TSTP Solution File: GRP378-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP378-1 : 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 : n007.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 16:21:29 EDT 2022
% Result : Unsatisfiable 0.20s 0.58s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 60
% Syntax : Number of formulae : 252 ( 9 unt; 0 def)
% Number of atoms : 886 ( 347 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1231 ( 597 ~; 606 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 97 ( 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f678,plain,
$false,
inference(avatar_sat_refutation,[],[f72,f81,f91,f99,f100,f110,f111,f117,f122,f132,f137,f142,f149,f150,f152,f164,f168,f170,f172,f173,f176,f177,f181,f185,f189,f191,f195,f196,f197,f198,f200,f201,f231,f243,f268,f352,f369,f376,f450,f478,f617,f623,f633,f672]) ).
fof(f672,plain,
( ~ spl3_23
| spl3_24
| ~ spl3_25 ),
inference(avatar_contradiction_clause,[],[f671]) ).
fof(f671,plain,
( $false
| ~ spl3_23
| spl3_24
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f670,f225]) ).
fof(f225,plain,
( identity = sk_c11
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f224,plain,
( spl3_23
<=> identity = sk_c11 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f670,plain,
( identity != sk_c11
| spl3_24
| ~ spl3_25 ),
inference(forward_demodulation,[],[f669,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f669,plain,
( sk_c11 != multiply(identity,identity)
| spl3_24
| ~ spl3_25 ),
inference(forward_demodulation,[],[f668,f361]) ).
fof(f361,plain,
identity = inverse(identity),
inference(superposition,[],[f357,f253]) ).
fof(f253,plain,
! [X4] : multiply(inverse(inverse(X4)),identity) = X4,
inference(superposition,[],[f216,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f216,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
inference(forward_demodulation,[],[f206,f1]) ).
fof(f206,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = multiply(identity,X7),
inference(superposition,[],[f3,f2]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f357,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f216,f253]) ).
fof(f668,plain,
( sk_c11 != multiply(identity,inverse(identity))
| spl3_24
| ~ spl3_25 ),
inference(forward_demodulation,[],[f230,f497]) ).
fof(f497,plain,
( identity = sk_c10
| ~ spl3_25 ),
inference(forward_demodulation,[],[f495,f2]) ).
fof(f495,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl3_25 ),
inference(superposition,[],[f216,f234]) ).
fof(f234,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f233,plain,
( spl3_25
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f230,plain,
( sk_c11 != multiply(sk_c10,inverse(sk_c10))
| spl3_24 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f228,plain,
( spl3_24
<=> sk_c11 = multiply(sk_c10,inverse(sk_c10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f633,plain,
( spl3_23
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f542,f233,f144,f134,f113,f83,f65,f224]) ).
fof(f65,plain,
( spl3_1
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f83,plain,
( spl3_5
<=> sk_c8 = inverse(sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f113,plain,
( spl3_11
<=> sk_c8 = inverse(sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f134,plain,
( spl3_15
<=> inverse(sk_c7) = sk_c6 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f144,plain,
( spl3_17
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f542,plain,
( identity = sk_c11
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(backward_demodulation,[],[f498,f539]) ).
fof(f539,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(backward_demodulation,[],[f403,f537]) ).
fof(f537,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(backward_demodulation,[],[f524,f534]) ).
fof(f534,plain,
( ! [X0] : multiply(sk_c11,X0) = X0
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(forward_demodulation,[],[f533,f524]) ).
fof(f533,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c11,X0))
| ~ spl3_1
| ~ spl3_17
| ~ spl3_25 ),
inference(backward_demodulation,[],[f487,f531]) ).
fof(f531,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c8,X0)
| ~ spl3_1
| ~ spl3_25 ),
inference(forward_demodulation,[],[f515,f1]) ).
fof(f515,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c8,multiply(identity,X0))
| ~ spl3_1
| ~ spl3_25 ),
inference(backward_demodulation,[],[f474,f497]) ).
fof(f474,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c8,multiply(sk_c10,X0))
| ~ spl3_1 ),
inference(superposition,[],[f3,f67]) ).
