TSTP Solution File: GRP343-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP343-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 16:21:22 EDT 2022
% Result : Unsatisfiable 1.52s 0.55s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 48
% Syntax : Number of formulae : 262 ( 15 unt; 0 def)
% Number of atoms : 1234 ( 331 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1973 (1001 ~; 949 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 94 ( 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f747,plain,
$false,
inference(avatar_sat_refutation,[],[f55,f60,f93,f102,f107,f108,f110,f122,f127,f132,f134,f135,f138,f142,f144,f145,f147,f148,f152,f156,f157,f158,f162,f164,f165,f167,f270,f285,f315,f350,f364,f378,f548,f672,f686,f695,f709,f732,f746]) ).
fof(f746,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(avatar_contradiction_clause,[],[f745]) ).
fof(f745,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f744]) ).
fof(f744,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(superposition,[],[f742,f294]) ).
fof(f294,plain,
identity = inverse(identity),
inference(superposition,[],[f187,f289]) ).
fof(f289,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f178,f187]) ).
fof(f178,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
inference(forward_demodulation,[],[f172,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f172,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = multiply(identity,X7),
inference(superposition,[],[f3,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f187,plain,
! [X4] : multiply(inverse(inverse(X4)),identity) = X4,
inference(superposition,[],[f178,f2]) ).
fof(f742,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(forward_demodulation,[],[f741,f294]) ).
fof(f741,plain,
( identity != inverse(inverse(identity))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f739]) ).
fof(f739,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(superposition,[],[f735,f2]) ).
fof(f735,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(forward_demodulation,[],[f734,f598]) ).
fof(f598,plain,
( identity = sk_c8
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(backward_demodulation,[],[f425,f521]) ).
fof(f521,plain,
( identity = sk_c9
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18 ),
inference(forward_demodulation,[],[f416,f2]) ).
fof(f416,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c8)
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18 ),
inference(backward_demodulation,[],[f189,f412]) ).
fof(f412,plain,
( sk_c8 = sk_c7
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18 ),
inference(backward_demodulation,[],[f79,f411]) ).
fof(f411,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl4_3
| ~ spl4_18 ),
inference(forward_demodulation,[],[f409,f59]) ).
fof(f59,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f57,plain,
( spl4_3
<=> sk_c8 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f409,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c9)
| ~ spl4_18 ),
inference(superposition,[],[f178,f131]) ).
fof(f131,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| ~ spl4_18 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f129,plain,
( spl4_18
<=> sk_c9 = multiply(sk_c4,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
fof(f79,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f78,plain,
( spl4_8
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f189,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c7)
| ~ spl4_8 ),
inference(superposition,[],[f178,f79]) ).
fof(f425,plain,
( sk_c8 = sk_c9
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(backward_demodulation,[],[f395,f421]) ).
fof(f421,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18 ),
inference(forward_demodulation,[],[f417,f178]) ).
fof(f417,plain,
( ! [X0] : multiply(inverse(sk_c8),multiply(sk_c8,X0)) = multiply(sk_c9,X0)
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18 ),
inference(backward_demodulation,[],[f199,f412]) ).
fof(f199,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c8),multiply(sk_c7,X0))
| ~ spl4_8 ),
inference(superposition,[],[f178,f173]) ).
fof(f173,plain,
( ! [X8] : multiply(sk_c7,X8) = multiply(sk_c8,multiply(sk_c9,X8))
| ~ spl4_8 ),
inference(superposition,[],[f3,f79]) ).
fof(f395,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl4_1
| ~ spl4_12 ),
inference(forward_demodulation,[],[f393,f97]) ).
fof(f97,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f95,plain,
( spl4_12
<=> sk_c9 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
fof(f393,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl4_1 ),
inference(superposition,[],[f178,f50]) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl4_1
<=> sk_c8 = multiply(sk_c3,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f734,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| sk_c8 != inverse(X6) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(forward_demodulation,[],[f733,f521]) ).
