference(fool_elimination,[],[f553]) ).
thf(f553,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0)),x) ),
inference(rectify,[],[f24]) ).
thf(f24,axiom,
! [X7: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X7),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),X7)),x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_flow0__defined) ).
thf(f4647,plain,
spl8_167,
inference(avatar_split_clause,[],[f1339,f4645]) ).
thf(f4645,plain,
( spl8_167
<=> ! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_167])]) ).
thf(f1339,plain,
! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f983]) ).
thf(f983,plain,
! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f536]) ).
thf(f536,plain,
! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
=> ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) = $true ) ),
inference(fool_elimination,[],[f535]) ).
thf(f535,plain,
! [X0: a,X1: real] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X0: a,X1: real] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_closed__orbit__flow0) ).
thf(f4643,plain,
spl8_166,
inference(avatar_split_clause,[],[f1234,f4641]) ).
thf(f4641,plain,
( spl8_166
<=> ! [X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = X0 )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_166])]) ).
thf(f1234,plain,
! [X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = X0 )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f932]) ).
thf(f932,plain,
! [X0: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = X0 )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f434]) ).
thf(f434,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) = $true )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = X0 ) ),
inference(fool_elimination,[],[f433]) ).
thf(f433,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0)
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = X0 ) ),
inference(rectify,[],[f148]) ).
thf(f148,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0)
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_periodic__orbit__period_I2_J) ).
thf(f4626,plain,
spl8_165,
inference(avatar_split_clause,[],[f1297,f4624]) ).
thf(f4622,plain,
spl8_164,
inference(avatar_split_clause,[],[f1296,f4620]) ).
thf(f4620,plain,
( spl8_164
<=> ! [X0: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,uminus_uminus_real,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_164])]) ).
thf(f1296,plain,
! [X0: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,uminus_uminus_real,X1)) ),
inference(cnf_transformation,[],[f836]) ).
thf(f836,plain,
! [X0: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),vAPP(real,real,uminus_uminus_real,X1)) ),
inference(rectify,[],[f57]) ).
thf(f57,axiom,
! [X6: a,X1: real] : ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X6),X1) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X6),vAPP(real,real,uminus_uminus_real,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_rev_Orev__eq__flow) ).
thf(f4616,plain,
spl8_163,
inference(avatar_split_clause,[],[f1243,f4614]) ).
thf(f4614,plain,
( spl8_163
<=> ! [X0: a] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_163])]) ).
thf(f1243,plain,
! [X0: a] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f942]) ).
thf(f942,plain,
! [X0: a] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f450]) ).
thf(f450,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) = $true ) ),
inference(fool_elimination,[],[f449]) ).
thf(f449,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ),
inference(rectify,[],[f212]) ).
thf(f212,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_rev_Operiodic__orbit__period_I1_J) ).
thf(f4612,plain,
( spl8_161
| ~ spl8_162
| spl8_6
| ~ spl8_155 ),
inference(avatar_split_clause,[],[f4569,f4563,f1989,f4609,f4605]) ).
thf(f4563,plain,
( spl8_155
<=> ! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_155])]) ).
thf(f4569,plain,
( ( xx != zero_zero_a )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) )
| spl8_6
| ~ spl8_155 ),
inference(superposition,[],[f1991,f4564]) ).
thf(f4564,plain,
( ! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) )
| ~ spl8_155 ),
inference(avatar_component_clause,[],[f4563]) ).
thf(f1991,plain,
( ( xx != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)) )
| spl8_6 ),
inference(avatar_component_clause,[],[f1989]) ).
thf(f4603,plain,
spl8_160,
inference(avatar_split_clause,[],[f1331,f4601]) ).
thf(f4601,plain,
( spl8_160
<=> ! [X0: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = X0 )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_160])]) ).
thf(f1331,plain,
! [X0: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = X0 )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f971]) ).
thf(f971,plain,
! [X0: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = X0 )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(flattening,[],[f970]) ).
thf(f970,plain,
! [X0: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = X0 )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f520]) ).
thf(f520,plain,
! [X0: a,X1: real] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = X0 ) ) ),
inference(fool_elimination,[],[f519]) ).
thf(f519,plain,
! [X0: a,X1: real] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = X0 ) ) ),
inference(rectify,[],[f59]) ).
thf(f59,axiom,
! [X0: a,X1: real] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rev_Ofixpoint__sol_I2_J) ).
thf(f4599,plain,
spl8_159,
inference(avatar_split_clause,[],[f1146,f4596]) ).
thf(f4596,plain,
( spl8_159
<=> ( vEQ(real) = vAPP(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,$o)),vAPP(sTfun(sTfun(real,real),sTfun(real,$o)),sTfun(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,$o))),bCOMB,vAPP(sTfun(real,$o),sTfun(sTfun(real,real),sTfun(real,$o)),bCOMB,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real))),minus_minus_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_159])]) ).
thf(f1146,plain,
vEQ(real) = vAPP(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,$o)),vAPP(sTfun(sTfun(real,real),sTfun(real,$o)),sTfun(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,$o))),bCOMB,vAPP(sTfun(real,$o),sTfun(sTfun(real,real),sTfun(real,$o)),bCOMB,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real))),minus_minus_real),
inference(cnf_transformation,[],[f350]) ).
thf(f350,plain,
vEQ(real) = vAPP(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,$o)),vAPP(sTfun(sTfun(real,real),sTfun(real,$o)),sTfun(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,$o))),bCOMB,vAPP(sTfun(real,$o),sTfun(sTfun(real,real),sTfun(real,$o)),bCOMB,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real))),minus_minus_real),
inference(fool_elimination,[],[f349]) ).
thf(f349,plain,
( ( ^ [X0: real,X1: real] : ( X0 = X1 ) )
= ( ^ [X2: real,X3: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X3) ) ) ),
inference(rectify,[],[f142]) ).
thf(f142,axiom,
( ( ^ [X20: real,X21: real] : ( X20 = X21 ) )
= ( ^ [X22: real,X23: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X22),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_eq__iff__diff__eq__0) ).
thf(f4594,plain,
spl8_158,
inference(avatar_split_clause,[],[f1145,f4591]) ).
thf(f4591,plain,
( spl8_158
<=> ( vEQ(a) = vAPP(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,a),sTfun(a,$o)),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,$o))),bCOMB,vAPP(sTfun(a,$o),sTfun(sTfun(a,a),sTfun(a,$o)),bCOMB,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a))),minus_minus_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_158])]) ).
thf(f1145,plain,
vEQ(a) = vAPP(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,a),sTfun(a,$o)),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,$o))),bCOMB,vAPP(sTfun(a,$o),sTfun(sTfun(a,a),sTfun(a,$o)),bCOMB,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a))),minus_minus_a),
inference(cnf_transformation,[],[f348]) ).
thf(f348,plain,
vEQ(a) = vAPP(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,$o)),vAPP(sTfun(sTfun(a,a),sTfun(a,$o)),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,$o))),bCOMB,vAPP(sTfun(a,$o),sTfun(sTfun(a,a),sTfun(a,$o)),bCOMB,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a))),minus_minus_a),
inference(fool_elimination,[],[f347]) ).
thf(f347,plain,
( ( ^ [X0: a,X1: a] : ( X0 = X1 ) )
= ( ^ [X2: a,X3: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X3) ) ) ),
inference(rectify,[],[f141]) ).
thf(f141,axiom,
( ( ^ [X20: a,X21: a] : ( X20 = X21 ) )
= ( ^ [X22: a,X23: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X22),X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_eq__iff__diff__eq__0) ).
thf(f4584,plain,
spl8_157,
inference(avatar_split_clause,[],[f1935,f4581]) ).
thf(f1935,plain,
$true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss))),
inference(forward_demodulation,[],[f1496,f1143]) ).
thf(f1143,plain,
vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss),
inference(cnf_transformation,[],[f3]) ).
thf(f3,axiom,
vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt) = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),ss),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_eq) ).
thf(f1496,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt))) = $true,
inference(cnf_transformation,[],[f746]) ).
thf(f746,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt))) = $true,
inference(fool_elimination,[],[f745]) ).
thf(f745,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt))),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,vAPP(real,real,uminus_uminus_real,tt)),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),xx),tt))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_neg__tt__ex) ).
thf(f4573,plain,
( spl8_148
| spl8_156 ),
inference(avatar_split_clause,[],[f1885,f4571,f4428]) ).
thf(f4428,plain,
( spl8_148
<=> ! [X0: real] : ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_148])]) ).
thf(f1885,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),zero_zero_real) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(forward_demodulation,[],[f1317,f1155]) ).
thf(f1155,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0) ),
inference(cnf_transformation,[],[f754]) ).
thf(f754,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0) ),
inference(rectify,[],[f112]) ).
thf(f112,axiom,
! [X8: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(f1317,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(cnf_transformation,[],[f953]) ).
thf(f953,plain,
! [X0: real,X1: a] :
( ( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) )
| ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
& ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ) )
& ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ) ),
inference(flattening,[],[f952]) ).
thf(f952,plain,
! [X0: real,X1: a] :
( ( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) )
| ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
& ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ) )
& ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ) ),
inference(ennf_transformation,[],[f504]) ).
thf(f504,plain,
! [X0: real,X1: a] :
( ( ~ ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
& ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) ) )
& ( ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
& ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 ) ) ),
inference(fool_elimination,[],[f503]) ).
thf(f503,plain,
! [X0: real,X1: a] :
( ( ~ ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) ) )
& ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 ) ) ),
inference(rectify,[],[f95]) ).
thf(f95,axiom,
! [X2: real,X3: a] :
( ( ~ ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),top_top_set_real) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X2)) ) )
& ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),top_top_set_real) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X2)) = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rev_Ogeneral_Oflow__initial__time__if) ).
thf(f4565,plain,
spl8_155,
inference(avatar_split_clause,[],[f1322,f4563]) ).
thf(f1322,plain,
! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f956]) ).
thf(f956,plain,
! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f840]) ).
thf(f840,plain,
! [X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) ) ),
inference(flattening,[],[f506]) ).
thf(f506,plain,
! [X0: real,X1: a] :
( ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) ) ),
inference(fool_elimination,[],[f505]) ).
thf(f505,plain,
! [X0: real,X1: a] :
( ~ vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),X0) ) ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
! [X1: real,X0: a] :
( ~ vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0))
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_local_Oflow__undefined0) ).
thf(f4553,plain,
spl8_154,
inference(avatar_split_clause,[],[f1143,f4550]) ).
thf(f4546,plain,
spl8_153,
inference(avatar_split_clause,[],[f1244,f4544]) ).
thf(f4544,plain,
( spl8_153
<=> ! [X0: a] :
( ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_153])]) ).
thf(f1244,plain,
! [X0: a] :
( ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f943]) ).
thf(f943,plain,
! [X0: a] :
( ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f452]) ).
thf(f452,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ),
inference(fool_elimination,[],[f451]) ).
thf(f451,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rev_Oclosed__orbit__global__existence) ).
thf(f4540,plain,
spl8_152,
inference(avatar_split_clause,[],[f1338,f4538]) ).
thf(f1338,plain,
! [X0: a,X1: real] :
( ( zero_zero_a != vAPP(a,a,f,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f982]) ).
thf(f982,plain,
! [X0: a,X1: real] :
( ( zero_zero_a != vAPP(a,a,f,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f534]) ).
thf(f534,plain,
! [X0: a,X1: real] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) = $true )
=> ( zero_zero_a != vAPP(a,a,f,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) ) ),
inference(fool_elimination,[],[f533]) ).
thf(f533,plain,
! [X0: a,X1: real] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0)
=> ( zero_zero_a != vAPP(a,a,f,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) ) ),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
! [X0: a,X1: real] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0)
=> ( zero_zero_a != vAPP(a,a,f,vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_periodic__orbit__imp__flow0__regular) ).
thf(f4494,plain,
( spl8_121
| spl8_151 ),
inference(avatar_split_clause,[],[f1884,f4492,f3968]) ).
thf(f4492,plain,
( spl8_151
<=> ! [X1: a] : ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),zero_zero_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_151])]) ).
thf(f1884,plain,
! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),zero_zero_real) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(forward_demodulation,[],[f1318,f1155]) ).
thf(f1318,plain,
! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(cnf_transformation,[],[f953]) ).
thf(f4490,plain,
spl8_150,
inference(avatar_split_clause,[],[f1355,f4488]) ).
thf(f4488,plain,
( spl8_150
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_150])]) ).
thf(f1355,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f1003]) ).
thf(f1003,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f568]) ).
thf(f568,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(fool_elimination,[],[f567]) ).
thf(f567,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),top_top_set_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_local_Orev_Omem__existence__ivl__subset) ).
thf(f4441,plain,
( ~ spl8_2
| ~ spl8_104
| ~ spl8_148 ),
inference(avatar_contradiction_clause,[],[f4440]) ).