fof(f67,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f487,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl3_17 ),
inference(superposition,[],[f3,f146]) ).
fof(f146,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f524,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c11,X0)) = X0
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_25 ),
inference(backward_demodulation,[],[f464,f521]) ).
fof(f521,plain,
( sk_c11 = sk_c7
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_25 ),
inference(backward_demodulation,[],[f466,f498]) ).
fof(f466,plain,
( sk_c7 = multiply(sk_c8,identity)
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15 ),
inference(forward_demodulation,[],[f463,f115]) ).
fof(f115,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f463,plain,
( sk_c7 = multiply(inverse(sk_c5),identity)
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15 ),
inference(superposition,[],[f253,f408]) ).
fof(f408,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15 ),
inference(backward_demodulation,[],[f136,f405]) ).
fof(f405,plain,
( sk_c5 = sk_c6
| ~ spl3_5
| ~ spl3_11 ),
inference(backward_demodulation,[],[f398,f402]) ).
fof(f402,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl3_11 ),
inference(superposition,[],[f253,f115]) ).
fof(f398,plain,
( sk_c6 = multiply(inverse(sk_c8),identity)
| ~ spl3_5 ),
inference(superposition,[],[f253,f85]) ).
fof(f85,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f136,plain,
( inverse(sk_c7) = sk_c6
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f464,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c7,X0)) = X0
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15 ),
inference(superposition,[],[f216,f408]) ).
fof(f403,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl3_11 ),
inference(superposition,[],[f216,f115]) ).
fof(f498,plain,
( sk_c11 = multiply(sk_c8,identity)
| ~ spl3_1
| ~ spl3_25 ),
inference(backward_demodulation,[],[f67,f497]) ).
fof(f623,plain,
( ~ spl3_1
| ~ spl3_5
| ~ spl3_9
| spl3_10
| ~ spl3_11
| ~ spl3_13
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(avatar_contradiction_clause,[],[f622]) ).
fof(f622,plain,
( $false
| ~ spl3_1
| ~ spl3_5
| ~ spl3_9
| spl3_10
| ~ spl3_11
| ~ spl3_13
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f621,f497]) ).
fof(f621,plain,
( identity != sk_c10
| ~ spl3_1
| ~ spl3_5
| ~ spl3_9
| spl3_10
| ~ spl3_11
| ~ spl3_13
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(forward_demodulation,[],[f620,f534]) ).
fof(f620,plain,
( sk_c10 != multiply(sk_c11,identity)
| ~ spl3_9
| spl3_10
| ~ spl3_13
| ~ spl3_25 ),
inference(forward_demodulation,[],[f108,f619]) ).
fof(f619,plain,
( identity = sk_c9
| ~ spl3_9
| ~ spl3_13
| ~ spl3_25 ),
inference(forward_demodulation,[],[f618,f1]) ).
fof(f618,plain,
( sk_c9 = multiply(identity,identity)
| ~ spl3_9
| ~ spl3_13
| ~ spl3_25 ),
inference(forward_demodulation,[],[f502,f595]) ).
fof(f595,plain,
( identity = sk_c4
| ~ spl3_13
| ~ spl3_25 ),
inference(forward_demodulation,[],[f511,f2]) ).
fof(f511,plain,
( sk_c4 = multiply(inverse(identity),identity)
| ~ spl3_13
| ~ spl3_25 ),
inference(backward_demodulation,[],[f413,f497]) ).
fof(f413,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl3_13 ),
inference(superposition,[],[f253,f126]) ).
fof(f126,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f124,plain,
( spl3_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f502,plain,
( sk_c9 = multiply(sk_c4,identity)
| ~ spl3_9
| ~ spl3_25 ),
inference(backward_demodulation,[],[f104,f497]) ).
fof(f104,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f102,plain,
( spl3_9
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f108,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| spl3_10 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f107,plain,
( spl3_10
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f617,plain,
( spl3_23
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_14
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f574,f233,f144,f134,f129,f113,f83,f65,f224]) ).