fof(f733,plain,
( ! [X6] :
( sk_c9 != multiply(X6,identity)
| sk_c8 != inverse(X6) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_21 ),
inference(forward_demodulation,[],[f155,f598]) ).
fof(f155,plain,
( ! [X6] :
( sk_c9 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6) )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f154,plain,
( spl4_21
<=> ! [X6] :
( sk_c9 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
fof(f732,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(avatar_contradiction_clause,[],[f731]) ).
fof(f731,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(trivial_inequality_removal,[],[f730]) ).
fof(f730,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(superposition,[],[f727,f294]) ).
fof(f727,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(trivial_inequality_removal,[],[f723]) ).
fof(f723,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(superposition,[],[f712,f1]) ).
fof(f712,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(forward_demodulation,[],[f711,f598]) ).
fof(f711,plain,
( ! [X5] :
( identity != inverse(X5)
| sk_c8 != multiply(X5,identity) )
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_18 ),
inference(forward_demodulation,[],[f710,f521]) ).
fof(f710,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c9)
| identity != inverse(X5) )
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8
| ~ spl4_18 ),
inference(forward_demodulation,[],[f72,f521]) ).
fof(f72,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c8 != multiply(X5,sk_c9) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f71,plain,
( spl4_6
<=> ! [X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f709,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(avatar_contradiction_clause,[],[f708]) ).
fof(f708,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f707]) ).
fof(f707,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(superposition,[],[f705,f294]) ).
fof(f705,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(forward_demodulation,[],[f704,f294]) ).
fof(f704,plain,
( identity != inverse(inverse(identity))
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f702]) ).
fof(f702,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(superposition,[],[f698,f2]) ).
fof(f698,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(forward_demodulation,[],[f697,f521]) ).
fof(f697,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c9 != inverse(X3) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(forward_demodulation,[],[f696,f521]) ).
fof(f696,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c9 != inverse(X3) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_22 ),
inference(forward_demodulation,[],[f161,f598]) ).
fof(f161,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3) )
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f160,plain,
( spl4_22
<=> ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
fof(f695,plain,
( ~ spl4_3
| ~ spl4_8
| ~ spl4_18
| ~ spl4_19 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f694,plain,
( $false
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18
| ~ spl4_19 ),
inference(trivial_inequality_removal,[],[f693]) ).
fof(f693,plain,
( identity != identity
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18
| ~ spl4_19 ),
inference(duplicate_literal_removal,[],[f691]) ).
fof(f691,plain,
( identity != identity
| identity != identity
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18
| ~ spl4_19 ),
inference(superposition,[],[f690,f294]) ).
fof(f690,plain,
( ! [X7] :
( inverse(X7) != X7
| identity != X7 )
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18
| ~ spl4_19 ),
inference(forward_demodulation,[],[f689,f303]) ).
fof(f303,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f187,f188]) ).
fof(f188,plain,
! [X6,X5] : multiply(X5,X6) = multiply(inverse(inverse(X5)),X6),
inference(superposition,[],[f178,f178]) ).
fof(f689,plain,
( ! [X7] :
( identity != X7
| inverse(X7) != multiply(X7,identity) )
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18
| ~ spl4_19 ),
inference(forward_demodulation,[],[f688,f521]) ).
fof(f688,plain,
( ! [X7] :
( sk_c9 != X7
| inverse(X7) != multiply(X7,identity) )
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18
| ~ spl4_19 ),
inference(forward_demodulation,[],[f687,f331]) ).
fof(f331,plain,
! [X6] : inverse(inverse(X6)) = X6,
inference(forward_demodulation,[],[f330,f303]) ).
fof(f330,plain,
! [X6] : multiply(X6,identity) = inverse(inverse(X6)),
inference(superposition,[],[f188,f303]) ).
fof(f687,plain,
( ! [X7] :
( sk_c9 != inverse(inverse(X7))
| inverse(X7) != multiply(X7,identity) )
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18
| ~ spl4_19 ),
inference(forward_demodulation,[],[f141,f521]) ).
