TSTP Solution File: GRP375-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP375-1 : 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 : n025.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 16:21:28 EDT 2022
% Result : Unsatisfiable 1.54s 0.59s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 62
% Syntax : Number of formulae : 315 ( 17 unt; 0 def)
% Number of atoms : 1415 ( 425 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 2188 (1088 ~;1076 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 127 ( 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1343,plain,
$false,
inference(avatar_sat_refutation,[],[f61,f81,f95,f111,f116,f121,f122,f123,f124,f125,f130,f134,f139,f140,f145,f146,f147,f148,f149,f150,f151,f153,f154,f155,f156,f157,f158,f162,f163,f164,f165,f166,f168,f169,f170,f171,f172,f173,f406,f414,f434,f458,f592,f599,f810,f951,f1272,f1303,f1332,f1342]) ).
fof(f1342,plain,
~ spl3_22,
inference(avatar_contradiction_clause,[],[f1341]) ).
fof(f1341,plain,
( $false
| ~ spl3_22 ),
inference(trivial_inequality_removal,[],[f1340]) ).
fof(f1340,plain,
( identity != identity
| ~ spl3_22 ),
inference(duplicate_literal_removal,[],[f1336]) ).
fof(f1336,plain,
( identity != identity
| identity != identity
| ~ spl3_22 ),
inference(superposition,[],[f591,f562]) ).
fof(f562,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f544,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f544,plain,
! [X10] : identity = inverse(multiply(inverse(X10),X10)),
inference(superposition,[],[f189,f503]) ).
fof(f503,plain,
! [X2,X1] : identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))),
inference(superposition,[],[f465,f3]) ).
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(f465,plain,
! [X4] : identity = multiply(X4,inverse(X4)),
inference(superposition,[],[f208,f2]) ).
fof(f208,plain,
! [X6,X5] : multiply(X5,X6) = multiply(inverse(inverse(X5)),X6),
inference(superposition,[],[f189,f189]) ).
fof(f189,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
inference(forward_demodulation,[],[f181,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f181,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = multiply(identity,X7),
inference(superposition,[],[f3,f2]) ).
fof(f591,plain,
( ! [X0] :
( inverse(X0) != X0
| identity != X0 )
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f590,plain,
( spl3_22
<=> ! [X0] :
( identity != X0
| inverse(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f1332,plain,
( ~ spl3_21
| spl3_22
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f1331,f108,f83,f75,f54,f590,f586]) ).
fof(f586,plain,
( spl3_21
<=> identity = multiply(identity,identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f54,plain,
( spl3_1
<=> inverse(sk_c10) = sk_c9 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f75,plain,
( spl3_6
<=> ! [X6,X8] :
( inverse(X8) != multiply(X8,inverse(X6))
| inverse(X6) != inverse(inverse(X8))
| sk_c10 != multiply(inverse(X6),sk_c9)
| sk_c10 != multiply(X6,inverse(X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f83,plain,
( spl3_8
<=> sk_c9 = multiply(sk_c1,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f108,plain,
( spl3_13
<=> sk_c10 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f1331,plain,
( ! [X0] :
( inverse(X0) != X0
| identity != multiply(identity,identity)
| identity != X0 )
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f1315,f463]) ).
fof(f463,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f208,f207]) ).
fof(f207,plain,
! [X4] : multiply(inverse(inverse(X4)),identity) = X4,
inference(superposition,[],[f189,f2]) ).
fof(f1315,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity) )
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(superposition,[],[f1309,f562]) ).
fof(f1309,plain,
( ! [X8,X6] :
( inverse(X8) != multiply(X8,inverse(X6))
| identity != multiply(inverse(X6),identity)
| inverse(X6) != X8 )
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(trivial_inequality_removal,[],[f1308]) ).
fof(f1308,plain,
( ! [X8,X6] :
( identity != multiply(inverse(X6),identity)
| inverse(X6) != X8
| inverse(X8) != multiply(X8,inverse(X6))
| identity != identity )
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f1307,f1069]) ).
fof(f1069,plain,
( identity = sk_c10
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f1068,f562]) ).
fof(f1068,plain,
( sk_c10 = inverse(identity)
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f969,f970]) ).
fof(f970,plain,
( identity = sk_c9
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f968,f953]) ).
fof(f953,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl3_1 ),
inference(superposition,[],[f2,f56]) ).
fof(f56,plain,
( inverse(sk_c10) = sk_c9
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f968,plain,
( sk_c9 = multiply(sk_c9,sk_c10)
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13 ),
inference(backward_demodulation,[],[f85,f965]) ).
fof(f965,plain,
( sk_c9 = sk_c1
| ~ spl3_1
| ~ spl3_13 ),
inference(forward_demodulation,[],[f964,f56]) ).
fof(f964,plain,
( inverse(sk_c10) = sk_c1
| ~ spl3_13 ),
inference(superposition,[],[f488,f110]) ).
fof(f110,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f488,plain,
! [X4] : inverse(inverse(X4)) = X4,
inference(forward_demodulation,[],[f478,f463]) ).
fof(f478,plain,
! [X4] : inverse(inverse(X4)) = multiply(X4,identity),
inference(superposition,[],[f463,f208]) ).
fof(f85,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f969,plain,
( sk_c10 = inverse(sk_c9)
| ~ spl3_1
| ~ spl3_13 ),
inference(backward_demodulation,[],[f110,f965]) ).