thf(f4440,plain,
( $false
| ~ spl8_2
| ~ spl8_104
| ~ spl8_148 ),
inference(trivial_inequality_removal,[],[f4439]) ).
thf(f4439,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_104
| ~ spl8_148 ),
inference(forward_demodulation,[],[f3901,f4436]) ).
thf(f4436,plain,
( ! [X0: real] : ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ~ spl8_2
| ~ spl8_148 ),
inference(trivial_inequality_removal,[],[f4435]) ).
thf(f4435,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $false = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) )
| ~ spl8_2
| ~ spl8_148 ),
inference(superposition,[],[f4429,f1943]) ).
thf(f4429,plain,
( ! [X0: real] : ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ~ spl8_148 ),
inference(avatar_component_clause,[],[f4428]) ).
thf(f3901,plain,
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true )
| ~ spl8_104 ),
inference(avatar_component_clause,[],[f3899]) ).
thf(f3899,plain,
( spl8_104
<=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_104])]) ).
thf(f4438,plain,
( ~ spl8_121
| ~ spl8_148 ),
inference(avatar_contradiction_clause,[],[f4437]) ).
thf(f4437,plain,
( $false
| ~ spl8_121
| ~ spl8_148 ),
inference(trivial_inequality_removal,[],[f4434]) ).
thf(f4434,plain,
( ( $true != $true )
| ~ spl8_121
| ~ spl8_148 ),
inference(superposition,[],[f4429,f3969]) ).
thf(f4433,plain,
( spl8_148
| spl8_149 ),
inference(avatar_split_clause,[],[f1882,f4431,f4428]) ).
thf(f1882,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),zero_zero_real) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(forward_demodulation,[],[f1314,f1155]) ).
thf(f1314,plain,
! [X0: real,X1: a] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(cnf_transformation,[],[f951]) ).
thf(f951,plain,
! [X0: real,X1: a] :
( ( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) )
| ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
& ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ) )
& ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ) ),
inference(flattening,[],[f950]) ).
thf(f950,plain,
! [X0: real,X1: a] :
( ( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) )
| ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
& ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ) )
& ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ) ),
inference(ennf_transformation,[],[f502]) ).
thf(f502,plain,
! [X0: real,X1: a] :
( ( ~ ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
& ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) ) )
& ( ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
& ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 ) ) ),
inference(fool_elimination,[],[f501]) ).
thf(f501,plain,
! [X0: real,X1: a] :
( ( ~ ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) ) )
& ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) = X1 ) ) ),
inference(rectify,[],[f36]) ).
thf(f36,axiom,
! [X2: real,X3: a] :
( ( ~ ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),top_top_set_real) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X2)) ) )
& ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X2),top_top_set_real) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X2)) = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_general_Oflow__initial__time__if) ).
thf(f4426,plain,
spl8_147,
inference(avatar_split_clause,[],[f1478,f4424]) ).
thf(f4424,plain,
( spl8_147
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_147])]) ).
thf(f1478,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(cnf_transformation,[],[f1109]) ).
thf(f1109,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(flattening,[],[f1108]) ).
thf(f1108,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(ennf_transformation,[],[f710]) ).
thf(f710,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) )
=> ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) ) ) ),
inference(fool_elimination,[],[f709]) ).
thf(f709,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1)
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) ) ),
inference(rectify,[],[f319]) ).
thf(f319,axiom,
! [X8: a,X9: a,X19: a,X18: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X9)
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X19),X18)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X18)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X9),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_diff__strict__mono) ).
thf(f4422,plain,
spl8_146,
inference(avatar_split_clause,[],[f1477,f4420]) ).
thf(f1477,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1107]) ).
thf(f1107,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(flattening,[],[f1106]) ).
thf(f1106,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f708]) ).
thf(f708,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ) ) ),
inference(fool_elimination,[],[f707]) ).
thf(f707,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X3)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ) ),
inference(rectify,[],[f320]) ).
thf(f320,axiom,
! [X8: real,X9: real,X19: real,X18: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X9)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X19),X18)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X18)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X9),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_diff__strict__mono) ).
thf(f4418,plain,
spl8_145,
inference(avatar_split_clause,[],[f1475,f4416]) ).
thf(f4416,plain,
( spl8_145
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X3)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_145])]) ).
thf(f1475,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X3)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(cnf_transformation,[],[f1103]) ).
thf(f1103,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X3)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(flattening,[],[f1102]) ).
thf(f1102,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X3)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(ennf_transformation,[],[f704]) ).
thf(f704,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3) )
& ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X3)) ) ),
inference(fool_elimination,[],[f703]) ).
thf(f703,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X2),X3)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X3)) ),
inference(rectify,[],[f293]) ).
thf(f293,axiom,
! [X28: a,X29: a,X27: a,X30: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X27),X30)
& vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X28),X29) )
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X28),X27)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X29),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_add__mono__thms__linordered__field_I5_J) ).
thf(f4414,plain,
spl8_144,
inference(avatar_split_clause,[],[f1473,f4412]) ).
thf(f1473,plain,
! [X2: real,X3: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1099]) ).
thf(f1099,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(flattening,[],[f1098]) ).
thf(f1098,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f700]) ).
thf(f700,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3) )
& ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) ) ),
inference(fool_elimination,[],[f699]) ).
thf(f699,plain,
! [X0: real,X1: real,X2: real,X3: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X2),X3)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X3)) ),
inference(rectify,[],[f294]) ).
thf(f294,axiom,
! [X28: real,X29: real,X27: real,X30: real] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X27),X30)
& vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X28),X29) )
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X28),X27)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X29),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_add__mono__thms__linordered__field_I5_J) ).
thf(f4410,plain,
spl8_143,
inference(avatar_split_clause,[],[f1231,f4408]) ).
thf(f4408,plain,
( spl8_143
<=> ! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_143])]) ).
thf(f1231,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f929]) ).
thf(f929,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(flattening,[],[f928]) ).
thf(f928,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f428]) ).
thf(f428,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true ) ) ),
inference(fool_elimination,[],[f427]) ).
thf(f427,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ),
inference(rectify,[],[f62]) ).
thf(f62,axiom,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J) ).
thf(f4406,plain,
spl8_142,
inference(avatar_split_clause,[],[f1230,f4404]) ).
thf(f4404,plain,
( spl8_142
<=> ! [X0: a] :
( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_142])]) ).
thf(f1230,plain,
! [X0: a] :
( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f927]) ).
thf(f927,plain,
! [X0: a] :
( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(flattening,[],[f926]) ).
thf(f926,plain,
! [X0: a] :
( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f426]) ).
thf(f426,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ) ),
inference(fool_elimination,[],[f425]) ).
thf(f425,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ) ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J) ).
thf(f4402,plain,
spl8_141,
inference(avatar_split_clause,[],[f1229,f4400]) ).
thf(f4400,plain,
( spl8_141
<=> ! [X0: a] :
( ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_141])]) ).
thf(f1229,plain,
! [X0: a] :
( ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f925]) ).
thf(f925,plain,
! [X0: a] :
( ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(flattening,[],[f924]) ).
thf(f924,plain,
! [X0: a] :
( ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) )
| ( zero_zero_a != vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f424]) ).
thf(f424,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ) ),
inference(fool_elimination,[],[f423]) ).
thf(f423,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ) ),
inference(rectify,[],[f79]) ).
thf(f79,axiom,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( zero_zero_a = vAPP(a,a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f),X0) )
=> ( top_top_set_real = vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_rev_Ofixpoint__sol_I1_J) ).
thf(f4396,plain,
spl8_140,
inference(avatar_split_clause,[],[f1235,f4394]) ).
thf(f4394,plain,
( spl8_140
<=> ! [X0: a] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_140])]) ).
thf(f1235,plain,
! [X0: a] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f933]) ).
thf(f933,plain,
! [X0: a] :
( ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f436]) ).
thf(f436,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) = $true )
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) = $true ) ),
inference(fool_elimination,[],[f435]) ).
thf(f435,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) ),
inference(rectify,[],[f170]) ).
thf(f170,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_periodic__orbit__period_I1_J) ).
thf(f4392,plain,
spl8_139,
inference(avatar_split_clause,[],[f1718,f4390]) ).
thf(f4390,plain,
( spl8_139
<=> ! [X0: real,X1: real] :
( ( vAPP(real,real,uminus_uminus_real,X1) = X0 )
| ( vAPP(real,real,uminus_uminus_real,X0) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_139])]) ).
thf(f1718,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,uminus_uminus_real,X1) = X0 )
| ( vAPP(real,real,uminus_uminus_real,X0) != X1 ) ),
inference(equality_proxy_clausification,[],[f1717]) ).
thf(f1717,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,uminus_uminus_real,X1) = X0 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X1) ) ),
inference(equality_proxy_clausification,[],[f1713]) ).
thf(f1713,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X1) ) ),
inference(binary_proxy_clausification,[],[f1298]) ).
thf(f1298,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X1) ),
inference(cnf_transformation,[],[f470]) ).
thf(f470,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X1) ),
inference(fool_elimination,[],[f469]) ).
thf(f469,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,uminus_uminus_real,X1) = X0 )
= ( vAPP(real,real,uminus_uminus_real,X0) = X1 ) ),
inference(rectify,[],[f134]) ).
thf(f134,axiom,
! [X8: real,X9: real] :
( ( vAPP(real,real,uminus_uminus_real,X9) = X8 )
= ( vAPP(real,real,uminus_uminus_real,X8) = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_equation__minus__iff) ).
thf(f4374,plain,
spl8_138,
inference(avatar_split_clause,[],[f1356,f4372]) ).
thf(f4372,plain,
( spl8_138
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_138])]) ).
thf(f1356,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(cnf_transformation,[],[f1004]) ).
thf(f1004,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) ) ),
inference(ennf_transformation,[],[f570]) ).
thf(f570,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) ) ),
inference(fool_elimination,[],[f569]) ).
thf(f569,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X1))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) ),
inference(rectify,[],[f116]) ).
thf(f116,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_local_Orev_Omem__existence__ivl__iv__defined_I2_J) ).
thf(f4370,plain,
spl8_137,
inference(avatar_split_clause,[],[f1233,f4368]) ).
thf(f1233,plain,
! [X0: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f931]) ).
thf(f931,plain,
! [X0: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f432]) ).
thf(f432,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ) ),
inference(fool_elimination,[],[f431]) ).
thf(f431,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
! [X3: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rev_Oexistence__ivl__zero) ).
thf(f4366,plain,
spl8_136,
inference(avatar_split_clause,[],[f1215,f4364]) ).
thf(f4364,plain,
( spl8_136
<=> ! [X0: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_136])]) ).
thf(f1215,plain,
! [X0: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true ) ),
inference(cnf_transformation,[],[f901]) ).
thf(f901,plain,
! [X0: a] :
( ( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) )
| ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
& ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) ) )
& ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ) ),
inference(flattening,[],[f900]) ).
thf(f900,plain,
! [X0: a] :
( ( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) )
| ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
& ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) ) )
& ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ) ),
inference(ennf_transformation,[],[f396]) ).
thf(f396,plain,
! [X0: a] :
( ( ~ ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
& ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) ) )
& ( ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
& ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) = X0 ) ) ),
inference(fool_elimination,[],[f395]) ).
thf(f395,plain,
! [X0: a] :
( ( ~ ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) ) )
& ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0),zero_zero_real) = X0 ) ) ),
inference(rectify,[],[f91]) ).
thf(f91,axiom,
! [X3: a] :
( ( ~ ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),zero_zero_real) ) )
& ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3),zero_zero_real) = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_local_Orev_Oflow__initial__time__if) ).
thf(f4352,plain,
spl8_135,
inference(avatar_split_clause,[],[f1330,f4350]) ).
thf(f4350,plain,
( spl8_135
<=> ! [X0: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = X0 )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_135])]) ).
thf(f1330,plain,
! [X0: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = X0 )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f969]) ).
thf(f969,plain,
! [X0: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = X0 )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(flattening,[],[f968]) ).
thf(f968,plain,
! [X0: a,X1: real] :
( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = X0 )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f518]) ).
thf(f518,plain,
! [X0: a,X1: real] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = X0 ) ) ),
inference(fool_elimination,[],[f517]) ).
thf(f517,plain,
! [X0: a,X1: real] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = X0 ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X0: a,X1: real] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_fixpoint__sol_I2_J) ).
thf(f4348,plain,
spl8_134,
inference(avatar_split_clause,[],[f1706,f4346]) ).
thf(f4346,plain,
( spl8_134
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,uminus_uminus_a,X1) = X0 )
| ( vAPP(a,a,uminus_uminus_a,X0) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_134])]) ).
thf(f1706,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,uminus_uminus_a,X1) = X0 )
| ( vAPP(a,a,uminus_uminus_a,X0) != X1 ) ),
inference(equality_proxy_clausification,[],[f1705]) ).