fof(f141,plain,
( ! [X7] :
( inverse(X7) != multiply(X7,sk_c9)
| sk_c9 != inverse(inverse(X7)) )
| ~ spl4_19 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl4_19
<=> ! [X7] :
( sk_c9 != inverse(inverse(X7))
| inverse(X7) != multiply(X7,sk_c9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
fof(f686,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_20 ),
inference(avatar_contradiction_clause,[],[f685]) ).
fof(f685,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f684]) ).
fof(f684,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_20 ),
inference(superposition,[],[f681,f294]) ).
fof(f681,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f677]) ).
fof(f677,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_20 ),
inference(superposition,[],[f620,f1]) ).
fof(f620,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_20 ),
inference(forward_demodulation,[],[f619,f598]) ).
fof(f619,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c8 != multiply(X4,identity) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_20 ),
inference(forward_demodulation,[],[f618,f601]) ).
fof(f601,plain,
( identity = sk_c7
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(backward_demodulation,[],[f412,f598]) ).
fof(f618,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c8 != multiply(X4,sk_c7) )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18
| ~ spl4_20 ),
inference(forward_demodulation,[],[f151,f598]) ).
fof(f151,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c7) )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f150,plain,
( spl4_20
<=> ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
fof(f672,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_14
| ~ spl4_18 ),
inference(avatar_contradiction_clause,[],[f671]) ).
fof(f671,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_14
| ~ spl4_18 ),
inference(trivial_inequality_removal,[],[f670]) ).
fof(f670,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_14
| ~ spl4_18 ),
inference(superposition,[],[f664,f294]) ).
fof(f664,plain,
( identity != inverse(identity)
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_14
| ~ spl4_18 ),
inference(backward_demodulation,[],[f612,f663]) ).
fof(f663,plain,
( identity = sk_c1
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(superposition,[],[f303,f593]) ).
fof(f593,plain,
( ! [X9] : multiply(sk_c1,X9) = X9
| ~ spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(backward_demodulation,[],[f424,f444]) ).
fof(f444,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_18 ),
inference(backward_demodulation,[],[f421,f425]) ).
fof(f424,plain,
( ! [X9] : multiply(sk_c1,multiply(sk_c8,X9)) = X9
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_18 ),
inference(backward_demodulation,[],[f174,f421]) ).
fof(f174,plain,
( ! [X9] : multiply(sk_c9,X9) = multiply(sk_c1,multiply(sk_c8,X9))
| ~ spl4_2 ),
inference(superposition,[],[f3,f54]) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f52,plain,
( spl4_2
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f612,plain,
( identity != inverse(sk_c1)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_14
| ~ spl4_18 ),
inference(backward_demodulation,[],[f589,f598]) ).
fof(f589,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_14
| ~ spl4_18 ),
inference(backward_demodulation,[],[f105,f425]) ).
fof(f105,plain,
( sk_c9 != inverse(sk_c1)
| spl4_14 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f104,plain,
( spl4_14
<=> sk_c9 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f548,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_18 ),
inference(avatar_contradiction_clause,[],[f547]) ).
fof(f547,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_18 ),
inference(trivial_inequality_removal,[],[f544]) ).
fof(f544,plain,
( identity != identity
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_18 ),
inference(superposition,[],[f468,f303]) ).
fof(f468,plain,
( identity != multiply(identity,identity)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_18 ),
inference(backward_demodulation,[],[f455,f465]) ).
fof(f465,plain,
( identity = sk_c2
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_14
| ~ spl4_17
| ~ spl4_18 ),
inference(forward_demodulation,[],[f451,f2]) ).
fof(f451,plain,
( sk_c2 = multiply(inverse(identity),identity)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_14
| ~ spl4_17
| ~ spl4_18 ),
inference(backward_demodulation,[],[f190,f446]) ).
fof(f446,plain,
( identity = sk_c8
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_14
| ~ spl4_18 ),
inference(backward_demodulation,[],[f418,f434]) ).