fof(f1307,plain,
( ! [X8,X6] :
( inverse(X8) != multiply(X8,inverse(X6))
| identity != multiply(inverse(X6),identity)
| identity != sk_c10
| inverse(X6) != X8 )
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f1306,f1069]) ).
fof(f1306,plain,
( ! [X8,X6] :
( sk_c10 != multiply(inverse(X6),identity)
| inverse(X6) != X8
| inverse(X8) != multiply(X8,inverse(X6))
| identity != sk_c10 )
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f1305,f465]) ).
fof(f1305,plain,
( ! [X8,X6] :
( inverse(X6) != X8
| sk_c10 != multiply(X6,inverse(X6))
| inverse(X8) != multiply(X8,inverse(X6))
| sk_c10 != multiply(inverse(X6),identity) )
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f1304,f488]) ).
fof(f1304,plain,
( ! [X8,X6] :
( inverse(X6) != inverse(inverse(X8))
| sk_c10 != multiply(inverse(X6),identity)
| inverse(X8) != multiply(X8,inverse(X6))
| sk_c10 != multiply(X6,inverse(X6)) )
| ~ spl3_1
| ~ spl3_6
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f76,f970]) ).
fof(f76,plain,
( ! [X8,X6] :
( inverse(X8) != multiply(X8,inverse(X6))
| sk_c10 != multiply(inverse(X6),sk_c9)
| sk_c10 != multiply(X6,inverse(X6))
| inverse(X6) != inverse(inverse(X8)) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f1303,plain,
( ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(avatar_contradiction_clause,[],[f1302]) ).
fof(f1302,plain,
( $false
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(trivial_inequality_removal,[],[f1301]) ).
fof(f1301,plain,
( identity != identity
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(superposition,[],[f1299,f562]) ).
fof(f1299,plain,
( identity != inverse(identity)
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(forward_demodulation,[],[f1298,f562]) ).
fof(f1298,plain,
( identity != inverse(inverse(identity))
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(trivial_inequality_removal,[],[f1296]) ).
fof(f1296,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(superposition,[],[f1277,f2]) ).
fof(f1277,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(forward_demodulation,[],[f1276,f1210]) ).
fof(f1210,plain,
( identity = sk_c8
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13 ),
inference(superposition,[],[f1133,f463]) ).
fof(f1133,plain,
( identity = multiply(sk_c8,identity)
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13 ),
inference(forward_demodulation,[],[f973,f1069]) ).
fof(f973,plain,
( identity = multiply(sk_c8,sk_c10)
| ~ spl3_1
| ~ spl3_5
| ~ spl3_8
| ~ spl3_13 ),
inference(backward_demodulation,[],[f72,f970]) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f71,plain,
( spl3_5
<=> sk_c9 = multiply(sk_c8,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f1276,plain,
( ! [X5] :
( sk_c8 != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(forward_demodulation,[],[f1275,f970]) ).
fof(f1275,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c8 != multiply(X5,identity) )
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_17 ),
inference(forward_demodulation,[],[f133,f970]) ).
fof(f133,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f132,plain,
( spl3_17
<=> ! [X5] :
( sk_c9 != inverse(X5)
| sk_c8 != multiply(X5,sk_c9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f1272,plain,
( ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(avatar_contradiction_clause,[],[f1271]) ).
fof(f1271,plain,
( $false
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(trivial_inequality_removal,[],[f1270]) ).
fof(f1270,plain,
( identity != identity
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(superposition,[],[f1269,f562]) ).
fof(f1269,plain,
( identity != inverse(identity)
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(forward_demodulation,[],[f1267,f562]) ).
fof(f1267,plain,
( identity != inverse(inverse(identity))
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(trivial_inequality_removal,[],[f1265]) ).
fof(f1265,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(superposition,[],[f1141,f2]) ).
fof(f1141,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(forward_demodulation,[],[f1140,f1069]) ).
fof(f1140,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| identity != multiply(X3,identity) )
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(forward_demodulation,[],[f977,f1069]) ).
fof(f977,plain,
( ! [X3] :
( identity != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl3_1
| ~ spl3_8
| ~ spl3_13
| ~ spl3_20 ),
inference(backward_demodulation,[],[f161,f970]) ).
fof(f161,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f160,plain,
( spl3_20
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f951,plain,
( ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(avatar_contradiction_clause,[],[f950]) ).
fof(f950,plain,
( $false
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(trivial_inequality_removal,[],[f949]) ).
fof(f949,plain,
( identity != identity
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(superposition,[],[f948,f562]) ).
fof(f948,plain,
( identity != inverse(identity)
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(forward_demodulation,[],[f946,f562]) ).
fof(f946,plain,
( identity != inverse(inverse(identity))
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(trivial_inequality_removal,[],[f944]) ).
fof(f944,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(superposition,[],[f870,f2]) ).
fof(f870,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(backward_demodulation,[],[f848,f857]) ).
fof(f857,plain,
( identity = sk_c9
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19 ),
inference(forward_demodulation,[],[f856,f562]) ).
fof(f856,plain,
( sk_c9 = inverse(identity)
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19 ),
inference(forward_demodulation,[],[f56,f825]) ).
fof(f825,plain,
( identity = sk_c10
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19 ),
inference(forward_demodulation,[],[f106,f608]) ).
fof(f608,plain,
( identity = multiply(sk_c4,sk_c7)
| ~ spl3_10
| ~ spl3_16
| ~ spl3_19 ),
inference(forward_demodulation,[],[f228,f607]) ).