thf(f1705,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,uminus_uminus_a,X1) = X0 )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),X1) ) ),
inference(equality_proxy_clausification,[],[f1701]) ).
thf(f1701,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X1)),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),X1) ) ),
inference(binary_proxy_clausification,[],[f1300]) ).
thf(f1300,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X1)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),X1) ),
inference(cnf_transformation,[],[f474]) ).
thf(f474,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X1)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),X1) ),
inference(fool_elimination,[],[f473]) ).
thf(f473,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,uminus_uminus_a,X1) = X0 )
= ( vAPP(a,a,uminus_uminus_a,X0) = X1 ) ),
inference(rectify,[],[f133]) ).
thf(f133,axiom,
! [X8: a,X9: a] :
( ( vAPP(a,a,uminus_uminus_a,X9) = X8 )
= ( vAPP(a,a,uminus_uminus_a,X8) = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_equation__minus__iff) ).
thf(f4344,plain,
spl8_133,
inference(avatar_split_clause,[],[f1238,f4342]) ).
thf(f4342,plain,
( spl8_133
<=> ! [X0: a] :
( ( vAPP(a,a,f,X0) = zero_zero_a )
| ( zero_zero_real != vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_133])]) ).
thf(f1238,plain,
! [X0: a] :
( ( vAPP(a,a,f,X0) = zero_zero_a )
| ( zero_zero_real != vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f938]) ).
thf(f938,plain,
! [X0: a] :
( ( vAPP(a,a,f,X0) = zero_zero_a )
| ( zero_zero_real != vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(flattening,[],[f937]) ).
thf(f937,plain,
! [X0: a] :
( ( vAPP(a,a,f,X0) = zero_zero_a )
| ( zero_zero_real != vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f442]) ).
thf(f442,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
=> ( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
=> ( vAPP(a,a,f,X0) = zero_zero_a ) ) ),
inference(fool_elimination,[],[f441]) ).
thf(f441,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> ( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
=> ( vAPP(a,a,f,X0) = zero_zero_a ) ) ),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> ( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
=> ( vAPP(a,a,f,X0) = zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_closed__orbit__period__zero__fixed__point) ).
thf(f4340,plain,
spl8_132,
inference(avatar_split_clause,[],[f1237,f4338]) ).
thf(f4338,plain,
( spl8_132
<=> ! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) = $true )
| ( vAPP(a,a,f,X0) = zero_zero_a )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_132])]) ).
thf(f1237,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) = $true )
| ( vAPP(a,a,f,X0) = zero_zero_a )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f936]) ).
thf(f936,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) = $true )
| ( vAPP(a,a,f,X0) = zero_zero_a )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(flattening,[],[f935]) ).
thf(f935,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) = $true )
| ( vAPP(a,a,f,X0) = zero_zero_a )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f440]) ).
thf(f440,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
=> ( ( vAPP(a,a,f,X0) != zero_zero_a )
=> ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) = $true ) ) ),
inference(fool_elimination,[],[f439]) ).
thf(f439,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> ( ( vAPP(a,a,f,X0) != zero_zero_a )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) ) ),
inference(rectify,[],[f27]) ).
thf(f27,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> ( ( vAPP(a,a,f,X0) != zero_zero_a )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period138238489rbit_a,f),x),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_closed__orbit__periodic) ).
thf(f4318,plain,
spl8_131,
inference(avatar_split_clause,[],[f1417,f4316]) ).
thf(f4316,plain,
( spl8_131
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_131])]) ).
thf(f1417,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) ) ),
inference(cnf_transformation,[],[f1029]) ).
thf(f1029,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) ) ),
inference(flattening,[],[f1028]) ).
thf(f1028,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) ) ),
inference(ennf_transformation,[],[f616]) ).
thf(f616,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0) )
=> ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ) ) ),
inference(fool_elimination,[],[f615]) ).
thf(f615,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X0)
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ) ),
inference(rectify,[],[f253]) ).
thf(f253,axiom,
! [X8: a,X9: a,X18: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,zero_zero_a),X8)
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X9),X18)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X9),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_pos__add__strict) ).
thf(f4314,plain,
spl8_130,
inference(avatar_split_clause,[],[f1416,f4312]) ).
thf(f1416,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) ) ),
inference(cnf_transformation,[],[f1027]) ).
thf(f1027,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) ) ),
inference(flattening,[],[f1026]) ).
thf(f1026,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) ) ),
inference(ennf_transformation,[],[f614]) ).
thf(f614,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ) ),
inference(fool_elimination,[],[f613]) ).
thf(f613,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X0)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ),
inference(rectify,[],[f254]) ).
thf(f254,axiom,
! [X8: real,X9: real,X18: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),X8)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X9),X18)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X9),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pos__add__strict) ).
thf(f4310,plain,
spl8_129,
inference(avatar_split_clause,[],[f1335,f4308]) ).
thf(f4308,plain,
( spl8_129
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),zero_zero_a) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_129])]) ).
thf(f1335,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),zero_zero_a) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) ) ),
inference(cnf_transformation,[],[f979]) ).
thf(f979,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),zero_zero_a) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) ) ),
inference(flattening,[],[f978]) ).
thf(f978,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),zero_zero_a) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) ) ),
inference(ennf_transformation,[],[f528]) ).
thf(f528,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a) )
=> ( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),zero_zero_a) ) ) ),
inference(fool_elimination,[],[f527]) ).
thf(f527,plain,
! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),zero_zero_a)
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),zero_zero_a)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),zero_zero_a) ) ),
inference(rectify,[],[f249]) ).
thf(f249,axiom,
! [X8: a,X9: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),zero_zero_a)
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X9),zero_zero_a)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)),zero_zero_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_add__neg__neg) ).
thf(f4306,plain,
spl8_128,
inference(avatar_split_clause,[],[f1333,f4304]) ).
thf(f4304,plain,
( spl8_128
<=> ! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_128])]) ).
thf(f1333,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) ),
inference(cnf_transformation,[],[f975]) ).
thf(f975,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) ),
inference(flattening,[],[f974]) ).
thf(f974,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) ) ),
inference(ennf_transformation,[],[f524]) ).
thf(f524,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real) )
=> ( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),zero_zero_real) ) ) ),
inference(fool_elimination,[],[f523]) ).
thf(f523,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),zero_zero_real) ) ),
inference(rectify,[],[f250]) ).
thf(f250,axiom,
! [X8: real,X9: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),zero_zero_real)
=> ( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X9),zero_zero_real)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)),zero_zero_real) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__neg__neg) ).
thf(f4302,plain,
spl8_127,
inference(avatar_split_clause,[],[f1694,f4300]) ).
thf(f4300,plain,
( spl8_127
<=> ! [X0: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,uminus_uminus_real,X1) != vAPP(real,real,uminus_uminus_real,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_127])]) ).
thf(f1694,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( vAPP(real,real,uminus_uminus_real,X1) != vAPP(real,real,uminus_uminus_real,X0) ) ),
inference(equality_proxy_clausification,[],[f1693]) ).
thf(f1693,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(equality_proxy_clausification,[],[f1689]) ).
thf(f1689,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1302]) ).
thf(f1302,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(cnf_transformation,[],[f478]) ).
thf(f478,plain,
! [X0: real,X1: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(fool_elimination,[],[f477]) ).
thf(f477,plain,
! [X0: real,X1: real] :
( ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,uminus_uminus_real,X0) )
= ( X0 = X1 ) ),
inference(rectify,[],[f41]) ).
thf(f41,axiom,
! [X8: real,X9: real] :
( ( vAPP(real,real,uminus_uminus_real,X8) = vAPP(real,real,uminus_uminus_real,X9) )
= ( X8 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_neg__equal__iff__equal) ).
thf(f4290,plain,
( spl8_126
| ~ spl8_121 ),
inference(avatar_split_clause,[],[f4275,f3968,f4288]) ).
thf(f4288,plain,
( spl8_126
<=> ! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_126])]) ).
thf(f4275,plain,
( ! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) )
| ~ spl8_121 ),
inference(trivial_inequality_removal,[],[f4274]) ).
thf(f4274,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) )
| ~ spl8_121 ),
inference(forward_demodulation,[],[f1221,f3969]) ).
thf(f1221,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ),
inference(cnf_transformation,[],[f909]) ).
thf(f909,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ),
inference(flattening,[],[f908]) ).
thf(f908,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ),
inference(ennf_transformation,[],[f408]) ).
thf(f408,plain,
! [X0: a] :
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != bot_bot_set_real ) ) ),
inference(fool_elimination,[],[f407]) ).
thf(f407,plain,
! [X0: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != bot_bot_set_real ) ) ),
inference(rectify,[],[f151]) ).
thf(f151,axiom,
! [X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3) != bot_bot_set_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_local_Orev_Oexistence__ivl__notempty) ).
thf(f4286,plain,
( ~ spl8_62
| ~ spl8_103 ),
inference(avatar_contradiction_clause,[],[f4285]) ).
thf(f4285,plain,
( $false
| ~ spl8_62
| ~ spl8_103 ),
inference(trivial_inequality_removal,[],[f4276]) ).
thf(f4276,plain,
( ( $true != $true )
| ~ spl8_62
| ~ spl8_103 ),
inference(superposition,[],[f3897,f2507]) ).
thf(f3897,plain,
( ! [X0: real,X1: a] : ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
| ~ spl8_103 ),
inference(avatar_component_clause,[],[f3896]) ).
thf(f3896,plain,
( spl8_103
<=> ! [X0: real,X1: a] : ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_103])]) ).
thf(f4284,plain,
( ~ spl8_63
| ~ spl8_103 ),
inference(avatar_contradiction_clause,[],[f4283]) ).
thf(f4283,plain,
( $false
| ~ spl8_63
| ~ spl8_103 ),
inference(trivial_inequality_removal,[],[f4277]) ).
thf(f4277,plain,
( ( $true != $true )
| ~ spl8_63
| ~ spl8_103 ),
inference(superposition,[],[f3897,f2512]) ).
thf(f4282,plain,
( ~ spl8_64
| ~ spl8_103 ),
inference(avatar_contradiction_clause,[],[f4281]) ).
thf(f4281,plain,
( $false
| ~ spl8_64
| ~ spl8_103 ),
inference(trivial_inequality_removal,[],[f4278]) ).
thf(f4278,plain,
( ( $true != $true )
| ~ spl8_64
| ~ spl8_103 ),
inference(superposition,[],[f3897,f2517]) ).
thf(f4269,plain,
( spl8_104
| ~ spl8_121 ),
inference(avatar_contradiction_clause,[],[f4268]) ).
thf(f4268,plain,
( $false
| spl8_104
| ~ spl8_121 ),
inference(trivial_inequality_removal,[],[f4265]) ).
thf(f4265,plain,
( ( $true != $true )
| spl8_104
| ~ spl8_121 ),
inference(superposition,[],[f3900,f3969]) ).
thf(f3900,plain,
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true )
| spl8_104 ),
inference(avatar_component_clause,[],[f3899]) ).
thf(f4264,plain,
( ~ spl8_104
| spl8_125 ),
inference(avatar_split_clause,[],[f1220,f4262,f3899]) ).
thf(f4262,plain,
( spl8_125
<=> ! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_125])]) ).
thf(f1220,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ),
inference(cnf_transformation,[],[f907]) ).
thf(f907,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ),
inference(flattening,[],[f906]) ).
thf(f906,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ),
inference(ennf_transformation,[],[f406]) ).
thf(f406,plain,
! [X0: a] :
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real ) ) ),
inference(fool_elimination,[],[f405]) ).
thf(f405,plain,
! [X0: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) != bot_bot_set_real ) ) ),
inference(rectify,[],[f152]) ).
thf(f152,axiom,
! [X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3) != bot_bot_set_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_local_Oexistence__ivl__notempty) ).
thf(f4258,plain,
spl8_124,
inference(avatar_split_clause,[],[f1247,f4256]) ).
thf(f4256,plain,
( spl8_124
<=> ! [X0: a] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK1,X0)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_124])]) ).
thf(f1247,plain,
! [X0: a] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK1,X0)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f1127]) ).
thf(f4008,plain,
( spl8_123
| ~ spl8_62
| ~ spl8_107 ),
inference(avatar_split_clause,[],[f3987,f3912,f2505,f4005]) ).
thf(f4005,plain,
( spl8_123
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,x2),x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_123])]) ).
thf(f3987,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,x2),x) )
| ~ spl8_62
| ~ spl8_107 ),
inference(trivial_inequality_removal,[],[f3980]) ).
thf(f3980,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,x2),x) )
| ~ spl8_62
| ~ spl8_107 ),
inference(superposition,[],[f3913,f2507]) ).
thf(f3973,plain,
( spl8_121
| spl8_122 ),
inference(avatar_split_clause,[],[f1881,f3971,f3968]) ).
thf(f1881,plain,
! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),zero_zero_real) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(forward_demodulation,[],[f1315,f1155]) ).