fof(f434,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| ~ spl4_14
| ~ spl4_18 ),
inference(backward_demodulation,[],[f168,f425]) ).
fof(f168,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl4_14 ),
inference(superposition,[],[f2,f106]) ).
fof(f106,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f418,plain,
( sk_c8 = multiply(sk_c8,sk_c1)
| ~ spl4_3
| ~ spl4_8
| ~ spl4_14
| ~ spl4_18 ),
inference(backward_demodulation,[],[f379,f412]) ).
fof(f379,plain,
( sk_c8 = multiply(sk_c7,sk_c1)
| ~ spl4_8
| ~ spl4_14 ),
inference(forward_demodulation,[],[f198,f303]) ).
fof(f198,plain,
( multiply(sk_c8,identity) = multiply(sk_c7,sk_c1)
| ~ spl4_8
| ~ spl4_14 ),
inference(superposition,[],[f173,f168]) ).
fof(f190,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl4_17 ),
inference(superposition,[],[f178,f169]) ).
fof(f169,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl4_17 ),
inference(superposition,[],[f2,f126]) ).
fof(f126,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f124,plain,
( spl4_17
<=> sk_c8 = inverse(sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
fof(f455,plain,
( identity != multiply(sk_c2,identity)
| ~ spl4_1
| ~ spl4_3
| ~ spl4_8
| ~ spl4_12
| spl4_13
| ~ spl4_14
| ~ spl4_18 ),
inference(backward_demodulation,[],[f414,f446]) ).
fof(f414,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl4_3
| ~ spl4_8
| spl4_13
| ~ spl4_18 ),
inference(backward_demodulation,[],[f100,f412]) ).
fof(f100,plain,
( sk_c8 != multiply(sk_c2,sk_c7)
| spl4_13 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f99,plain,
( spl4_13
<=> sk_c8 = multiply(sk_c2,sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
fof(f378,plain,
( ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f377,plain,
( $false
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f376]) ).
fof(f376,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(superposition,[],[f375,f240]) ).
fof(f240,plain,
( identity = inverse(identity)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f232,f238]) ).
fof(f238,plain,
( identity = sk_c1
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(forward_demodulation,[],[f233,f2]) ).
fof(f233,plain,
( sk_c1 = multiply(inverse(identity),identity)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f214,f229]) ).
fof(f229,plain,
( identity = sk_c8
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(forward_demodulation,[],[f225,f2]) ).
fof(f225,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f203,f223]) ).
fof(f223,plain,
( sk_c8 = sk_c7
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f196,f215]) ).
fof(f215,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f197,f205]) ).
fof(f205,plain,
( sk_c8 = sk_c9
| ~ spl4_8
| ~ spl4_13
| ~ spl4_17 ),
inference(backward_demodulation,[],[f189,f203]) ).
fof(f197,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl4_2
| ~ spl4_14 ),
inference(forward_demodulation,[],[f192,f106]) ).
fof(f192,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c9)
| ~ spl4_2 ),
inference(superposition,[],[f178,f54]) ).
fof(f196,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl4_13
| ~ spl4_17 ),
inference(forward_demodulation,[],[f193,f126]) ).
fof(f193,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c8)
| ~ spl4_13 ),
inference(superposition,[],[f178,f101]) ).
fof(f101,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f203,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c7)
| ~ spl4_13
| ~ spl4_17 ),
inference(superposition,[],[f178,f196]) ).
fof(f214,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f191,f205]) ).
fof(f191,plain,
( sk_c1 = multiply(inverse(sk_c9),identity)
| ~ spl4_14 ),
inference(superposition,[],[f178,f168]) ).
fof(f232,plain,
( identity = inverse(sk_c1)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f209,f229]) ).
fof(f209,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f106,f205]) ).
fof(f375,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(forward_demodulation,[],[f373,f240]) ).
fof(f373,plain,
( identity != inverse(inverse(identity))
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f371]) ).
fof(f371,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(superposition,[],[f367,f2]) ).
fof(f367,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(forward_demodulation,[],[f366,f230]) ).