fof(f607,plain,
( sk_c7 = sk_c6
| ~ spl3_10
| ~ spl3_19 ),
inference(forward_demodulation,[],[f221,f463]) ).
fof(f221,plain,
( sk_c6 = multiply(sk_c7,identity)
| ~ spl3_10
| ~ spl3_19 ),
inference(forward_demodulation,[],[f218,f94]) ).
fof(f94,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f92,plain,
( spl3_10
<=> sk_c7 = inverse(sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f218,plain,
( sk_c6 = multiply(inverse(sk_c5),identity)
| ~ spl3_19 ),
inference(superposition,[],[f189,f177]) ).
fof(f177,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl3_19 ),
inference(superposition,[],[f2,f144]) ).
fof(f144,plain,
( inverse(sk_c6) = sk_c5
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f142,plain,
( spl3_19
<=> inverse(sk_c6) = sk_c5 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f228,plain,
( identity = multiply(sk_c4,sk_c6)
| ~ spl3_10
| ~ spl3_16
| ~ spl3_19 ),
inference(backward_demodulation,[],[f177,f224]) ).
fof(f224,plain,
( sk_c4 = sk_c5
| ~ spl3_10
| ~ spl3_16 ),
inference(forward_demodulation,[],[f216,f215]) ).
fof(f215,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl3_16 ),
inference(superposition,[],[f189,f176]) ).
fof(f176,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl3_16 ),
inference(superposition,[],[f2,f129]) ).
fof(f129,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f127,plain,
( spl3_16
<=> sk_c7 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f216,plain,
( sk_c5 = multiply(inverse(sk_c7),identity)
| ~ spl3_10 ),
inference(superposition,[],[f189,f178]) ).
fof(f178,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl3_10 ),
inference(superposition,[],[f2,f94]) ).
fof(f106,plain,
( sk_c10 = multiply(sk_c4,sk_c7)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f104,plain,
( spl3_12
<=> sk_c10 = multiply(sk_c4,sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f848,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c9 != multiply(X3,identity) )
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(forward_demodulation,[],[f847,f825]) ).
fof(f847,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,identity) )
| ~ spl3_10
| ~ spl3_12
| ~ spl3_16
| ~ spl3_19
| ~ spl3_20 ),
inference(forward_demodulation,[],[f161,f825]) ).
fof(f810,plain,
( ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_17
| ~ spl3_18
| ~ spl3_19 ),
inference(avatar_contradiction_clause,[],[f809]) ).
fof(f809,plain,
( $false
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_17
| ~ spl3_18
| ~ spl3_19 ),
inference(trivial_inequality_removal,[],[f808]) ).
fof(f808,plain,
( identity != identity
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_17
| ~ spl3_18
| ~ spl3_19 ),
inference(superposition,[],[f806,f562]) ).
fof(f806,plain,
( identity != inverse(identity)
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_17
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f805,f562]) ).
fof(f805,plain,
( identity != inverse(inverse(identity))
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_17
| ~ spl3_18
| ~ spl3_19 ),
inference(trivial_inequality_removal,[],[f803]) ).
fof(f803,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_17
| ~ spl3_18
| ~ spl3_19 ),
inference(superposition,[],[f790,f2]) ).
fof(f790,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_17
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f611,f784]) ).
fof(f784,plain,
( identity = sk_c8
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(superposition,[],[f463,f780]) ).
fof(f780,plain,
( identity = multiply(sk_c8,identity)
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f675,f277]) ).
fof(f277,plain,
( identity = sk_c9
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f274,f2]) ).
fof(f274,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl3_15
| ~ spl3_18 ),
inference(superposition,[],[f189,f220]) ).
fof(f220,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f211,f120]) ).
fof(f120,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f118,plain,
( spl3_15
<=> sk_c10 = inverse(sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f211,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c9)
| ~ spl3_18 ),
inference(superposition,[],[f189,f138]) ).
fof(f138,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f136,plain,
( spl3_18
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f675,plain,
( sk_c9 = multiply(sk_c8,identity)
| ~ spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f72,f622]) ).
fof(f622,plain,
( identity = sk_c10
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f281,f621]) ).
fof(f621,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f195,f619]) ).
fof(f619,plain,
( ! [X0] : multiply(sk_c4,X0) = X0
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f613,f615]) ).
fof(f615,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f270,f613]) ).
fof(f270,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c4,multiply(sk_c10,X0))
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f266,f248]) ).
fof(f248,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c9,X0))
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f246,f120]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c2),multiply(sk_c9,X0))
| ~ spl3_18 ),
inference(superposition,[],[f189,f182]) ).
fof(f182,plain,
( ! [X8] : multiply(sk_c2,multiply(sk_c10,X8)) = multiply(sk_c9,X8)
| ~ spl3_18 ),
inference(superposition,[],[f3,f138]) ).
fof(f266,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c10,X0)) = multiply(sk_c10,multiply(sk_c9,X0))
| ~ spl3_12
| ~ spl3_14 ),
inference(superposition,[],[f184,f185]) ).
fof(f185,plain,
( ! [X11] : multiply(sk_c7,multiply(sk_c9,X11)) = multiply(sk_c10,X11)
| ~ spl3_14 ),
inference(superposition,[],[f3,f115]) ).
fof(f115,plain,
( sk_c10 = multiply(sk_c7,sk_c9)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f113,plain,
( spl3_14
<=> sk_c10 = multiply(sk_c7,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f184,plain,
( ! [X10] : multiply(sk_c10,X10) = multiply(sk_c4,multiply(sk_c7,X10))
| ~ spl3_12 ),
inference(superposition,[],[f3,f106]) ).