thf(f1315,plain,
! [X0: real,X1: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X1),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X0)) )
| ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(cnf_transformation,[],[f951]) ).
thf(f3966,plain,
spl8_120,
inference(avatar_split_clause,[],[f1432,f3964]) ).
thf(f1432,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ) ),
inference(cnf_transformation,[],[f1047]) ).
thf(f1047,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ) ),
inference(ennf_transformation,[],[f646]) ).
thf(f646,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) ) ),
inference(fool_elimination,[],[f645]) ).
thf(f645,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2))
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X1),X2) ),
inference(rectify,[],[f257]) ).
thf(f257,axiom,
! [X18: a,X8: a,X9: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X18),X8)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X18),X9))
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add__less__imp__less__left) ).
thf(f3962,plain,
spl8_119,
inference(avatar_split_clause,[],[f1431,f3960]) ).
thf(f1431,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ) ),
inference(cnf_transformation,[],[f1046]) ).
thf(f1046,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X2) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ) ),
inference(ennf_transformation,[],[f644]) ).
thf(f644,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X2) ) ),
inference(fool_elimination,[],[f643]) ).
thf(f643,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1))
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X2) ),
inference(rectify,[],[f255]) ).
thf(f255,axiom,
! [X8: a,X18: a,X9: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X18)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X18))
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_add__less__imp__less__right) ).
thf(f3958,plain,
spl8_118,
inference(avatar_split_clause,[],[f1430,f3956]) ).
thf(f1430,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) ),
inference(cnf_transformation,[],[f1045]) ).
thf(f1045,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) ),
inference(ennf_transformation,[],[f642]) ).
thf(f642,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) ) ),
inference(fool_elimination,[],[f641]) ).
thf(f641,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1))
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X2) ),
inference(rectify,[],[f256]) ).
thf(f256,axiom,
! [X8: real,X18: real,X9: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X18)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X18))
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add__less__imp__less__right) ).
thf(f3954,plain,
spl8_117,
inference(avatar_split_clause,[],[f1692,f3952]) ).
thf(f3952,plain,
( spl8_117
<=> ! [X0: real,X1: real] :
( ( X0 != X1 )
| ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,uminus_uminus_real,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_117])]) ).
thf(f1692,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
| ( vAPP(real,real,uminus_uminus_real,X1) = vAPP(real,real,uminus_uminus_real,X0) ) ),
inference(equality_proxy_clausification,[],[f1691]) ).
thf(f1691,plain,
! [X0: real,X1: real] :
( ( X0 != X1 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(equality_proxy_clausification,[],[f1690]) ).
thf(f1690,plain,
! [X0: real,X1: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),X0),X1) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1302]) ).
thf(f3950,plain,
spl8_116,
inference(avatar_split_clause,[],[f1429,f3948]) ).
thf(f1429,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ),
inference(cnf_transformation,[],[f1044]) ).
thf(f1044,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ) ),
inference(ennf_transformation,[],[f640]) ).
thf(f640,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ) ),
inference(fool_elimination,[],[f639]) ).
thf(f639,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2))
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X1),X2) ),
inference(rectify,[],[f258]) ).
thf(f258,axiom,
! [X18: real,X8: real,X9: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X18),X8)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X18),X9))
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add__less__imp__less__left) ).
thf(f3946,plain,
spl8_115,
inference(avatar_split_clause,[],[f1425,f3944]) ).
thf(f3944,plain,
( spl8_115
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_115])]) ).
thf(f1425,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(cnf_transformation,[],[f1037]) ).
thf(f1037,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(ennf_transformation,[],[f632]) ).
thf(f632,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) ) ),
inference(fool_elimination,[],[f631]) ).
thf(f631,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) ),
inference(rectify,[],[f259]) ).
thf(f259,axiom,
! [X8: a,X9: a,X18: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X9)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X18)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_add__strict__right__mono) ).
thf(f3942,plain,
spl8_114,
inference(avatar_split_clause,[],[f1424,f3940]) ).
thf(f3940,plain,
( spl8_114
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_114])]) ).
thf(f1424,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(cnf_transformation,[],[f1036]) ).
thf(f1036,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(ennf_transformation,[],[f630]) ).
thf(f630,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ) ),
inference(fool_elimination,[],[f629]) ).
thf(f629,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ),
inference(rectify,[],[f261]) ).
thf(f261,axiom,
! [X8: a,X9: a,X18: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X9)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X18),X8)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X18),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_add__strict__left__mono) ).
thf(f3938,plain,
spl8_113,
inference(avatar_split_clause,[],[f1423,f3936]) ).
thf(f3936,plain,
( spl8_113
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_113])]) ).
thf(f1423,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(cnf_transformation,[],[f1035]) ).
thf(f1035,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(ennf_transformation,[],[f628]) ).
thf(f628,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) ) ),
inference(fool_elimination,[],[f627]) ).
thf(f627,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) ),
inference(rectify,[],[f313]) ).
thf(f313,axiom,
! [X8: a,X9: a,X18: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X9)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X18)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_diff__strict__right__mono) ).
thf(f3934,plain,
spl8_112,
inference(avatar_split_clause,[],[f1422,f3932]) ).
thf(f3932,plain,
( spl8_112
<=> ! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_112])]) ).
thf(f1422,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(cnf_transformation,[],[f1034]) ).
thf(f1034,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(ennf_transformation,[],[f626]) ).
thf(f626,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) ) ),
inference(fool_elimination,[],[f625]) ).
thf(f625,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X2),X0)) ),
inference(rectify,[],[f315]) ).
thf(f315,axiom,
! [X9: a,X8: a,X18: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X9),X8)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X18),X8)),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X18),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_diff__strict__left__mono) ).
thf(f3930,plain,
spl8_111,
inference(avatar_split_clause,[],[f1421,f3928]) ).
thf(f1421,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1033]) ).
thf(f1033,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f624]) ).
thf(f624,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ) ),
inference(fool_elimination,[],[f623]) ).
thf(f623,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ),
inference(rectify,[],[f314]) ).
thf(f314,axiom,
! [X8: real,X9: real,X18: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X9)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X18)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_diff__strict__right__mono) ).
thf(f3926,plain,
spl8_110,
inference(avatar_split_clause,[],[f1420,f3924]) ).
thf(f1420,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1032]) ).
thf(f1032,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f622]) ).
thf(f622,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) ) ),
inference(fool_elimination,[],[f621]) ).
thf(f621,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X0)) ),
inference(rectify,[],[f316]) ).
thf(f316,axiom,
! [X9: real,X8: real,X18: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X9),X8)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X18),X8)),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X18),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_diff__strict__left__mono) ).
thf(f3922,plain,
spl8_109,
inference(avatar_split_clause,[],[f1419,f3920]) ).
thf(f1419,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1031]) ).
thf(f1031,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f620]) ).
thf(f620,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ) ),
inference(fool_elimination,[],[f619]) ).
thf(f619,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ),
inference(rectify,[],[f262]) ).
thf(f262,axiom,
! [X8: real,X9: real,X18: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X9)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X18),X8)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X18),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_add__strict__left__mono) ).
thf(f3918,plain,
spl8_108,
inference(avatar_split_clause,[],[f1418,f3916]) ).
thf(f1418,plain,
! [X2: real,X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f1030]) ).
thf(f1030,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f618]) ).
thf(f618,plain,
! [X0: real,X1: real,X2: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) ) ),
inference(fool_elimination,[],[f617]) ).
thf(f617,plain,
! [X0: real,X1: real,X2: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) ),
inference(rectify,[],[f260]) ).
thf(f260,axiom,
! [X8: real,X9: real,X18: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X9)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X18)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_add__strict__right__mono) ).
thf(f3914,plain,
spl8_107,
inference(avatar_split_clause,[],[f1347,f3912]) ).
thf(f1347,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f993]) ).
thf(f993,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f552]) ).
thf(f552,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) ) ),
inference(fool_elimination,[],[f551]) ).
thf(f551,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),x) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_local_Omem__existence__ivl__iv__defined_I2_J) ).
thf(f3910,plain,
spl8_106,
inference(avatar_split_clause,[],[f1688,f3908]) ).
thf(f1688,plain,
! [X0: a,X1: a] :
( ( X0 = X1 )
| ( vAPP(a,a,uminus_uminus_a,X0) != vAPP(a,a,uminus_uminus_a,X1) ) ),
inference(equality_proxy_clausification,[],[f1687]) ).
thf(f1687,plain,
! [X0: a,X1: a] :
( ( X0 = X1 )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ) ),
inference(equality_proxy_clausification,[],[f1683]) ).
thf(f1683,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ) ),
inference(binary_proxy_clausification,[],[f1303]) ).
thf(f1303,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ),
inference(cnf_transformation,[],[f480]) ).
thf(f480,plain,
! [X0: a,X1: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ),
inference(fool_elimination,[],[f479]) ).
thf(f479,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,uminus_uminus_a,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f40]) ).
thf(f40,axiom,
! [X8: a,X9: a] :
( ( vAPP(a,a,uminus_uminus_a,X8) = vAPP(a,a,uminus_uminus_a,X9) )
= ( X8 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_neg__equal__iff__equal) ).
thf(f3906,plain,
spl8_105,
inference(avatar_split_clause,[],[f1346,f3904]) ).
thf(f3904,plain,
( spl8_105
<=> ! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_105])]) ).
thf(f1346,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f992]) ).
thf(f992,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f550]) ).
thf(f550,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ) ),
inference(fool_elimination,[],[f549]) ).
thf(f549,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),top_top_set_real) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),top_top_set_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_local_Omem__existence__ivl__subset) ).
thf(f3902,plain,
( spl8_103
| spl8_104 ),
inference(avatar_split_clause,[],[f1345,f3899,f3896]) ).
thf(f1345,plain,
! [X0: real,X1: a] :
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(cnf_transformation,[],[f991]) ).
thf(f991,plain,
! [X0: real,X1: a] :
( ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true )
| ( $true != vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) ) ),
inference(ennf_transformation,[],[f548]) ).
thf(f548,plain,
! [X0: real,X1: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1)) )
=> ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) ),
inference(fool_elimination,[],[f547]) ).
thf(f547,plain,
! [X0: real,X1: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X0),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X1))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) ),
inference(rectify,[],[f121]) ).
thf(f121,axiom,
! [X1: real,X3: a] :
( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3))
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_local_Omem__existence__ivl__iv__defined_I1_J) ).
thf(f3894,plain,
spl8_102,
inference(avatar_split_clause,[],[f1236,f3892]) ).
thf(f3892,plain,
( spl8_102
<=> ! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_102])]) ).
thf(f1236,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f934]) ).
thf(f934,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f438]) ).
thf(f438,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real ) ),
inference(fool_elimination,[],[f437]) ).
thf(f437,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real ) ),
inference(rectify,[],[f83]) ).
thf(f83,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_closed__orbit__global__existence) ).
thf(f3890,plain,
spl8_101,
inference(avatar_split_clause,[],[f1232,f3888]) ).
thf(f1232,plain,
! [X0: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f930]) ).
thf(f930,plain,
! [X0: a] :
( ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f430]) ).
thf(f430,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( $true = vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) ) ),
inference(fool_elimination,[],[f429]) ).
thf(f429,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) ),
inference(rectify,[],[f53]) ).
thf(f53,axiom,
! [X3: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
=> vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_existence__ivl__zero) ).
thf(f3886,plain,
spl8_100,
inference(avatar_split_clause,[],[f1212,f3884]) ).
thf(f3884,plain,
( spl8_100
<=> ! [X0: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_100])]) ).
thf(f1212,plain,
! [X0: a] :
( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true ) ),
inference(cnf_transformation,[],[f899]) ).
thf(f899,plain,
! [X0: a] :
( ( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) )
| ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
& ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) ) )
& ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ) ),
inference(flattening,[],[f898]) ).
thf(f898,plain,
! [X0: a] :
( ( ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) )
| ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
& ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) ) )
& ( ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true )
| ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) != $true ) ) ),
inference(ennf_transformation,[],[f394]) ).
thf(f394,plain,
! [X0: a] :
( ( ~ ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
& ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) ) )
& ( ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
& ( vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) = $true ) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) = X0 ) ) ),
inference(fool_elimination,[],[f393]) ).
thf(f393,plain,
! [X0: a] :
( ( ~ ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) ) )
& ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X0),zero_zero_real) = X0 ) ) ),
inference(rectify,[],[f92]) ).
thf(f92,axiom,
! [X3: a] :
( ( ~ ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) )
=> ( zero_zero_a = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),zero_zero_real) ) )
& ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),x)
& vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,zero_zero_real),top_top_set_real) )
=> ( vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),X3),zero_zero_real) = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_local_Oflow__initial__time__if) ).
thf(f3880,plain,
spl8_99,
inference(avatar_split_clause,[],[f1249,f3878]) ).
thf(f3878,plain,
( spl8_99
<=> ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_99])]) ).