fof(f129,plain,
( spl3_14
<=> sk_c6 = multiply(sk_c7,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f574,plain,
( identity = sk_c11
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_14
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(forward_demodulation,[],[f573,f556]) ).
fof(f556,plain,
( identity = sk_c5
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(forward_demodulation,[],[f555,f537]) ).
fof(f555,plain,
( sk_c5 = multiply(sk_c5,identity)
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(forward_demodulation,[],[f548,f523]) ).
fof(f523,plain,
( inverse(sk_c11) = sk_c5
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_25 ),
inference(backward_demodulation,[],[f408,f521]) ).
fof(f548,plain,
( sk_c5 = multiply(inverse(sk_c11),identity)
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(backward_demodulation,[],[f402,f543]) ).
fof(f543,plain,
( sk_c11 = sk_c8
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(backward_demodulation,[],[f488,f539]) ).
fof(f488,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl3_11
| ~ spl3_17 ),
inference(forward_demodulation,[],[f486,f115]) ).
fof(f486,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl3_17 ),
inference(superposition,[],[f216,f146]) ).
fof(f573,plain,
( sk_c11 = sk_c5
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_14
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(forward_demodulation,[],[f541,f543]) ).
fof(f541,plain,
( sk_c5 = sk_c8
| ~ spl3_1
| ~ spl3_5
| ~ spl3_11
| ~ spl3_14
| ~ spl3_15
| ~ spl3_17
| ~ spl3_25 ),
inference(backward_demodulation,[],[f491,f537]) ).
fof(f491,plain,
( sk_c8 = multiply(sk_c5,sk_c5)
| ~ spl3_5
| ~ spl3_11
| ~ spl3_14
| ~ spl3_15 ),
inference(forward_demodulation,[],[f489,f408]) ).
fof(f489,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c5)
| ~ spl3_5
| ~ spl3_11
| ~ spl3_14 ),
inference(superposition,[],[f216,f407]) ).
fof(f407,plain,
( sk_c5 = multiply(sk_c7,sk_c8)
| ~ spl3_5
| ~ spl3_11
| ~ spl3_14 ),
inference(backward_demodulation,[],[f131,f405]) ).
fof(f131,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f478,plain,
( spl3_25
| ~ spl3_3
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f477,f139,f74,f233]) ).
fof(f74,plain,
( spl3_3
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f139,plain,
( spl3_16
<=> sk_c11 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f477,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl3_3
| ~ spl3_16 ),
inference(forward_demodulation,[],[f475,f141]) ).
fof(f141,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f475,plain,
( sk_c11 = multiply(inverse(sk_c3),sk_c10)
| ~ spl3_3 ),
inference(superposition,[],[f216,f76]) ).
fof(f76,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f450,plain,
( ~ spl3_3
| spl3_6
| ~ spl3_16
| ~ spl3_23 ),
inference(avatar_contradiction_clause,[],[f449]) ).
fof(f449,plain,
( $false
| ~ spl3_3
| spl3_6
| ~ spl3_16
| ~ spl3_23 ),
inference(subsumption_resolution,[],[f448,f385]) ).
fof(f385,plain,
( identity != sk_c10
| spl3_6
| ~ spl3_23 ),
inference(backward_demodulation,[],[f384,f361]) ).
fof(f384,plain,
( sk_c10 != inverse(identity)
| spl3_6
| ~ spl3_23 ),
inference(forward_demodulation,[],[f88,f225]) ).
fof(f88,plain,
( inverse(sk_c11) != sk_c10
| spl3_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f87,plain,
( spl3_6
<=> inverse(sk_c11) = sk_c10 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f448,plain,
( identity = sk_c10
| ~ spl3_3
| ~ spl3_16
| ~ spl3_23 ),
inference(forward_demodulation,[],[f447,f1]) ).
fof(f447,plain,
( sk_c10 = multiply(identity,identity)
| ~ spl3_3
| ~ spl3_16
| ~ spl3_23 ),
inference(backward_demodulation,[],[f377,f444]) ).