fof(f613,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c10,X0)) = X0
| ~ spl3_10
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f612,f298]) ).
fof(f298,plain,
( ! [X11] : multiply(sk_c10,X11) = multiply(sk_c7,X11)
| ~ spl3_14
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f286,f1]) ).
fof(f286,plain,
( ! [X11] : multiply(sk_c7,multiply(identity,X11)) = multiply(sk_c10,X11)
| ~ spl3_14
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f185,f277]) ).
fof(f612,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c7,X0)) = X0
| ~ spl3_10
| ~ spl3_16
| ~ spl3_19 ),
inference(forward_demodulation,[],[f231,f607]) ).
fof(f231,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c6,X0)) = X0
| ~ spl3_10
| ~ spl3_16
| ~ spl3_19 ),
inference(backward_demodulation,[],[f197,f224]) ).
fof(f197,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = X0
| ~ spl3_19 ),
inference(forward_demodulation,[],[f196,f1]) ).
fof(f196,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl3_19 ),
inference(superposition,[],[f3,f177]) ).
fof(f195,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c4,X0)) = X0
| ~ spl3_16 ),
inference(forward_demodulation,[],[f194,f1]) ).
fof(f194,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c4,X0))
| ~ spl3_16 ),
inference(superposition,[],[f3,f176]) ).
fof(f281,plain,
( sk_c10 = multiply(sk_c7,identity)
| ~ spl3_14
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f115,f277]) ).
fof(f611,plain,
( ! [X5] :
( sk_c8 != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(forward_demodulation,[],[f610,f277]) ).
fof(f610,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c9)
| identity != inverse(X5) )
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(forward_demodulation,[],[f133,f277]) ).
fof(f599,plain,
spl3_21,
inference(avatar_contradiction_clause,[],[f598]) ).
fof(f598,plain,
( $false
| spl3_21 ),
inference(trivial_inequality_removal,[],[f594]) ).
fof(f594,plain,
( identity != identity
| spl3_21 ),
inference(superposition,[],[f588,f1]) ).
fof(f588,plain,
( identity != multiply(identity,identity)
| spl3_21 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f592,plain,
( ~ spl3_21
| spl3_22
| ~ spl3_2
| ~ spl3_6
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f584,f142,f136,f127,f118,f113,f104,f92,f75,f58,f590,f586]) ).
fof(f58,plain,
( spl3_2
<=> sk_c9 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f584,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != X0
| identity != multiply(identity,identity) )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f577,f463]) ).
fof(f577,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity) )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(duplicate_literal_removal,[],[f571]) ).
fof(f571,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != multiply(X0,identity)
| identity != multiply(identity,identity)
| identity != multiply(identity,identity) )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(superposition,[],[f489,f309]) ).
fof(f309,plain,
( identity = inverse(identity)
| ~ spl3_2
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f279,f306]) ).
fof(f306,plain,
( identity = sk_c3
| ~ spl3_2
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f288,f2]) ).
fof(f288,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl3_2
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f210,f277]) ).
fof(f210,plain,
( sk_c3 = multiply(inverse(sk_c9),identity)
| ~ spl3_2 ),
inference(superposition,[],[f189,f175]) ).
fof(f175,plain,
( identity = multiply(sk_c9,sk_c3)
| ~ spl3_2 ),
inference(superposition,[],[f2,f60]) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f279,plain,
( identity = inverse(sk_c3)
| ~ spl3_2
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f60,f277]) ).
fof(f489,plain,
( ! [X8,X6] :
( inverse(X8) != multiply(X8,inverse(X6))
| identity != multiply(inverse(X6),identity)
| inverse(X6) != X8
| identity != multiply(X6,inverse(X6)) )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f461,f488]) ).
fof(f461,plain,
( ! [X8,X6] :
( inverse(X8) != multiply(X8,inverse(X6))
| inverse(X6) != inverse(inverse(X8))
| identity != multiply(inverse(X6),identity)
| identity != multiply(X6,inverse(X6)) )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f460,f346]) ).
fof(f346,plain,
( identity = sk_c10
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f341,f282]) ).
fof(f282,plain,
( identity = multiply(sk_c2,sk_c10)
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f138,f277]) ).
fof(f341,plain,
( sk_c10 = multiply(sk_c2,sk_c10)
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f261,f339]) ).
fof(f339,plain,
( sk_c2 = sk_c4
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f338,f321]) ).
fof(f321,plain,
( sk_c2 = multiply(sk_c4,identity)
| ~ spl3_2
| ~ spl3_10
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f209,f317]) ).
fof(f317,plain,
( inverse(sk_c10) = sk_c4
| ~ spl3_2
| ~ spl3_10
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f227,f314]) ).
fof(f314,plain,
( sk_c10 = sk_c6
| ~ spl3_2
| ~ spl3_10
| ~ spl3_14
| ~ spl3_15
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f308,f290]) ).
fof(f290,plain,
( sk_c10 = multiply(sk_c10,identity)
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f220,f277]) ).
fof(f308,plain,
( sk_c6 = multiply(sk_c10,identity)
| ~ spl3_2
| ~ spl3_10
| ~ spl3_14
| ~ spl3_15
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f269,f306]) ).
fof(f269,plain,
( sk_c6 = multiply(sk_c10,sk_c3)
| ~ spl3_2
| ~ spl3_10
| ~ spl3_14
| ~ spl3_19 ),
inference(forward_demodulation,[],[f265,f221]) ).