thf(f1249,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(cnf_transformation,[],[f949]) ).
thf(f949,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) != $true ) ),
inference(ennf_transformation,[],[f460]) ).
thf(f460,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0) = $true )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true ) ),
inference(fool_elimination,[],[f459]) ).
thf(f459,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rev_Oclosed__orbit__in__domain) ).
thf(f3804,plain,
( spl8_98
| ~ spl8_51
| ~ spl8_53
| ~ spl8_96 ),
inference(avatar_split_clause,[],[f2819,f2816,f2272,f2264,f3802]) ).
thf(f3800,plain,
spl8_97,
inference(avatar_split_clause,[],[f1686,f3798]) ).
thf(f3798,plain,
( spl8_97
<=> ! [X0: a,X1: a] :
( ( X0 != X1 )
| ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,uminus_uminus_a,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_97])]) ).
thf(f1686,plain,
! [X0: a,X1: a] :
( ( X0 != X1 )
| ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,uminus_uminus_a,X1) ) ),
inference(equality_proxy_clausification,[],[f1685]) ).
thf(f1685,plain,
! [X0: a,X1: a] :
( ( X0 != X1 )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ) ),
inference(equality_proxy_clausification,[],[f1684]) ).
thf(f1684,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X1) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ) ),
inference(binary_proxy_clausification,[],[f1303]) ).
thf(f2818,plain,
spl8_96,
inference(avatar_split_clause,[],[f1906,f2816]) ).
thf(f2810,plain,
spl8_95,
inference(avatar_split_clause,[],[f1903,f2808]) ).
thf(f1903,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X2),X1)) ),
inference(forward_demodulation,[],[f1375,f1373]) ).
thf(f1375,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ),
inference(cnf_transformation,[],[f859]) ).
thf(f859,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2)) ),
inference(rectify,[],[f334]) ).
thf(f334,axiom,
! [X8: real,X9: real,X18: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X18)),X9) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_diff__diff__eq2) ).
thf(f2806,plain,
spl8_94,
inference(avatar_split_clause,[],[f1902,f2804]) ).
thf(f2802,plain,
spl8_93,
inference(avatar_split_clause,[],[f1388,f2800]) ).
thf(f1388,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) ),
inference(cnf_transformation,[],[f872]) ).
thf(f872,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) ),
inference(rectify,[],[f333]) ).
thf(f333,axiom,
! [X8: a,X9: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X18)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_diff__diff__eq2) ).
thf(f2798,plain,
spl8_92,
inference(avatar_split_clause,[],[f1386,f2796]) ).
thf(f1386,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),X1) ),
inference(cnf_transformation,[],[f870]) ).
thf(f870,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2)),X1) ),
inference(rectify,[],[f329]) ).
thf(f329,axiom,
! [X8: a,X9: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X18)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_diff__add__eq__diff__diff__swap) ).
thf(f2794,plain,
spl8_91,
inference(avatar_split_clause,[],[f1385,f2792]) ).
thf(f1385,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) ),
inference(cnf_transformation,[],[f869]) ).
thf(f869,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) ),
inference(rectify,[],[f327]) ).
thf(f327,axiom,
! [X8: a,X9: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9)),X18) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_diff__diff__add) ).
thf(f2790,plain,
spl8_90,
inference(avatar_split_clause,[],[f1383,f2788]) ).
thf(f1383,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) ),
inference(cnf_transformation,[],[f867]) ).
thf(f867,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) ),
inference(rectify,[],[f295]) ).
thf(f295,axiom,
! [X8: a,X9: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X18)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(f2786,plain,
spl8_89,
inference(avatar_split_clause,[],[f1382,f2784]) ).
thf(f1382,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ),
inference(cnf_transformation,[],[f866]) ).
thf(f866,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ),
inference(rectify,[],[f273]) ).
thf(f273,axiom,
! [X9: a,X8: a,X18: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X18)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_add_Oleft__commute) ).
thf(f2781,plain,
spl8_88,
inference(avatar_split_clause,[],[f1381,f2779]) ).
thf(f2779,plain,
( spl8_88
<=> ! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_88])]) ).
thf(f2777,plain,
spl8_87,
inference(avatar_split_clause,[],[f1377,f2775]) ).
thf(f1377,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),X1) ),
inference(cnf_transformation,[],[f861]) ).
thf(f861,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2)),X1) ),
inference(rectify,[],[f330]) ).
thf(f330,axiom,
! [X8: real,X9: real,X18: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X18)),X9) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_diff__add__eq__diff__diff__swap) ).
thf(f2773,plain,
spl8_86,
inference(avatar_split_clause,[],[f1376,f2771]) ).
thf(f1376,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) ),
inference(cnf_transformation,[],[f860]) ).
thf(f860,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) ),
inference(rectify,[],[f328]) ).
thf(f328,axiom,
! [X8: real,X9: real,X18: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9)),X18) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_diff__diff__add) ).
thf(f2769,plain,
( spl8_85
| ~ spl8_2
| ~ spl8_20 ),
inference(avatar_split_clause,[],[f2088,f2048,f1942,f2767]) ).
thf(f2048,plain,
( spl8_20
<=> ! [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
thf(f2088,plain,
( ! [X0: a] : ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) )
| ~ spl8_2
| ~ spl8_20 ),
inference(trivial_inequality_removal,[],[f2087]) ).
thf(f2087,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) ) )
| ~ spl8_2
| ~ spl8_20 ),
inference(superposition,[],[f2049,f1943]) ).
thf(f2049,plain,
( ! [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) )
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f2048]) ).
thf(f2765,plain,
spl8_84,
inference(avatar_split_clause,[],[f1373,f2763]) ).
thf(f2761,plain,
spl8_83,
inference(avatar_split_clause,[],[f1371,f2759]) ).
thf(f1371,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) ),
inference(cnf_transformation,[],[f855]) ).
thf(f855,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X2) ),
inference(rectify,[],[f296]) ).
thf(f296,axiom,
! [X8: real,X9: real,X18: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X18)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(f2757,plain,
spl8_82,
inference(avatar_split_clause,[],[f1370,f2755]) ).
thf(f1370,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ),
inference(cnf_transformation,[],[f854]) ).
thf(f854,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X2)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ),
inference(rectify,[],[f274]) ).
thf(f274,axiom,
! [X9: real,X8: real,X18: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X18)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_add_Oleft__commute) ).
thf(f2753,plain,
spl8_81,
inference(avatar_split_clause,[],[f1367,f2751]) ).
thf(f1367,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ),
inference(cnf_transformation,[],[f851]) ).
thf(f851,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X2),X1)) ),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
! [X8: a,X18: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X18)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_add__diff__cancel__right) ).
thf(f2749,plain,
spl8_80,
inference(avatar_split_clause,[],[f1366,f2747]) ).
thf(f1366,plain,
! [X2: a,X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ),
inference(cnf_transformation,[],[f850]) ).
thf(f850,plain,
! [X0: a,X1: a,X2: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X2)) ),
inference(rectify,[],[f206]) ).
thf(f206,axiom,
! [X18: a,X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X18),X8)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X18),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_add__diff__cancel__left) ).
thf(f2745,plain,
spl8_79,
inference(avatar_split_clause,[],[f1363,f2743]) ).
thf(f1363,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ),
inference(cnf_transformation,[],[f847]) ).
thf(f847,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X2)) ),
inference(rectify,[],[f207]) ).
thf(f207,axiom,
! [X18: real,X8: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X18),X8)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X18),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_add__diff__cancel__left) ).
thf(f2741,plain,
spl8_78,
inference(avatar_split_clause,[],[f1362,f2739]) ).
thf(f1362,plain,
! [X2: real,X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ),
inference(cnf_transformation,[],[f846]) ).
thf(f846,plain,
! [X0: real,X1: real,X2: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X2) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X2),X1)) ),
inference(rectify,[],[f203]) ).
thf(f203,axiom,
! [X8: real,X18: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X18)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X9),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_add__diff__cancel__right) ).
thf(f2737,plain,
spl8_77,
inference(avatar_split_clause,[],[f1228,f2735]) ).
thf(f1228,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f923]) ).
thf(f923,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(flattening,[],[f922]) ).
thf(f922,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f422]) ).
thf(f422,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true ) ) ),
inference(fool_elimination,[],[f421]) ).
thf(f421,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) ) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_fixed__point__imp__closed__orbit__period__zero_I1_J) ).
thf(f2733,plain,
spl8_76,
inference(avatar_split_clause,[],[f1227,f2731]) ).
thf(f1227,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f921]) ).
thf(f921,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(flattening,[],[f920]) ).
thf(f920,plain,
! [X0: a] :
( ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f420]) ).
thf(f420,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real ) ) ),
inference(fool_elimination,[],[f419]) ).
thf(f419,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real ) ) ),
inference(rectify,[],[f80]) ).
thf(f80,axiom,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0) = top_top_set_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_fixpoint__sol_I1_J) ).
thf(f2729,plain,
spl8_75,
inference(avatar_split_clause,[],[f1226,f2727]) ).
thf(f1226,plain,
! [X0: a] :
( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(cnf_transformation,[],[f919]) ).
thf(f919,plain,
! [X0: a] :
( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(flattening,[],[f918]) ).
thf(f918,plain,
! [X0: a] :
( ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) )
| ( vAPP(a,a,f,X0) != zero_zero_a )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) != $true ) ),
inference(ennf_transformation,[],[f418]) ).
thf(f418,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) ) ) ),
inference(fool_elimination,[],[f417]) ).
thf(f417,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) ) ) ),
inference(rectify,[],[f150]) ).
thf(f150,axiom,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x)
=> ( ( vAPP(a,a,f,X0) = zero_zero_a )
=> ( zero_zero_real = vAPP(a,real,vAPP(set_a,sTfun(a,real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,real)),period1305449585riod_a,f),x),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_fixed__point__imp__closed__orbit__period__zero_I2_J) ).
thf(f2725,plain,
( spl8_74
| ~ spl8_2
| ~ spl8_19 ),
inference(avatar_split_clause,[],[f2086,f2044,f1942,f2723]) ).
thf(f2723,plain,
( spl8_74
<=> ! [X0: real] : ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).
thf(f2044,plain,
( spl8_19
<=> ! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
thf(f2086,plain,
( ! [X0: real] : ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) )
| ~ spl8_2
| ~ spl8_19 ),
inference(trivial_inequality_removal,[],[f2085]) ).
thf(f2085,plain,
( ! [X0: real] :
( ( $true != $true )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) ) )
| ~ spl8_2
| ~ spl8_19 ),
inference(superposition,[],[f2045,f1943]) ).
thf(f2045,plain,
( ! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) )
| ~ spl8_19 ),
inference(avatar_component_clause,[],[f2044]) ).
thf(f2719,plain,
spl8_73,
inference(avatar_split_clause,[],[f1239,f2717]) ).
thf(f1239,plain,
! [X0: a] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),vAPP(a,real,sK0,X0)) )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f1125]) ).
thf(f2713,plain,
spl8_72,
inference(avatar_split_clause,[],[f1241,f2711]) ).
thf(f1241,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(cnf_transformation,[],[f940]) ).
thf(f940,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true )
| ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) != $true ) ),
inference(ennf_transformation,[],[f446]) ).
thf(f446,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0) = $true )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) = $true ) ),
inference(fool_elimination,[],[f445]) ).
thf(f445,plain,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
! [X0: a] :
( vAPP(a,$o,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,$o)),period720806154rbit_a,f),x),X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_closed__orbit__in__domain) ).
thf(f2567,plain,
spl8_71,
inference(avatar_split_clause,[],[f1295,f2565]) ).
thf(f1295,plain,
! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(cnf_transformation,[],[f835]) ).
thf(f835,plain,
! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(rectify,[],[f323]) ).
thf(f323,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X9)),vAPP(a,a,uminus_uminus_a,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_add_Oinverse__distrib__swap) ).
thf(f2560,plain,
spl8_70,
inference(avatar_split_clause,[],[f1294,f2558]) ).
thf(f1294,plain,
! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ),
inference(cnf_transformation,[],[f834]) ).
thf(f834,plain,
! [X0: a,X1: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,uminus_uminus_a,X1)) ),
inference(rectify,[],[f198]) ).
thf(f198,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X8)),vAPP(a,a,uminus_uminus_a,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_minus__add__distrib) ).
thf(f2556,plain,
spl8_69,
inference(avatar_split_clause,[],[f1293,f2554]) ).
thf(f1293,plain,
! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) ),
inference(cnf_transformation,[],[f833]) ).
thf(f833,plain,
! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,uminus_uminus_real,X1)) ),
inference(rectify,[],[f199]) ).
thf(f199,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X8)),vAPP(real,real,uminus_uminus_real,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_minus__add__distrib) ).
thf(f2552,plain,
spl8_68,
inference(avatar_split_clause,[],[f1292,f2550]) ).