fof(f444,plain,
( identity = sk_c3
| ~ spl3_16
| ~ spl3_23 ),
inference(forward_demodulation,[],[f439,f2]) ).
fof(f439,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl3_16
| ~ spl3_23 ),
inference(superposition,[],[f253,f394]) ).
fof(f394,plain,
( identity = inverse(sk_c3)
| ~ spl3_16
| ~ spl3_23 ),
inference(forward_demodulation,[],[f141,f225]) ).
fof(f377,plain,
( sk_c10 = multiply(sk_c3,identity)
| ~ spl3_3
| ~ spl3_23 ),
inference(forward_demodulation,[],[f76,f225]) ).
fof(f376,plain,
( ~ spl3_6
| ~ spl3_10
| ~ spl3_22
| ~ spl3_23 ),
inference(avatar_contradiction_clause,[],[f375]) ).
fof(f375,plain,
( $false
| ~ spl3_6
| ~ spl3_10
| ~ spl3_22
| ~ spl3_23 ),
inference(subsumption_resolution,[],[f374,f1]) ).
fof(f374,plain,
( identity != multiply(identity,identity)
| ~ spl3_6
| ~ spl3_10
| ~ spl3_22
| ~ spl3_23 ),
inference(trivial_inequality_removal,[],[f373]) ).
fof(f373,plain,
( identity != multiply(identity,identity)
| identity != identity
| ~ spl3_6
| ~ spl3_10
| ~ spl3_22
| ~ spl3_23 ),
inference(superposition,[],[f372,f312]) ).
fof(f312,plain,
( identity = inverse(identity)
| ~ spl3_6
| ~ spl3_10
| ~ spl3_23 ),
inference(forward_demodulation,[],[f272,f290]) ).
fof(f290,plain,
( identity = sk_c10
| ~ spl3_6
| ~ spl3_10
| ~ spl3_23 ),
inference(forward_demodulation,[],[f289,f2]) ).
fof(f289,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl3_6
| ~ spl3_10
| ~ spl3_23 ),
inference(backward_demodulation,[],[f258,f287]) ).
fof(f287,plain,
( sk_c10 = sk_c9
| ~ spl3_6
| ~ spl3_10
| ~ spl3_23 ),
inference(backward_demodulation,[],[f217,f285]) ).
fof(f285,plain,
( ! [X9] : multiply(sk_c10,X9) = X9
| ~ spl3_6
| ~ spl3_23 ),
inference(forward_demodulation,[],[f279,f1]) ).
fof(f279,plain,
( ! [X9] : multiply(sk_c10,multiply(identity,X9)) = X9
| ~ spl3_6
| ~ spl3_23 ),
inference(backward_demodulation,[],[f212,f225]) ).
fof(f212,plain,
( ! [X9] : multiply(sk_c10,multiply(sk_c11,X9)) = X9
| ~ spl3_6 ),
inference(forward_demodulation,[],[f208,f1]) ).
fof(f208,plain,
( ! [X9] : multiply(identity,X9) = multiply(sk_c10,multiply(sk_c11,X9))
| ~ spl3_6 ),
inference(superposition,[],[f3,f202]) ).
fof(f202,plain,
( identity = multiply(sk_c10,sk_c11)
| ~ spl3_6 ),
inference(superposition,[],[f2,f89]) ).
fof(f89,plain,
( inverse(sk_c11) = sk_c10
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f217,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl3_6
| ~ spl3_10 ),
inference(superposition,[],[f212,f109]) ).
fof(f109,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f258,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c9)
| ~ spl3_6
| ~ spl3_10 ),
inference(superposition,[],[f216,f217]) ).
fof(f272,plain,
( sk_c10 = inverse(identity)
| ~ spl3_6
| ~ spl3_23 ),
inference(backward_demodulation,[],[f89,f225]) ).
fof(f372,plain,
( ! [X5] :
( identity != inverse(X5)
| identity != multiply(X5,identity) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_22
| ~ spl3_23 ),
inference(forward_demodulation,[],[f371,f290]) ).