fof(f265,plain,
( multiply(sk_c10,sk_c3) = multiply(sk_c7,identity)
| ~ spl3_2
| ~ spl3_14 ),
inference(superposition,[],[f185,f175]) ).
fof(f227,plain,
( sk_c4 = inverse(sk_c6)
| ~ spl3_10
| ~ spl3_16
| ~ spl3_19 ),
inference(backward_demodulation,[],[f144,f224]) ).
fof(f209,plain,
( sk_c2 = multiply(inverse(sk_c10),identity)
| ~ spl3_15 ),
inference(superposition,[],[f189,f174]) ).
fof(f174,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl3_15 ),
inference(superposition,[],[f2,f120]) ).
fof(f338,plain,
( sk_c4 = multiply(sk_c4,identity)
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f334,f317]) ).
fof(f334,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f215,f329]) ).
fof(f329,plain,
( sk_c10 = sk_c7
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f223,f324]) ).
fof(f324,plain,
( ! [X11] : multiply(sk_c7,X11) = X11
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f298,f323]) ).
fof(f323,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f270,f319]) ).
fof(f319,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c10,X0)) = X0
| ~ spl3_2
| ~ spl3_10
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f231,f314]) ).
fof(f223,plain,
( sk_c7 = multiply(sk_c7,sk_c10)
| ~ spl3_12
| ~ spl3_16 ),
inference(forward_demodulation,[],[f213,f129]) ).
fof(f213,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c10)
| ~ spl3_12 ),
inference(superposition,[],[f189,f106]) ).
fof(f261,plain,
( sk_c10 = multiply(sk_c4,sk_c10)
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f257,f220]) ).
fof(f257,plain,
( multiply(sk_c10,sk_c9) = multiply(sk_c4,sk_c10)
| ~ spl3_12
| ~ spl3_14 ),
inference(superposition,[],[f184,f115]) ).
fof(f460,plain,
( ! [X8,X6] :
( sk_c10 != multiply(inverse(X6),identity)
| inverse(X6) != inverse(inverse(X8))
| inverse(X8) != multiply(X8,inverse(X6))
| identity != multiply(X6,inverse(X6)) )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f459,f277]) ).
fof(f459,plain,
( ! [X8,X6] :
( sk_c10 != multiply(inverse(X6),sk_c9)
| identity != multiply(X6,inverse(X6))
| inverse(X8) != multiply(X8,inverse(X6))
| inverse(X6) != inverse(inverse(X8)) )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f76,f346]) ).
fof(f458,plain,
( ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f457,plain,
( $false
| ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(trivial_inequality_removal,[],[f456]) ).
fof(f456,plain,
( identity != identity
| ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(superposition,[],[f452,f309]) ).
fof(f452,plain,
( identity != inverse(identity)
| ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(forward_demodulation,[],[f451,f309]) ).
fof(f451,plain,
( identity != inverse(inverse(identity))
| ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(trivial_inequality_removal,[],[f446]) ).
fof(f446,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(superposition,[],[f437,f2]) ).
fof(f437,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(forward_demodulation,[],[f436,f388]) ).
fof(f388,plain,
( identity = sk_c8
| ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f387,f1]) ).
fof(f387,plain,
( sk_c8 = multiply(identity,identity)
| ~ spl3_2
| ~ spl3_9
| ~ spl3_15
| ~ spl3_18 ),
inference(forward_demodulation,[],[f280,f306]) ).
fof(f280,plain,
( sk_c8 = multiply(sk_c3,identity)
| ~ spl3_9
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f89,f277]) ).
fof(f89,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f87,plain,
( spl3_9
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f436,plain,
( ! [X5] :
( sk_c8 != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(forward_demodulation,[],[f435,f277]) ).
fof(f435,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c9)
| identity != inverse(X5) )
| ~ spl3_15
| ~ spl3_17
| ~ spl3_18 ),
inference(forward_demodulation,[],[f133,f277]) ).
fof(f434,plain,
( ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f433,plain,
( $false
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(trivial_inequality_removal,[],[f432]) ).
fof(f432,plain,
( identity != identity
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(superposition,[],[f431,f309]) ).
fof(f431,plain,
( identity != inverse(identity)
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(forward_demodulation,[],[f430,f309]) ).
fof(f430,plain,
( identity != inverse(inverse(identity))
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(trivial_inequality_removal,[],[f427]) ).
fof(f427,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(superposition,[],[f417,f2]) ).
fof(f417,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(forward_demodulation,[],[f416,f346]) ).
fof(f416,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| identity != multiply(X3,identity) )
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(forward_demodulation,[],[f415,f277]) ).
fof(f415,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19
| ~ spl3_20 ),
inference(forward_demodulation,[],[f161,f346]) ).
fof(f414,plain,
( ~ spl3_2
| spl3_5
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f413,plain,
( $false
| ~ spl3_2
| spl3_5
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(trivial_inequality_removal,[],[f412]) ).
fof(f412,plain,
( identity != identity
| ~ spl3_2
| spl3_5
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(superposition,[],[f411,f277]) ).
fof(f411,plain,
( identity != sk_c9
| ~ spl3_2
| spl3_5
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f410,f1]) ).
fof(f410,plain,
( sk_c9 != multiply(identity,identity)
| ~ spl3_2
| spl3_5
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f409,f388]) ).