fof(f230,plain,
( identity = sk_c9
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f205,f229]) ).
fof(f366,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(forward_demodulation,[],[f365,f229]) ).
fof(f365,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c8)
| identity != inverse(X3) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_22 ),
inference(forward_demodulation,[],[f161,f230]) ).
fof(f364,plain,
( ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(avatar_contradiction_clause,[],[f363]) ).
fof(f363,plain,
( $false
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f362]) ).
fof(f362,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(superposition,[],[f360,f240]) ).
fof(f360,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(forward_demodulation,[],[f359,f240]) ).
fof(f359,plain,
( identity != inverse(inverse(identity))
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(trivial_inequality_removal,[],[f357]) ).
fof(f357,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(superposition,[],[f353,f2]) ).
fof(f353,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(forward_demodulation,[],[f352,f230]) ).
fof(f352,plain,
( ! [X6] :
( identity != inverse(X6)
| sk_c9 != multiply(X6,identity) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(forward_demodulation,[],[f351,f229]) ).
fof(f351,plain,
( ! [X6] :
( sk_c8 != inverse(X6)
| sk_c9 != multiply(X6,identity) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_21 ),
inference(forward_demodulation,[],[f155,f229]) ).
fof(f350,plain,
( ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_20 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f349,plain,
( $false
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f348]) ).
fof(f348,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_20 ),
inference(superposition,[],[f345,f240]) ).
fof(f345,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f341]) ).
fof(f341,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_20 ),
inference(superposition,[],[f318,f1]) ).
fof(f318,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_20 ),
inference(forward_demodulation,[],[f317,f229]) ).
fof(f317,plain,
( ! [X4] :
( sk_c8 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_20 ),
inference(forward_demodulation,[],[f316,f237]) ).
fof(f237,plain,
( identity = sk_c7
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(backward_demodulation,[],[f223,f229]) ).
fof(f316,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c8 != multiply(X4,sk_c7) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_20 ),
inference(forward_demodulation,[],[f151,f229]) ).
fof(f315,plain,
( ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_19 ),
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f314,plain,
( $false
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_19 ),
inference(trivial_inequality_removal,[],[f313]) ).
fof(f313,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_19 ),
inference(superposition,[],[f312,f240]) ).
fof(f312,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_19 ),
inference(trivial_inequality_removal,[],[f311]) ).
fof(f311,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_19 ),
inference(superposition,[],[f310,f240]) ).
fof(f310,plain,
( ! [X7] :
( identity != inverse(inverse(X7))
| inverse(X7) != X7 )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_19 ),
inference(backward_demodulation,[],[f287,f303]) ).
fof(f287,plain,
( ! [X7] :
( identity != inverse(inverse(X7))
| inverse(X7) != multiply(X7,identity) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_19 ),
inference(forward_demodulation,[],[f286,f230]) ).
fof(f286,plain,
( ! [X7] :
( sk_c9 != inverse(inverse(X7))
| inverse(X7) != multiply(X7,identity) )
| ~ spl4_2
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17
| ~ spl4_19 ),
inference(forward_demodulation,[],[f141,f230]) ).
fof(f285,plain,
( ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(avatar_contradiction_clause,[],[f284]) ).
fof(f284,plain,
( $false
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(trivial_inequality_removal,[],[f283]) ).
fof(f283,plain,
( identity != identity
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(superposition,[],[f282,f240]) ).
fof(f282,plain,
( identity != inverse(identity)
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(forward_demodulation,[],[f281,f240]) ).
fof(f281,plain,
( identity != inverse(inverse(identity))
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(trivial_inequality_removal,[],[f279]) ).
fof(f279,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(superposition,[],[f276,f2]) ).
fof(f276,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(forward_demodulation,[],[f275,f229]) ).
fof(f275,plain,
( ! [X5] :
( identity != inverse(X5)
| sk_c8 != multiply(X5,identity) )
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(forward_demodulation,[],[f274,f230]) ).