thf(f1292,plain,
! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(cnf_transformation,[],[f832]) ).
thf(f832,plain,
! [X0: real,X1: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(rectify,[],[f324]) ).
thf(f324,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X9)),vAPP(real,real,uminus_uminus_real,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_add_Oinverse__distrib__swap) ).
thf(f2548,plain,
spl8_67,
inference(avatar_split_clause,[],[f1253,f2546]) ).
thf(f2546,plain,
( spl8_67
<=> ! [X0: a] : ( $true = vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
thf(f1253,plain,
! [X0: a] : ( $true = vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ),
inference(cnf_transformation,[],[f468]) ).
thf(f468,plain,
! [X0: a] : ( $true = vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)) ),
inference(fool_elimination,[],[f467]) ).
thf(f467,plain,
! [X0: a] : vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X0)),
inference(rectify,[],[f61]) ).
thf(f61,axiom,
! [X3: a] : vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,vAPP(sTfun(a,a),sTfun(a,a),uminus_uminus_a_a,f)),x),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rev_Omvar_Ointerval__axioms) ).
thf(f2527,plain,
spl8_66,
inference(avatar_split_clause,[],[f1337,f2525]) ).
thf(f2525,plain,
( spl8_66
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).
thf(f1337,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(cnf_transformation,[],[f981]) ).
thf(f981,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) )
| ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) ) ),
inference(ennf_transformation,[],[f532]) ).
thf(f532,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1) )
=> ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) ) ),
inference(fool_elimination,[],[f531]) ).
thf(f531,plain,
! [X0: a,X1: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X1)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X1)),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(rectify,[],[f307]) ).
thf(f307,axiom,
! [X8: a,X9: a] :
( vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X9)
=> vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,vAPP(a,a,uminus_uminus_a,X9)),vAPP(a,a,uminus_uminus_a,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_verit__negate__coefficient_I2_J) ).
thf(f2523,plain,
spl8_65,
inference(avatar_split_clause,[],[f1336,f2521]) ).
thf(f1336,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(cnf_transformation,[],[f980]) ).
thf(f980,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) )
| ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) ) ),
inference(ennf_transformation,[],[f530]) ).
thf(f530,plain,
! [X0: real,X1: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1) )
=> ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(fool_elimination,[],[f529]) ).
thf(f529,plain,
! [X0: real,X1: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X1)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X1)),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(rectify,[],[f308]) ).
thf(f308,axiom,
! [X8: real,X9: real] :
( vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X9)
=> vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,vAPP(real,real,uminus_uminus_real,X9)),vAPP(real,real,uminus_uminus_real,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_verit__negate__coefficient_I2_J) ).
thf(f2518,plain,
spl8_64,
inference(avatar_split_clause,[],[f1495,f2515]) ).
thf(f1495,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,tt),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) = $true,
inference(cnf_transformation,[],[f744]) ).
thf(f744,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,tt),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)) = $true,
inference(fool_elimination,[],[f743]) ).
thf(f743,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,tt),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,tt),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),xx)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_tt__ex) ).
thf(f2513,plain,
spl8_63,
inference(avatar_split_clause,[],[f1494,f2510]) ).
thf(f1494,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) = $true,
inference(cnf_transformation,[],[f742]) ).
thf(f742,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) = $true,
inference(fool_elimination,[],[f741]) ).
thf(f741,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,ss),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ss__ex) ).
thf(f2508,plain,
spl8_62,
inference(avatar_split_clause,[],[f1493,f2505]) ).
thf(f1493,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,t),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) = $true,
inference(cnf_transformation,[],[f740]) ).
thf(f740,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,t),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)) = $true,
inference(fool_elimination,[],[f739]) ).
thf(f739,plain,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,t),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,t),vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),x2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I8_J) ).
thf(f2456,plain,
( spl8_61
| ~ spl8_51
| ~ spl8_53
| ~ spl8_59 ),
inference(avatar_split_clause,[],[f2448,f2445,f2272,f2264,f2454]) ).
thf(f2445,plain,
( spl8_59
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).
thf(f2448,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) )
| ~ spl8_51
| ~ spl8_53
| ~ spl8_59 ),
inference(forward_demodulation,[],[f2446,f2374]) ).
thf(f2446,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X1)),X0) )
| ~ spl8_59 ),
inference(avatar_component_clause,[],[f2445]) ).
thf(f2452,plain,
( spl8_60
| ~ spl8_48
| ~ spl8_52
| ~ spl8_58 ),
inference(avatar_split_clause,[],[f2443,f2440,f2268,f2249,f2450]) ).
thf(f2440,plain,
( spl8_58
<=> ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).
thf(f2443,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,real,uminus_uminus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) )
| ~ spl8_48
| ~ spl8_52
| ~ spl8_58 ),
inference(forward_demodulation,[],[f2441,f2361]) ).
thf(f2441,plain,
( ! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X1)),X0) )
| ~ spl8_58 ),
inference(avatar_component_clause,[],[f2440]) ).
thf(f2447,plain,
spl8_59,
inference(avatar_split_clause,[],[f1279,f2445]) ).
thf(f1279,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X1)),X0) ),
inference(cnf_transformation,[],[f819]) ).
thf(f819,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X1)),X0) ),
inference(rectify,[],[f143]) ).
thf(f143,axiom,
! [X9: a,X8: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X9)),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,uminus_uminus_a,X8)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_minus__diff__commute) ).
thf(f2442,plain,
spl8_58,
inference(avatar_split_clause,[],[f1276,f2440]) ).
thf(f1276,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X1)),X0) ),
inference(cnf_transformation,[],[f816]) ).
thf(f816,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X1)),X0) ),
inference(rectify,[],[f144]) ).
thf(f144,axiom,
! [X9: real,X8: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X9)),X8) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,uminus_uminus_real,X8)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_minus__diff__commute) ).
thf(f2433,plain,
spl8_57,
inference(avatar_split_clause,[],[f1209,f2431]) ).
thf(f2431,plain,
( spl8_57
<=> ! [X0: set_a] : ( vAPP(sTfun(a,$o),set_a,collect_a,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).
thf(f1209,plain,
! [X0: set_a] : ( vAPP(sTfun(a,$o),set_a,collect_a,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0)) = X0 ),
inference(cnf_transformation,[],[f392]) ).
thf(f392,plain,
! [X0: set_a] : ( vAPP(sTfun(a,$o),set_a,collect_a,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0)) = X0 ),
inference(fool_elimination,[],[f391]) ).
thf(f391,plain,
! [X0: set_a] :
( vAPP(sTfun(a,$o),set_a,collect_a,
^ [X1: a] : vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),X0)) = X0 ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
! [X12: set_a] :
( vAPP(sTfun(a,$o),set_a,collect_a,
^ [X10: a] : vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X10),X12)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Collect__mem__eq) ).
thf(f2429,plain,
spl8_56,
inference(avatar_split_clause,[],[f1208,f2427]) ).
thf(f2427,plain,
( spl8_56
<=> ! [X0: set_real] : ( vAPP(sTfun(real,$o),set_real,collect_real,vAPP(set_real,sTfun(real,$o),vAPP(sTfun(real,sTfun(set_real,$o)),sTfun(set_real,sTfun(real,$o)),cCOMB,member_real),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
thf(f1208,plain,
! [X0: set_real] : ( vAPP(sTfun(real,$o),set_real,collect_real,vAPP(set_real,sTfun(real,$o),vAPP(sTfun(real,sTfun(set_real,$o)),sTfun(set_real,sTfun(real,$o)),cCOMB,member_real),X0)) = X0 ),
inference(cnf_transformation,[],[f390]) ).
thf(f390,plain,
! [X0: set_real] : ( vAPP(sTfun(real,$o),set_real,collect_real,vAPP(set_real,sTfun(real,$o),vAPP(sTfun(real,sTfun(set_real,$o)),sTfun(set_real,sTfun(real,$o)),cCOMB,member_real),X0)) = X0 ),
inference(fool_elimination,[],[f389]) ).
thf(f389,plain,
! [X0: set_real] :
( vAPP(sTfun(real,$o),set_real,collect_real,
^ [X1: real] : vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X1),X0)) = X0 ),
inference(rectify,[],[f50]) ).
thf(f50,axiom,
! [X12: set_real] :
( vAPP(sTfun(real,$o),set_real,collect_real,
^ [X10: real] : vAPP(set_real,$o,vAPP(real,sTfun(set_real,$o),member_real,X10),X12)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(f2282,plain,
spl8_55,
inference(avatar_split_clause,[],[f1273,f2280]) ).
thf(f1273,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = X1 ),
inference(cnf_transformation,[],[f813]) ).
thf(f813,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)) = X1 ),
inference(rectify,[],[f196]) ).
thf(f196,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X8)),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_minus__add__cancel) ).
thf(f2278,plain,
spl8_54,
inference(avatar_split_clause,[],[f1271,f2276]) ).
thf(f1271,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = X1 ),
inference(cnf_transformation,[],[f811]) ).
thf(f811,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)) = X1 ),
inference(rectify,[],[f197]) ).
thf(f197,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X8)),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_minus__add__cancel) ).
thf(f2274,plain,
spl8_53,
inference(avatar_split_clause,[],[f1269,f2272]) ).
thf(f1269,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ),
inference(cnf_transformation,[],[f809]) ).
thf(f809,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)) ),
inference(rectify,[],[f113]) ).
thf(f113,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9)) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_minus__diff__eq) ).
thf(f2270,plain,
spl8_52,
inference(avatar_split_clause,[],[f1268,f2268]) ).
thf(f2266,plain,
spl8_51,
inference(avatar_split_clause,[],[f1267,f2264]) ).
thf(f1267,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,uminus_uminus_a,X1)) ),
inference(cnf_transformation,[],[f807]) ).
thf(f807,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),vAPP(a,a,uminus_uminus_a,X1)) ),
inference(rectify,[],[f241]) ).
thf(f241,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),vAPP(a,a,uminus_uminus_a,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_diff__minus__eq__add) ).
thf(f2262,plain,
spl8_50,
inference(avatar_split_clause,[],[f1266,f2260]) ).
thf(f1266,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) ),
inference(cnf_transformation,[],[f806]) ).
thf(f806,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X1) ),
inference(rectify,[],[f239]) ).
thf(f239,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X9),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X8)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_uminus__add__conv__diff) ).
thf(f2258,plain,
spl8_49,
inference(avatar_split_clause,[],[f1265,f2256]) ).
thf(f1265,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) ),
inference(cnf_transformation,[],[f805]) ).
thf(f805,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X1) ),
inference(rectify,[],[f240]) ).
thf(f240,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X9),X8) = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X8)),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_uminus__add__conv__diff) ).
thf(f2251,plain,
spl8_48,
inference(avatar_split_clause,[],[f1264,f2249]) ).
thf(f1264,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,uminus_uminus_real,X1)) ),
inference(cnf_transformation,[],[f804]) ).
thf(f804,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),vAPP(real,real,uminus_uminus_real,X1)) ),
inference(rectify,[],[f242]) ).
thf(f242,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9) = vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),vAPP(real,real,uminus_uminus_real,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_diff__minus__eq__add) ).
thf(f2247,plain,
spl8_47,
inference(avatar_split_clause,[],[f1252,f2245]) ).
thf(f2245,plain,
( spl8_47
<=> ! [X0: a] : ( $true = vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
thf(f1252,plain,
! [X0: a] : ( $true = vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) ),
inference(cnf_transformation,[],[f466]) ).
thf(f466,plain,
! [X0: a] : ( $true = vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)) ),
inference(fool_elimination,[],[f465]) ).
thf(f465,plain,
! [X0: a] : vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X0)),
inference(rectify,[],[f25]) ).
thf(f25,axiom,
! [X3: a] : vAPP(set_real,$o,initia826609931terval,vAPP(a,set_real,vAPP(set_a,sTfun(a,set_real),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,set_real)),auto_l612940ivl0_a,f),x),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_mvar_Ointerval__axioms) ).
thf(f2190,plain,
spl8_46,
inference(avatar_split_clause,[],[f1873,f2188]) ).
thf(f1873,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X1),X0)) = X1 ),
inference(forward_demodulation,[],[f1272,f1266]) ).
thf(f1272,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X1)) = X1 ),
inference(cnf_transformation,[],[f812]) ).
thf(f812,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X1)) = X1 ),
inference(rectify,[],[f194]) ).
thf(f194,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X8)),X9)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_add__minus__cancel) ).
thf(f2186,plain,
spl8_45,
inference(avatar_split_clause,[],[f1872,f2184]) ).
thf(f1872,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X1),X0)) = X1 ),
inference(forward_demodulation,[],[f1270,f1265]) ).
thf(f1270,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X1)) = X1 ),
inference(cnf_transformation,[],[f810]) ).
thf(f810,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X1)) = X1 ),
inference(rectify,[],[f195]) ).