fof(f409,plain,
( sk_c9 != multiply(sk_c8,identity)
| ~ spl3_2
| spl3_5
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(forward_demodulation,[],[f73,f346]) ).
fof(f73,plain,
( sk_c9 != multiply(sk_c8,sk_c10)
| spl3_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f406,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f405,plain,
( $false
| spl3_1
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(trivial_inequality_removal,[],[f404]) ).
fof(f404,plain,
( identity != identity
| spl3_1
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(superposition,[],[f350,f309]) ).
fof(f350,plain,
( identity != inverse(identity)
| spl3_1
| ~ spl3_2
| ~ spl3_10
| ~ spl3_12
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16
| ~ spl3_18
| ~ spl3_19 ),
inference(backward_demodulation,[],[f278,f346]) ).
fof(f278,plain,
( identity != inverse(sk_c10)
| spl3_1
| ~ spl3_15
| ~ spl3_18 ),
inference(backward_demodulation,[],[f55,f277]) ).
fof(f55,plain,
( inverse(sk_c10) != sk_c9
| spl3_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f173,plain,
( spl3_8
| spl3_12 ),
inference(avatar_split_clause,[],[f18,f104,f83]) ).
fof(f18,axiom,
( sk_c10 = multiply(sk_c4,sk_c7)
| sk_c9 = multiply(sk_c1,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f172,plain,
( spl3_19
| spl3_8 ),
inference(avatar_split_clause,[],[f21,f83,f142]) ).
fof(f21,axiom,
( sk_c9 = multiply(sk_c1,sk_c10)
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f171,plain,
( spl3_9
| spl3_5 ),
inference(avatar_split_clause,[],[f36,f71,f87]) ).
fof(f36,axiom,
( sk_c9 = multiply(sk_c8,sk_c10)
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f170,plain,
( spl3_2
| spl3_13 ),
inference(avatar_split_clause,[],[f27,f108,f58]) ).
fof(f27,axiom,
( sk_c10 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f169,plain,
( spl3_18
| spl3_1 ),
inference(avatar_split_clause,[],[f4,f54,f136]) ).
fof(f4,axiom,
( inverse(sk_c10) = sk_c9
| sk_c9 = multiply(sk_c2,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f168,plain,
( spl3_3
| spl3_20 ),
inference(avatar_split_clause,[],[f49,f160,f63]) ).
fof(f63,plain,
( spl3_3
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f49,plain,
! [X4] :
( sk_c10 != inverse(X4)
| sP1
| sk_c9 != multiply(X4,sk_c10) ),
inference(cnf_transformation,[],[f49_D]) ).
fof(f49_D,plain,
( ! [X4] :
( sk_c10 != inverse(X4)
| sk_c9 != multiply(X4,sk_c10) )
<=> ~ sP1 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f166,plain,
( spl3_1
| spl3_14 ),
inference(avatar_split_clause,[],[f10,f113,f54]) ).
fof(f10,axiom,
( sk_c10 = multiply(sk_c7,sk_c9)
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f165,plain,
( spl3_14
| spl3_8 ),
inference(avatar_split_clause,[],[f20,f83,f113]) ).
fof(f20,axiom,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c7,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f164,plain,
( spl3_5
| spl3_2 ),
inference(avatar_split_clause,[],[f37,f58,f71]) ).
fof(f37,axiom,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c8,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f163,plain,
( spl3_19
| spl3_1 ),
inference(avatar_split_clause,[],[f11,f54,f142]) ).
fof(f11,axiom,
( inverse(sk_c10) = sk_c9
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f162,plain,
( spl3_4
| spl3_20 ),
inference(avatar_split_clause,[],[f47,f160,f67]) ).
fof(f67,plain,
( spl3_4
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f47,plain,
! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sP0 ),
inference(cnf_transformation,[],[f47_D]) ).
fof(f47_D,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
<=> ~ sP0 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f158,plain,
( spl3_13
| spl3_19 ),
inference(avatar_split_clause,[],[f31,f142,f108]) ).
fof(f31,axiom,
( inverse(sk_c6) = sk_c5
| sk_c10 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f157,plain,
( spl3_13
| spl3_9 ),
inference(avatar_split_clause,[],[f26,f87,f108]) ).
fof(f26,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| sk_c10 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f156,plain,
( spl3_16
| spl3_1 ),
inference(avatar_split_clause,[],[f9,f54,f127]) ).
fof(f9,axiom,
( inverse(sk_c10) = sk_c9
| sk_c7 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f155,plain,
( spl3_12
| spl3_1 ),
inference(avatar_split_clause,[],[f8,f54,f104]) ).
fof(f8,axiom,
( inverse(sk_c10) = sk_c9
| sk_c10 = multiply(sk_c4,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f154,plain,
( spl3_8
| spl3_18 ),
inference(avatar_split_clause,[],[f14,f136,f83]) ).
fof(f14,axiom,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c9 = multiply(sk_c1,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f153,plain,
( spl3_18
| spl3_5 ),
inference(avatar_split_clause,[],[f34,f71,f136]) ).
fof(f34,axiom,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c9 = multiply(sk_c2,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f151,plain,
( spl3_10
| spl3_5 ),
inference(avatar_split_clause,[],[f42,f71,f92]) ).
fof(f42,axiom,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c7 = inverse(sk_c5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f150,plain,
( spl3_15
| spl3_5 ),
inference(avatar_split_clause,[],[f35,f71,f118]) ).