fof(f274,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c8 != multiply(X5,identity) )
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(forward_demodulation,[],[f72,f230]) ).
fof(f270,plain,
( ~ spl4_2
| spl4_5
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(avatar_contradiction_clause,[],[f269]) ).
fof(f269,plain,
( $false
| ~ spl4_2
| spl4_5
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(trivial_inequality_removal,[],[f268]) ).
fof(f268,plain,
( identity != identity
| ~ spl4_2
| spl4_5
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(superposition,[],[f261,f1]) ).
fof(f261,plain,
( identity != multiply(identity,identity)
| ~ spl4_2
| spl4_5
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(forward_demodulation,[],[f260,f229]) ).
fof(f260,plain,
( sk_c8 != multiply(sk_c8,identity)
| ~ spl4_2
| spl4_5
| ~ spl4_8
| ~ spl4_13
| ~ spl4_14
| ~ spl4_17 ),
inference(forward_demodulation,[],[f207,f237]) ).
fof(f207,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| spl4_5
| ~ spl4_8
| ~ spl4_13
| ~ spl4_17 ),
inference(backward_demodulation,[],[f69,f205]) ).
fof(f69,plain,
( sk_c8 != multiply(sk_c9,sk_c7)
| spl4_5 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl4_5
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f167,plain,
( spl4_3
| spl4_13 ),
inference(avatar_split_clause,[],[f33,f99,f57]) ).
fof(f33,axiom,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f165,plain,
( spl4_17
| spl4_18 ),
inference(avatar_split_clause,[],[f24,f129,f124]) ).
fof(f24,axiom,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f164,plain,
( spl4_18
| spl4_2 ),
inference(avatar_split_clause,[],[f16,f52,f129]) ).
fof(f16,axiom,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f162,plain,
( spl4_9
| spl4_22 ),
inference(avatar_split_clause,[],[f39,f160,f82]) ).
fof(f82,plain,
( spl4_9
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f39,plain,
! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sP0 ),
inference(cnf_transformation,[],[f39_D]) ).
fof(f39_D,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8) )
<=> ~ sP0 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f158,plain,
( spl4_5
| spl4_13 ),
inference(avatar_split_clause,[],[f31,f99,f67]) ).
fof(f31,axiom,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c8 = multiply(sk_c9,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f157,plain,
( spl4_17
| spl4_12 ),
inference(avatar_split_clause,[],[f22,f95,f124]) ).
fof(f22,axiom,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f156,plain,
( spl4_11
| spl4_21 ),
inference(avatar_split_clause,[],[f41,f154,f90]) ).
fof(f90,plain,
( spl4_11
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f41,plain,
! [X6] :
( sk_c9 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6)
| sP1 ),
inference(cnf_transformation,[],[f41_D]) ).
fof(f41_D,plain,
( ! [X6] :
( sk_c9 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6) )
<=> ~ sP1 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f152,plain,
( spl4_20
| spl4_7 ),
inference(avatar_split_clause,[],[f45,f74,f150]) ).
fof(f74,plain,
( spl4_7
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f45,plain,
! [X4] :
( sP3
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c7) ),
inference(cnf_transformation,[],[f45_D]) ).
fof(f45_D,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c7) )
<=> ~ sP3 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f148,plain,
( spl4_3
| spl4_17 ),
inference(avatar_split_clause,[],[f25,f124,f57]) ).
fof(f25,axiom,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f147,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f15,f52,f67]) ).
fof(f15,axiom,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f145,plain,
( spl4_3
| spl4_14 ),
inference(avatar_split_clause,[],[f9,f104,f57]) ).
fof(f9,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f144,plain,
( spl4_1
| spl4_14 ),
inference(avatar_split_clause,[],[f5,f104,f48]) ).
fof(f5,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c3,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f142,plain,
( spl4_10
| spl4_19 ),
inference(avatar_split_clause,[],[f43,f140,f86]) ).
fof(f86,plain,
( spl4_10
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f43,plain,
! [X7] :
( sk_c9 != inverse(inverse(X7))
| inverse(X7) != multiply(X7,sk_c9)
| sP2 ),
inference(cnf_transformation,[],[f43_D]) ).