thf(f195,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X8)),X9)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_add__minus__cancel) ).
thf(f2182,plain,
spl8_44,
inference(avatar_split_clause,[],[f1263,f2180]) ).
thf(f1263,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X1) = X0 ),
inference(cnf_transformation,[],[f803]) ).
thf(f803,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X1)),X1) = X0 ),
inference(rectify,[],[f208]) ).
thf(f208,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X9)),X9) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_diff__add__cancel) ).
thf(f2178,plain,
spl8_43,
inference(avatar_split_clause,[],[f1261,f2176]) ).
thf(f1261,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) = X1 ),
inference(cnf_transformation,[],[f801]) ).
thf(f801,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X0) = X1 ),
inference(rectify,[],[f204]) ).
thf(f204,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)),X8) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add__diff__cancel__left_H) ).
thf(f2174,plain,
spl8_42,
inference(avatar_split_clause,[],[f1260,f2172]) ).
thf(f1260,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) = X0 ),
inference(cnf_transformation,[],[f800]) ).
thf(f800,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),X1)),X1) = X0 ),
inference(rectify,[],[f210]) ).
thf(f210,axiom,
! [X8: a,X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),X9)),X9) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_add__diff__cancel) ).
thf(f2170,plain,
spl8_41,
inference(avatar_split_clause,[],[f1259,f2168]) ).
thf(f1259,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) = X1 ),
inference(cnf_transformation,[],[f799]) ).
thf(f799,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X0) = X1 ),
inference(rectify,[],[f205]) ).
thf(f205,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)),X8) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__diff__cancel__left_H) ).
thf(f2166,plain,
spl8_40,
inference(avatar_split_clause,[],[f1257,f2164]) ).
thf(f1257,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) = X0 ),
inference(cnf_transformation,[],[f797]) ).
thf(f797,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),X1)),X1) = X0 ),
inference(rectify,[],[f201]) ).
thf(f201,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),X9)),X9) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_add__diff__cancel__right_H) ).
thf(f2162,plain,
spl8_39,
inference(avatar_split_clause,[],[f1256,f2160]) ).
thf(f1256,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X1) = X0 ),
inference(cnf_transformation,[],[f796]) ).
thf(f796,plain,
! [X0: real,X1: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),X1)),X1) = X0 ),
inference(rectify,[],[f209]) ).
thf(f209,axiom,
! [X8: real,X9: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),X9)),X9) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_diff__add__cancel) ).
thf(f2158,plain,
spl8_38,
inference(avatar_split_clause,[],[f1853,f2156]) ).
thf(f2156,plain,
( spl8_38
<=> ! [X0: a] :
( ( zero_zero_a = X0 )
| ( zero_zero_a != vAPP(a,a,uminus_uminus_a,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
thf(f1853,plain,
! [X0: a] :
( ( zero_zero_a = X0 )
| ( zero_zero_a != vAPP(a,a,uminus_uminus_a,X0) ) ),
inference(equality_proxy_clausification,[],[f1852]) ).
thf(f1852,plain,
! [X0: a] :
( ( zero_zero_a = X0 )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ) ),
inference(equality_proxy_clausification,[],[f1848]) ).
thf(f1848,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ) ),
inference(binary_proxy_clausification,[],[f1192]) ).
thf(f1192,plain,
! [X0: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(cnf_transformation,[],[f358]) ).
thf(f358,plain,
! [X0: a] : ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(fool_elimination,[],[f357]) ).
thf(f357,plain,
! [X0: a] :
( ( zero_zero_a = vAPP(a,a,uminus_uminus_a,X0) )
= ( zero_zero_a = X0 ) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X8: a] :
( ( zero_zero_a = vAPP(a,a,uminus_uminus_a,X8) )
= ( zero_zero_a = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_neg__0__equal__iff__equal) ).
thf(f2154,plain,
spl8_37,
inference(avatar_split_clause,[],[f1148,f2151]) ).
thf(f2151,plain,
( spl8_37
<=> ( plus_plus_real = vAPP(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,real)),cCOMB,plus_plus_real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
thf(f1148,plain,
plus_plus_real = vAPP(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,real)),cCOMB,plus_plus_real),
inference(cnf_transformation,[],[f354]) ).
thf(f354,plain,
plus_plus_real = vAPP(sTfun(real,sTfun(real,real)),sTfun(real,sTfun(real,real)),cCOMB,plus_plus_real),
inference(fool_elimination,[],[f353]) ).
thf(f353,plain,
( plus_plus_real
= ( ^ [X0: real,X1: real] : vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X1),X0) ) ),
inference(rectify,[],[f276]) ).
thf(f276,axiom,
( plus_plus_real
= ( ^ [X22: real,X23: real] : vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X23),X22) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_add_Ocommute) ).
thf(f2149,plain,
spl8_36,
inference(avatar_split_clause,[],[f1147,f2146]) ).
thf(f2146,plain,
( spl8_36
<=> ( plus_plus_a = vAPP(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,a)),cCOMB,plus_plus_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
thf(f1147,plain,
plus_plus_a = vAPP(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,a)),cCOMB,plus_plus_a),
inference(cnf_transformation,[],[f352]) ).
thf(f352,plain,
plus_plus_a = vAPP(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(a,a)),cCOMB,plus_plus_a),
inference(fool_elimination,[],[f351]) ).
thf(f351,plain,
( plus_plus_a
= ( ^ [X0: a,X1: a] : vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X1),X0) ) ),
inference(rectify,[],[f275]) ).
thf(f275,axiom,
( plus_plus_a
= ( ^ [X22: a,X23: a] : vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X23),X22) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_add_Ocommute) ).
thf(f2120,plain,
spl8_35,
inference(avatar_split_clause,[],[f1179,f2118]) ).
thf(f1179,plain,
! [X0: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),X0) ),
inference(cnf_transformation,[],[f778]) ).
thf(f778,plain,
! [X0: a] : ( vAPP(a,a,uminus_uminus_a,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),X0) ),
inference(rectify,[],[f31]) ).
thf(f31,axiom,
! [X9: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,zero_zero_a),X9) = vAPP(a,a,uminus_uminus_a,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_verit__minus__simplify_I3_J) ).
thf(f2116,plain,
spl8_34,
inference(avatar_split_clause,[],[f1177,f2114]) ).
thf(f2112,plain,
spl8_33,
inference(avatar_split_clause,[],[f1851,f2110]) ).
thf(f1851,plain,
! [X0: a] :
( ( zero_zero_a != X0 )
| ( zero_zero_a = vAPP(a,a,uminus_uminus_a,X0) ) ),
inference(equality_proxy_clausification,[],[f1850]) ).
thf(f1850,plain,
! [X0: a] :
( ( zero_zero_a != X0 )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ) ),
inference(equality_proxy_clausification,[],[f1849]) ).
thf(f1849,plain,
! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),zero_zero_a),vAPP(a,a,uminus_uminus_a,X0)) ) ),
inference(binary_proxy_clausification,[],[f1192]) ).
thf(f2108,plain,
spl8_32,
inference(avatar_split_clause,[],[f1176,f2106]) ).
thf(f1176,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ),
inference(cnf_transformation,[],[f775]) ).
thf(f775,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X0)),X0) ),
inference(rectify,[],[f236]) ).
thf(f236,axiom,
! [X8: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,vAPP(real,real,uminus_uminus_real,X8)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add_Oleft__inverse) ).
thf(f2104,plain,
spl8_31,
inference(avatar_split_clause,[],[f1175,f2102]) ).
thf(f1175,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(cnf_transformation,[],[f774]) ).
thf(f774,plain,
! [X0: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(rectify,[],[f238]) ).
thf(f238,axiom,
! [X8: real] : ( zero_zero_real = vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),vAPP(real,real,uminus_uminus_real,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add_Oright__inverse) ).
thf(f2100,plain,
spl8_30,
inference(avatar_split_clause,[],[f1174,f2098]) ).
thf(f1174,plain,
! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X0) ),
inference(cnf_transformation,[],[f773]) ).
thf(f773,plain,
! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X0)),X0) ),
inference(rectify,[],[f235]) ).
thf(f235,axiom,
! [X8: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,vAPP(a,a,uminus_uminus_a,X8)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add_Oleft__inverse) ).
thf(f2096,plain,
spl8_29,
inference(avatar_split_clause,[],[f1173,f2094]) ).
thf(f1173,plain,
! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(cnf_transformation,[],[f772]) ).
thf(f772,plain,
! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),vAPP(a,a,uminus_uminus_a,X0)) ),
inference(rectify,[],[f237]) ).
thf(f237,axiom,
! [X8: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),vAPP(a,a,uminus_uminus_a,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_add_Oright__inverse) ).
thf(f2092,plain,
spl8_28,
inference(avatar_split_clause,[],[f1841,f2090]) ).
thf(f2090,plain,
( spl8_28
<=> ! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(real,real,uminus_uminus_real,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
thf(f1841,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( zero_zero_real != vAPP(real,real,uminus_uminus_real,X0) ) ),
inference(equality_proxy_clausification,[],[f1840]) ).
thf(f1840,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(equality_proxy_clausification,[],[f1836]) ).
thf(f1836,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1194]) ).
thf(f1194,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(cnf_transformation,[],[f362]) ).
thf(f362,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ),
inference(fool_elimination,[],[f361]) ).
thf(f361,plain,
! [X0: real] :
( ( zero_zero_real = vAPP(real,real,uminus_uminus_real,X0) )
= ( zero_zero_real = X0 ) ),
inference(rectify,[],[f102]) ).
thf(f102,axiom,
! [X8: real] :
( ( zero_zero_real = vAPP(real,real,uminus_uminus_real,X8) )
= ( zero_zero_real = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_neg__0__equal__iff__equal) ).
thf(f2084,plain,
spl8_27,
inference(avatar_split_clause,[],[f1839,f2082]) ).
thf(f2082,plain,
( spl8_27
<=> ! [X0: real] :
( ( zero_zero_real != X0 )
| ( zero_zero_real = vAPP(real,real,uminus_uminus_real,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
thf(f1839,plain,
! [X0: real] :
( ( zero_zero_real != X0 )
| ( zero_zero_real = vAPP(real,real,uminus_uminus_real,X0) ) ),
inference(equality_proxy_clausification,[],[f1838]) ).
thf(f1838,plain,
! [X0: real] :
( ( zero_zero_real != X0 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(equality_proxy_clausification,[],[f1837]) ).
thf(f1837,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),vAPP(real,real,uminus_uminus_real,X0)) ) ),
inference(binary_proxy_clausification,[],[f1194]) ).
thf(f2080,plain,
spl8_26,
inference(avatar_split_clause,[],[f1492,f2077]) ).
thf(f1492,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),tt) = $true,
inference(cnf_transformation,[],[f738]) ).
thf(f738,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),tt) = $true,
inference(fool_elimination,[],[f737]) ).
thf(f737,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),tt),
inference(rectify,[],[f115]) ).
thf(f115,axiom,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),tt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_tt_I1_J) ).
thf(f2075,plain,
spl8_25,
inference(avatar_split_clause,[],[f1491,f2072]) ).
thf(f1491,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),d) = $true,
inference(cnf_transformation,[],[f736]) ).
thf(f736,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),d) = $true,
inference(fool_elimination,[],[f735]) ).
thf(f735,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),d),
inference(rectify,[],[f159]) ).
thf(f159,axiom,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_d) ).
thf(f2070,plain,
spl8_24,
inference(avatar_split_clause,[],[f1490,f2067]) ).
thf(f1490,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),i1) = $true,
inference(cnf_transformation,[],[f734]) ).
thf(f734,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),i1) = $true,
inference(fool_elimination,[],[f733]) ).
thf(f733,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),i1),
inference(rectify,[],[f154]) ).
thf(f154,axiom,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,zero_zero_real),i1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_i2_I2_J) ).
thf(f2065,plain,
spl8_23,
inference(avatar_split_clause,[],[f1489,f2062]) ).
thf(f1489,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,tt),d) = $true,
inference(cnf_transformation,[],[f732]) ).
thf(f732,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,tt),d) = $true,
inference(fool_elimination,[],[f731]) ).
thf(f731,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,tt),d),
inference(rectify,[],[f214]) ).
thf(f214,axiom,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,tt),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_tt_I2_J) ).
thf(f2060,plain,
spl8_22,
inference(avatar_split_clause,[],[f1488,f2057]) ).
thf(f1488,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,i1),i2) = $true,
inference(cnf_transformation,[],[f730]) ).
thf(f730,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,i1),i2) = $true,
inference(fool_elimination,[],[f729]) ).
thf(f729,plain,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,i1),i2),
inference(rectify,[],[f163]) ).
thf(f163,axiom,
vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,i1),i2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_i2_I3_J) ).
thf(f2055,plain,
spl8_21,
inference(avatar_split_clause,[],[f1487,f2052]) ).