fof(f35,axiom,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c10 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f149,plain,
( spl3_8
| spl3_2 ),
inference(avatar_split_clause,[],[f17,f58,f83]) ).
fof(f17,axiom,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c1,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f148,plain,
( spl3_1
| spl3_10 ),
inference(avatar_split_clause,[],[f12,f92,f54]) ).
fof(f12,axiom,
( sk_c7 = inverse(sk_c5)
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f147,plain,
( spl3_16
| spl3_13 ),
inference(avatar_split_clause,[],[f29,f108,f127]) ).
fof(f29,axiom,
( sk_c10 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f146,plain,
( spl3_8
| spl3_16 ),
inference(avatar_split_clause,[],[f19,f127,f83]) ).
fof(f19,axiom,
( sk_c7 = inverse(sk_c4)
| sk_c9 = multiply(sk_c1,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f145,plain,
( spl3_5
| spl3_19 ),
inference(avatar_split_clause,[],[f41,f142,f71]) ).
fof(f41,axiom,
( inverse(sk_c6) = sk_c5
| sk_c9 = multiply(sk_c8,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f140,plain,
( spl3_12
| spl3_5 ),
inference(avatar_split_clause,[],[f38,f71,f104]) ).
fof(f38,axiom,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f139,plain,
( spl3_18
| spl3_13 ),
inference(avatar_split_clause,[],[f24,f108,f136]) ).
fof(f24,axiom,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c2,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f134,plain,
( spl3_17
| spl3_7 ),
inference(avatar_split_clause,[],[f51,f78,f132]) ).
fof(f78,plain,
( spl3_7
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f51,plain,
! [X5] :
( sP2
| sk_c9 != inverse(X5)
| sk_c8 != multiply(X5,sk_c9) ),
inference(cnf_transformation,[],[f51_D]) ).
fof(f51_D,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c8 != multiply(X5,sk_c9) )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f130,plain,
( spl3_5
| spl3_16 ),
inference(avatar_split_clause,[],[f39,f127,f71]) ).
fof(f39,axiom,
( sk_c7 = inverse(sk_c4)
| sk_c9 = multiply(sk_c8,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f125,plain,
( spl3_15
| spl3_13 ),
inference(avatar_split_clause,[],[f25,f108,f118]) ).
fof(f25,axiom,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f124,plain,
( spl3_13
| spl3_10 ),
inference(avatar_split_clause,[],[f32,f92,f108]) ).
fof(f32,axiom,
( sk_c7 = inverse(sk_c5)
| sk_c10 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f123,plain,
( spl3_8
| spl3_15 ),
inference(avatar_split_clause,[],[f15,f118,f83]) ).
fof(f15,axiom,
( sk_c10 = inverse(sk_c2)
| sk_c9 = multiply(sk_c1,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f122,plain,
( spl3_14
| spl3_5 ),
inference(avatar_split_clause,[],[f40,f71,f113]) ).
fof(f40,axiom,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c10 = multiply(sk_c7,sk_c9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f121,plain,
( spl3_15
| spl3_1 ),
inference(avatar_split_clause,[],[f5,f54,f118]) ).
fof(f5,axiom,
( inverse(sk_c10) = sk_c9
| sk_c10 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f116,plain,
( spl3_13
| spl3_14 ),
inference(avatar_split_clause,[],[f30,f113,f108]) ).
fof(f30,axiom,
( sk_c10 = multiply(sk_c7,sk_c9)
| sk_c10 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f111,plain,
( spl3_12
| spl3_13 ),
inference(avatar_split_clause,[],[f28,f108,f104]) ).
fof(f28,axiom,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f95,plain,
( spl3_8
| spl3_10 ),
inference(avatar_split_clause,[],[f22,f92,f83]) ).
fof(f22,axiom,
( sk_c7 = inverse(sk_c5)
| sk_c9 = multiply(sk_c1,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f81,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| spl3_6
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f52,f78,f75,f71,f67,f63,f54]) ).
fof(f52,plain,
! [X8,X6] :
( ~ sP2
| inverse(X8) != multiply(X8,inverse(X6))
| sk_c9 != multiply(sk_c8,sk_c10)
| ~ sP0
| sk_c10 != multiply(X6,inverse(X6))
| ~ sP1
| inverse(sk_c10) != sk_c9
| sk_c10 != multiply(inverse(X6),sk_c9)
| inverse(X6) != inverse(inverse(X8)) ),
inference(general_splitting,[],[f50,f51_D]) ).
fof(f50,plain,
! [X8,X6,X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c10)
| inverse(X6) != inverse(inverse(X8))
| sk_c10 != multiply(inverse(X6),sk_c9)
| inverse(sk_c10) != sk_c9
| inverse(X8) != multiply(X8,inverse(X6))
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X6,inverse(X6))
| ~ sP0
| ~ sP1 ),
inference(general_splitting,[],[f48,f49_D]) ).
fof(f48,plain,
! [X8,X6,X4,X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(X4,sk_c10)
| inverse(X6) != inverse(inverse(X8))
| sk_c10 != multiply(inverse(X6),sk_c9)
| inverse(sk_c10) != sk_c9
| inverse(X8) != multiply(X8,inverse(X6))
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X6,inverse(X6))
| ~ sP0 ),
inference(general_splitting,[],[f46,f47_D]) ).
fof(f46,plain,
! [X3,X8,X6,X4,X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| inverse(X6) != inverse(inverse(X8))
| sk_c10 != multiply(inverse(X6),sk_c9)
| inverse(sk_c10) != sk_c9
| inverse(X8) != multiply(X8,inverse(X6))
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X6,inverse(X6)) ),
inference(equality_resolution,[],[f45]) ).