fof(f43_D,plain,
( ! [X7] :
( sk_c9 != inverse(inverse(X7))
| inverse(X7) != multiply(X7,sk_c9) )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f138,plain,
( spl4_18
| spl4_14 ),
inference(avatar_split_clause,[],[f8,f104,f129]) ).
fof(f8,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f135,plain,
spl4_8,
inference(avatar_split_clause,[],[f4,f78]) ).
fof(f4,axiom,
multiply(sk_c8,sk_c9) = sk_c7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f134,plain,
( spl4_5
| spl4_17 ),
inference(avatar_split_clause,[],[f23,f124,f67]) ).
fof(f23,axiom,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f132,plain,
( spl4_18
| spl4_13 ),
inference(avatar_split_clause,[],[f32,f99,f129]) ).
fof(f32,axiom,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c9 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f127,plain,
( spl4_17
| spl4_1 ),
inference(avatar_split_clause,[],[f21,f48,f124]) ).
fof(f21,axiom,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f122,plain,
( spl4_12
| spl4_14 ),
inference(avatar_split_clause,[],[f6,f104,f95]) ).
fof(f6,axiom,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f110,plain,
( spl4_13
| spl4_1 ),
inference(avatar_split_clause,[],[f29,f48,f99]) ).
fof(f29,axiom,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = multiply(sk_c2,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f108,plain,
( spl4_12
| spl4_2 ),
inference(avatar_split_clause,[],[f14,f52,f95]) ).
fof(f14,axiom,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f107,plain,
( spl4_14
| spl4_5 ),
inference(avatar_split_clause,[],[f7,f67,f104]) ).
fof(f7,axiom,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f102,plain,
( spl4_12
| spl4_13 ),
inference(avatar_split_clause,[],[f30,f99,f95]) ).
fof(f30,axiom,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c9 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f93,plain,
( ~ spl4_5
| spl4_6
| ~ spl4_7
| ~ spl4_8
| ~ spl4_9
| ~ spl4_10
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f46,f90,f86,f82,f78,f74,f71,f67]) ).
fof(f46,plain,
! [X5] :
( ~ sP1
| ~ sP2
| ~ sP0
| multiply(sk_c8,sk_c9) != sk_c7
| ~ sP3
| sk_c8 != multiply(X5,sk_c9)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X5) ),
inference(general_splitting,[],[f44,f45_D]) ).
fof(f44,plain,
! [X4,X5] :
( sk_c9 != inverse(X5)
| sk_c8 != multiply(sk_c9,sk_c7)
| multiply(sk_c8,sk_c9) != sk_c7
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X5,sk_c9)
| sk_c8 != multiply(X4,sk_c7)
| ~ sP0
| ~ sP1
| ~ sP2 ),
inference(general_splitting,[],[f42,f43_D]) ).
fof(f42,plain,
! [X7,X4,X5] :
( sk_c9 != inverse(inverse(X7))
| sk_c9 != inverse(X5)
| sk_c8 != multiply(sk_c9,sk_c7)
| multiply(sk_c8,sk_c9) != sk_c7
| inverse(X7) != multiply(X7,sk_c9)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X5,sk_c9)
| sk_c8 != multiply(X4,sk_c7)
| ~ sP0
| ~ sP1 ),
inference(general_splitting,[],[f40,f41_D]) ).
fof(f40,plain,
! [X6,X7,X4,X5] :
( sk_c9 != inverse(inverse(X7))
| sk_c9 != inverse(X5)
| sk_c8 != multiply(sk_c9,sk_c7)
| multiply(sk_c8,sk_c9) != sk_c7
| inverse(X7) != multiply(X7,sk_c9)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X5,sk_c9)
| sk_c8 != inverse(X6)
| sk_c9 != multiply(X6,sk_c8)
| sk_c8 != multiply(X4,sk_c7)
| ~ sP0 ),
inference(general_splitting,[],[f38,f39_D]) ).