thf(f1487,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,xx),x) = $true,
inference(cnf_transformation,[],[f728]) ).
thf(f728,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,xx),x) = $true,
inference(fool_elimination,[],[f727]) ).
thf(f727,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,xx),x),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,xx),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062xx_A_092_060in_062_AX_092_060close_062) ).
thf(f2050,plain,
spl8_20,
inference(avatar_split_clause,[],[f1251,f2048]) ).
thf(f1251,plain,
! [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) ),
inference(cnf_transformation,[],[f793]) ).
thf(f793,plain,
! [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) ),
inference(flattening,[],[f464]) ).
thf(f464,plain,
! [X0: a] : ( $true != vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0) ),
inference(fool_elimination,[],[f463]) ).
thf(f463,plain,
! [X0: a] : ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X0),X0),
inference(rectify,[],[f297]) ).
thf(f297,axiom,
! [X8: a] : ~ vAPP(a,$o,vAPP(a,sTfun(a,$o),ord_less_a,X8),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_verit__comp__simplify1_I1_J) ).
thf(f2046,plain,
spl8_19,
inference(avatar_split_clause,[],[f1250,f2044]) ).
thf(f1250,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) ),
inference(cnf_transformation,[],[f792]) ).
thf(f792,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) ),
inference(flattening,[],[f462]) ).
thf(f462,plain,
! [X0: real] : ( $true != vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0) ),
inference(fool_elimination,[],[f461]) ).
thf(f461,plain,
! [X0: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X0),X0),
inference(rectify,[],[f298]) ).
thf(f298,axiom,
! [X8: real] : ~ vAPP(real,$o,vAPP(real,sTfun(real,$o),ord_less_real,X8),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_verit__comp__simplify1_I1_J) ).
thf(f2042,plain,
spl8_18,
inference(avatar_split_clause,[],[f1170,f2040]) ).
thf(f1170,plain,
! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),zero_zero_a) = X0 ),
inference(cnf_transformation,[],[f769]) ).
thf(f769,plain,
! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X0),zero_zero_a) = X0 ),
inference(rectify,[],[f303]) ).
thf(f303,axiom,
! [X8: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,X8),zero_zero_a) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_add_Ocomm__neutral) ).
thf(f2038,plain,
spl8_17,
inference(avatar_split_clause,[],[f1168,f2036]) ).
thf(f1168,plain,
! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),zero_zero_a) = X0 ),
inference(cnf_transformation,[],[f767]) ).
thf(f767,plain,
! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),zero_zero_a) = X0 ),
inference(rectify,[],[f107]) ).
thf(f107,axiom,
! [X8: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),zero_zero_a) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_diff__0__right) ).
thf(f2034,plain,
spl8_16,
inference(avatar_split_clause,[],[f1829,f2032]) ).
thf(f2032,plain,
( spl8_16
<=> ! [X0: real] :
( ( zero_zero_real = X0 )
| ( vAPP(real,real,uminus_uminus_real,X0) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
thf(f1829,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( vAPP(real,real,uminus_uminus_real,X0) != X0 ) ),
inference(equality_proxy_clausification,[],[f1828]) ).
thf(f1828,plain,
! [X0: real] :
( ( zero_zero_real = X0 )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X0) ) ),
inference(equality_proxy_clausification,[],[f1824]) ).
thf(f1824,plain,
! [X0: real] :
( ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) )
| ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X0) ) ),
inference(binary_proxy_clausification,[],[f1196]) ).
thf(f1196,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X0) ),
inference(cnf_transformation,[],[f366]) ).
thf(f366,plain,
! [X0: real] : ( vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X0) ),
inference(fool_elimination,[],[f365]) ).
thf(f365,plain,
! [X0: real] :
( ( vAPP(real,real,uminus_uminus_real,X0) = X0 )
= ( zero_zero_real = X0 ) ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X8: real] :
( ( vAPP(real,real,uminus_uminus_real,X8) = X8 )
= ( zero_zero_real = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_equal__neg__zero) ).
thf(f2030,plain,
spl8_15,
inference(avatar_split_clause,[],[f1165,f2028]) ).
thf(f1165,plain,
! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,zero_zero_a),X0) = X0 ),
inference(cnf_transformation,[],[f764]) ).
thf(f764,plain,
! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,zero_zero_a),X0) = X0 ),
inference(rectify,[],[f305]) ).
thf(f305,axiom,
! [X8: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),plus_plus_a,zero_zero_a),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_add_Ogroup__left__neutral) ).
thf(f2026,plain,
spl8_14,
inference(avatar_split_clause,[],[f1163,f2024]) ).
thf(f1163,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real) = X0 ),
inference(cnf_transformation,[],[f762]) ).
thf(f762,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X0),zero_zero_real) = X0 ),
inference(rectify,[],[f110]) ).
thf(f110,axiom,
! [X8: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,X8),zero_zero_real) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_diff__zero) ).
thf(f2022,plain,
spl8_13,
inference(avatar_split_clause,[],[f1160,f2020]) ).
thf(f1160,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real) = X0 ),
inference(cnf_transformation,[],[f759]) ).
thf(f759,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X0),zero_zero_real) = X0 ),
inference(rectify,[],[f176]) ).
thf(f176,axiom,
! [X8: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,X8),zero_zero_real) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add_Oright__neutral) ).
thf(f2018,plain,
spl8_12,
inference(avatar_split_clause,[],[f1157,f2016]) ).
thf(f1157,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0) = X0 ),
inference(cnf_transformation,[],[f756]) ).
thf(f756,plain,
! [X0: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X0) = X0 ),
inference(rectify,[],[f174]) ).
thf(f174,axiom,
! [X8: real] : ( vAPP(real,real,vAPP(real,sTfun(real,real),plus_plus_real,zero_zero_real),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_add_Oleft__neutral) ).
thf(f2014,plain,
spl8_11,
inference(avatar_split_clause,[],[f1155,f2012]) ).
thf(f2010,plain,
spl8_10,
inference(avatar_split_clause,[],[f1153,f2008]) ).
thf(f2008,plain,
( spl8_10
<=> ! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
thf(f1153,plain,
! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X0) ),
inference(cnf_transformation,[],[f752]) ).
thf(f752,plain,
! [X0: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X0),X0) ),
inference(rectify,[],[f111]) ).
thf(f111,axiom,
! [X8: a] : ( zero_zero_a = vAPP(a,a,vAPP(a,sTfun(a,a),minus_minus_a,X8),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(f2004,plain,
spl8_9,
inference(avatar_split_clause,[],[f1151,f2002]) ).
thf(f1151,plain,
! [X0: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,uminus_uminus_a,X0)) = X0 ),
inference(cnf_transformation,[],[f750]) ).
thf(f750,plain,
! [X0: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,uminus_uminus_a,X0)) = X0 ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
! [X8: a] : ( vAPP(a,a,uminus_uminus_a,vAPP(a,a,uminus_uminus_a,X8)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add_Oinverse__inverse) ).
thf(f2000,plain,
spl8_8,
inference(avatar_split_clause,[],[f1149,f1998]) ).
thf(f1149,plain,
! [X0: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,uminus_uminus_real,X0)) = X0 ),
inference(cnf_transformation,[],[f748]) ).
thf(f748,plain,
! [X0: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,uminus_uminus_real,X0)) = X0 ),
inference(rectify,[],[f45]) ).
thf(f45,axiom,
! [X9: real] : ( vAPP(real,real,uminus_uminus_real,vAPP(real,real,uminus_uminus_real,X9)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_verit__minus__simplify_I4_J) ).
thf(f1996,plain,
spl8_7,
inference(avatar_split_clause,[],[f1827,f1994]) ).
thf(f1994,plain,
( spl8_7
<=> ! [X0: real] :
( ( zero_zero_real != X0 )
| ( vAPP(real,real,uminus_uminus_real,X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
thf(f1827,plain,
! [X0: real] :
( ( zero_zero_real != X0 )
| ( vAPP(real,real,uminus_uminus_real,X0) = X0 ) ),
inference(equality_proxy_clausification,[],[f1826]) ).
thf(f1826,plain,
! [X0: real] :
( ( zero_zero_real != X0 )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X0) ) ),
inference(equality_proxy_clausification,[],[f1825]) ).
thf(f1825,plain,
! [X0: real] :
( ( $false = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),zero_zero_real),X0) )
| ( $true = vAPP(real,$o,vAPP(real,sTfun(real,$o),vEQ(real),vAPP(real,real,uminus_uminus_real,X0)),X0) ) ),
inference(binary_proxy_clausification,[],[f1196]) ).
thf(f1992,plain,
~ spl8_6,
inference(avatar_split_clause,[],[f1140,f1989]) ).
thf(f1140,plain,
xx != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),
inference(cnf_transformation,[],[f747]) ).
thf(f747,plain,
xx != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),
inference(flattening,[],[f344]) ).
thf(f344,negated_conjecture,
xx != vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),
inference(negated_conjecture,[],[f343]) ).
thf(f343,conjecture,
xx = vAPP(real,a,vAPP(a,sTfun(real,a),vAPP(set_a,sTfun(a,sTfun(real,a)),vAPP(sTfun(a,a),sTfun(set_a,sTfun(a,sTfun(real,a))),auto_ll_on_flow0_a,f),x),x2),vAPP(real,real,vAPP(real,sTfun(real,real),minus_minus_real,ss),tt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f1987,plain,
spl8_5,
inference(avatar_split_clause,[],[f1486,f1984]) ).
thf(f1984,plain,
( spl8_5
<=> ( vAPP(set_real,$o,initia826609931terval,top_top_set_real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
thf(f1486,plain,
vAPP(set_real,$o,initia826609931terval,top_top_set_real) = $true,
inference(cnf_transformation,[],[f726]) ).
thf(f726,plain,
vAPP(set_real,$o,initia826609931terval,top_top_set_real) = $true,
inference(fool_elimination,[],[f725]) ).
thf(f725,plain,
vAPP(set_real,$o,initia826609931terval,top_top_set_real),
inference(rectify,[],[f37]) ).
thf(f37,axiom,
vAPP(set_real,$o,initia826609931terval,top_top_set_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_interval__axioms) ).
thf(f1982,plain,
spl8_4,
inference(avatar_split_clause,[],[f1142,f1979]) ).
thf(f1142,plain,
zero_zero_real = vAPP(real,real,uminus_uminus_real,zero_zero_real),
inference(cnf_transformation,[],[f104]) ).
thf(f104,axiom,
zero_zero_real = vAPP(real,real,uminus_uminus_real,zero_zero_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Oinverse__neutral) ).
thf(f1977,plain,
spl8_3,
inference(avatar_split_clause,[],[f1141,f1974]) ).
thf(f1141,plain,
zero_zero_a = vAPP(a,a,uminus_uminus_a,zero_zero_a),
inference(cnf_transformation,[],[f103]) ).
thf(f103,axiom,
zero_zero_a = vAPP(a,a,uminus_uminus_a,zero_zero_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_add_Oinverse__neutral) ).
thf(f1944,plain,
spl8_2,
inference(avatar_split_clause,[],[f346,f1942]) ).
thf(f346,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1940,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f345,f1937]) ).
thf(f1937,plain,
( spl8_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
thf(f345,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ITP146^1 : TPTP v8.2.0. Released v7.5.0.
% 0.08/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.17/0.38 % Computer : n004.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sat May 18 17:21:08 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.17/0.38 % (24375)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.42 % (24378)WARNING: value z3 for option sas not known
% 0.25/0.42 % (24376)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.25/0.42 % (24380)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)
% 0.25/0.42 % (24379)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.25/0.42 % (24381)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.25/0.42 % (24377)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.25/0.42 % (24378)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)
% 0.25/0.42 % (24382)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)
% 0.25/0.45 % (24382)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.25/0.46 % Exception at run slice level% Exception at run slice level
% 0.25/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.46
% 0.25/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.46 % Exception at run slice level
% 0.25/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.48 % (24383)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.25/0.48 % (24384)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.25/0.48 % (24385)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.25/0.50 % (24384)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.25/0.50 % (24383)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.25/0.51 % Exception at run slice level
% 0.25/0.51 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.53 % (24386)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 3.95/1.01 % (24380)First to succeed.
% 4.65/1.05 % (24380)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24375"
% 4.65/1.05 % (24380)Refutation found. Thanks to Tanya!
% 4.65/1.05 % SZS status Theorem for theBenchmark
% 4.65/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 4.65/1.06 % (24380)------------------------------
% 4.65/1.06 % (24380)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.65/1.06 % (24380)Termination reason: Refutation
% 4.65/1.06
% 4.65/1.06 % (24380)Memory used [KB]: 8556
% 4.65/1.06 % (24380)Time elapsed: 0.627 s
% 4.65/1.06 % (24380)Instructions burned: 2153 (million)
% 4.65/1.06 % (24375)Success in time 0.666 s
%------------------------------------------------------------------------------