fof(f45,plain,
! [X3,X8,X6,X9,X4,X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| inverse(X8) != X9
| inverse(X6) != inverse(X9)
| sk_c10 != multiply(inverse(X6),sk_c9)
| inverse(sk_c10) != sk_c9
| multiply(X8,inverse(X6)) != X9
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X6,inverse(X6)) ),
inference(equality_resolution,[],[f44]) ).
fof(f44,axiom,
! [X3,X8,X6,X9,X7,X4,X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X3)
| inverse(X6) != X7
| sk_c9 != multiply(X4,sk_c10)
| sk_c9 != multiply(X3,sk_c10)
| inverse(X8) != X9
| inverse(X9) != X7
| sk_c10 != multiply(X7,sk_c9)
| inverse(sk_c10) != sk_c9
| multiply(X8,X7) != X9
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f61,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f7,f58,f54]) ).
fof(f7,axiom,
( sk_c9 = inverse(sk_c3)
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP375-1 : 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
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 22:35:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.50 % (15201)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)
% 0.19/0.50 % (15185)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)
% 0.19/0.50 % (15193)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)
% 0.19/0.50 % (15187)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.51 TRYING [1]
% 0.19/0.51 % (15203)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.51 % (15194)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)
% 0.19/0.51 % (15187)Instruction limit reached!
% 0.19/0.51 % (15187)------------------------------
% 0.19/0.51 % (15187)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (15187)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (15187)Termination reason: Unknown
% 0.19/0.51 % (15187)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (15187)Memory used [KB]: 5373
% 0.19/0.51 % (15187)Time elapsed: 0.003 s
% 0.19/0.51 % (15187)Instructions burned: 2 (million)
% 0.19/0.51 % (15187)------------------------------
% 0.19/0.51 % (15187)------------------------------
% 0.19/0.51 TRYING [2]
% 0.19/0.51 % (15178)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 TRYING [3]
% 0.19/0.51 TRYING [2]
% 0.19/0.52 % (15189)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 % (15206)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)
% 0.19/0.52 % (15181)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)
% 0.19/0.52 % (15183)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 TRYING [4]
% 0.19/0.52 % (15205)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 % (15180)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)
% 0.19/0.52 % (15182)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (15199)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.52 % (15195)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.53 % (15198)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)
% 0.19/0.53 % (15196)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.53 % (15197)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53 TRYING [3]
% 0.19/0.53 TRYING [1]
% 1.40/0.53 % (15190)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)
% 1.40/0.53 % (15204)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.40/0.53 % (15188)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)
% 1.40/0.53 % (15184)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)
% 1.40/0.54 % (15191)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.40/0.54 % (15207)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)
% 1.40/0.54 % (15185)Instruction limit reached!
% 1.40/0.54 % (15185)------------------------------
% 1.40/0.54 % (15185)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.40/0.54 % (15208)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.40/0.54 % (15192)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.40/0.54 % (15185)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.54 % (15185)Termination reason: Unknown
% 1.40/0.54 % (15185)Termination phase: Finite model building SAT solving
% 1.40/0.54
% 1.40/0.54 % (15185)Memory used [KB]: 7036
% 1.40/0.54 % (15185)Time elapsed: 0.118 s
% 1.40/0.54 % (15185)Instructions burned: 53 (million)
% 1.40/0.54 % (15185)------------------------------
% 1.40/0.54 % (15185)------------------------------
% 1.40/0.55 % (15186)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.54/0.55 % (15209)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)
% 1.54/0.55 % (15186)Instruction limit reached!
% 1.54/0.55 % (15186)------------------------------
% 1.54/0.55 % (15186)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.54/0.55 % (15186)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.54/0.55 % (15186)Termination reason: Unknown
% 1.54/0.55 % (15186)Termination phase: Saturation
% 1.54/0.55
% 1.54/0.55 % (15186)Memory used [KB]: 5628
% 1.54/0.55 % (15186)Time elapsed: 0.152 s
% 1.54/0.55 % (15186)Instructions burned: 8 (million)
% 1.54/0.55 % (15186)------------------------------
% 1.54/0.55 % (15186)------------------------------
% 1.54/0.56 TRYING [2]
% 1.54/0.56 % (15200)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.54/0.56 TRYING [3]
% 1.54/0.56 TRYING [4]
% 1.54/0.57 % (15189)First to succeed.
% 1.54/0.58 TRYING [4]
% 1.54/0.59 % (15193)Instruction limit reached!
% 1.54/0.59 % (15193)------------------------------
% 1.54/0.59 % (15193)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.54/0.59 % (15189)Refutation found. Thanks to Tanya!
% 1.54/0.59 % SZS status Unsatisfiable for theBenchmark
% 1.54/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.54/0.59 % (15189)------------------------------
% 1.54/0.59 % (15189)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.54/0.59 % (15189)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.54/0.59 % (15189)Termination reason: Refutation
% 1.54/0.59
% 1.54/0.59 % (15189)Memory used [KB]: 6140
% 1.54/0.59 % (15189)Time elapsed: 0.148 s
% 1.54/0.59 % (15189)Instructions burned: 39 (million)
% 1.54/0.59 % (15189)------------------------------
% 1.54/0.59 % (15189)------------------------------
% 1.54/0.59 % (15173)Success in time 0.239 s
%------------------------------------------------------------------------------