fof(f38,plain,
! [X3,X6,X7,X4,X5] :
( sk_c9 != inverse(inverse(X7))
| sk_c9 != inverse(X5)
| sk_c8 != multiply(sk_c9,sk_c7)
| multiply(sk_c8,sk_c9) != sk_c7
| sk_c9 != multiply(X3,sk_c8)
| inverse(X7) != multiply(X7,sk_c9)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X5,sk_c9)
| sk_c8 != inverse(X6)
| sk_c9 != multiply(X6,sk_c8)
| sk_c8 != multiply(X4,sk_c7)
| sk_c9 != inverse(X3) ),
inference(equality_resolution,[],[f37]) ).
fof(f37,axiom,
! [X3,X8,X6,X7,X4,X5] :
( sk_c9 != inverse(X8)
| inverse(X7) != X8
| sk_c9 != inverse(X5)
| sk_c8 != multiply(sk_c9,sk_c7)
| multiply(sk_c8,sk_c9) != sk_c7
| sk_c9 != multiply(X3,sk_c8)
| multiply(X7,sk_c9) != X8
| sk_c8 != inverse(X4)
| sk_c8 != multiply(X5,sk_c9)
| sk_c8 != inverse(X6)
| sk_c9 != multiply(X6,sk_c8)
| sk_c8 != multiply(X4,sk_c7)
| sk_c9 != inverse(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f60,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f17,f52,f57]) ).
fof(f17,axiom,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f55,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f13,f52,f48]) ).
fof(f13,axiom,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP343-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 22:23:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (23434)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.51 TRYING [1]
% 0.19/0.51 % (23445)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.52 % (23446)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.52 TRYING [2]
% 0.19/0.52 TRYING [3]
% 0.19/0.52 % (23461)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.52 % (23459)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.52 % (23438)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (23455)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.52 % (23444)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52 % (23453)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.52 % (23439)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52 % (23456)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.53 % (23448)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.53 % (23458)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.53 % (23447)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.53 % (23436)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.53 % (23435)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53 % (23452)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53 % (23451)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.54 % (23440)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.54 % (23437)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.52/0.54 % (23462)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.52/0.54 % (23463)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.52/0.54 % (23442)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.52/0.54 % (23460)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.52/0.54 % (23442)Instruction limit reached!
% 1.52/0.54 % (23442)------------------------------
% 1.52/0.54 % (23442)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.54 % (23442)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.54 % (23442)Termination reason: Unknown
% 1.52/0.54 % (23442)Termination phase: Saturation
% 1.52/0.54
% 1.52/0.54 % (23442)Memory used [KB]: 5373
% 1.52/0.54 % (23442)Time elapsed: 0.002 s
% 1.52/0.54 % (23442)Instructions burned: 2 (million)
% 1.52/0.54 % (23442)------------------------------
% 1.52/0.54 % (23442)------------------------------
% 1.52/0.54 % (23441)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.52/0.54 % (23450)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.52/0.54 % (23454)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.52/0.54 % (23449)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.52/0.55 % (23444)First to succeed.
% 1.52/0.55 % (23457)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.52/0.55 % (23443)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.52/0.55 TRYING [4]
% 1.52/0.55 % (23444)Refutation found. Thanks to Tanya!
% 1.52/0.55 % SZS status Unsatisfiable for theBenchmark
% 1.52/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.65/0.55 % (23444)------------------------------
% 1.65/0.55 % (23444)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.55 % (23444)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.55 % (23444)Termination reason: Refutation
% 1.65/0.55
% 1.65/0.55 % (23444)Memory used [KB]: 5756
% 1.65/0.55 % (23444)Time elapsed: 0.158 s
% 1.65/0.55 % (23444)Instructions burned: 20 (million)
% 1.65/0.55 % (23444)------------------------------
% 1.65/0.55 % (23444)------------------------------
% 1.65/0.55 % (23433)Success in time 0.209 s
%------------------------------------------------------------------------------