fof(f371,plain,
( ! [X5] :
( identity != inverse(X5)
| sk_c10 != multiply(X5,identity) )
| ~ spl3_22
| ~ spl3_23 ),
inference(forward_demodulation,[],[f370,f225]) ).
fof(f370,plain,
( ! [X5] :
( sk_c10 != multiply(X5,sk_c11)
| identity != inverse(X5) )
| ~ spl3_22
| ~ spl3_23 ),
inference(forward_demodulation,[],[f188,f225]) ).
fof(f188,plain,
( ! [X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(X5,sk_c11) )
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f187,plain,
( spl3_22
<=> ! [X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(X5,sk_c11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f369,plain,
( ~ spl3_6
| ~ spl3_10
| ~ spl3_21
| ~ spl3_23 ),
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f368,plain,
( $false
| ~ spl3_6
| ~ spl3_10
| ~ spl3_21
| ~ spl3_23 ),
inference(subsumption_resolution,[],[f367,f1]) ).
fof(f367,plain,
( identity != multiply(identity,identity)
| ~ spl3_6
| ~ spl3_10
| ~ spl3_21
| ~ spl3_23 ),
inference(trivial_inequality_removal,[],[f366]) ).
fof(f366,plain,
( identity != identity
| identity != multiply(identity,identity)
| ~ spl3_6
| ~ spl3_10
| ~ spl3_21
| ~ spl3_23 ),
inference(superposition,[],[f355,f312]) ).
fof(f355,plain,
( ! [X6] :
( identity != inverse(X6)
| identity != multiply(X6,identity) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_21
| ~ spl3_23 ),
inference(forward_demodulation,[],[f354,f293]) ).
fof(f293,plain,
( identity = sk_c9
| ~ spl3_6
| ~ spl3_10
| ~ spl3_23 ),
inference(backward_demodulation,[],[f287,f290]) ).
fof(f354,plain,
( ! [X6] :
( identity != inverse(X6)
| sk_c9 != multiply(X6,identity) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_21
| ~ spl3_23 ),
inference(forward_demodulation,[],[f353,f290]) ).
fof(f353,plain,
( ! [X6] :
( identity != inverse(X6)
| sk_c9 != multiply(X6,sk_c10) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_21
| ~ spl3_23 ),
inference(forward_demodulation,[],[f180,f290]) ).
fof(f180,plain,
( ! [X6] :
( sk_c10 != inverse(X6)
| sk_c9 != multiply(X6,sk_c10) )
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f179,plain,
( spl3_21
<=> ! [X6] :
( sk_c10 != inverse(X6)
| sk_c9 != multiply(X6,sk_c10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f352,plain,
( ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f351,plain,
( $false
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(subsumption_resolution,[],[f350,f312]) ).
fof(f350,plain,
( identity != inverse(identity)
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f349,f312]) ).
fof(f349,plain,
( identity != inverse(inverse(identity))
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f348,f312]) ).
fof(f348,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(subsumption_resolution,[],[f347,f312]) ).
fof(f347,plain,
( identity != inverse(inverse(inverse(identity)))
| identity != inverse(identity)
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f342,f312]) ).
fof(f342,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(superposition,[],[f339,f2]) ).
fof(f339,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(subsumption_resolution,[],[f338,f1]) ).
fof(f338,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| identity != inverse(inverse(X0))
| inverse(X0) != multiply(X0,identity) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f337,f312]) ).
fof(f337,plain,
( ! [X0] :
( identity != multiply(identity,inverse(identity))
| inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f336,f312]) ).
fof(f336,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,inverse(identity))
| identity != multiply(identity,inverse(identity))
| identity != inverse(inverse(X0)) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f335,f312]) ).
fof(f335,plain,
( ! [X0] :
( inverse(inverse(X0)) != inverse(identity)
| identity != multiply(identity,inverse(identity))
| inverse(X0) != multiply(X0,inverse(identity)) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(trivial_inequality_removal,[],[f333]) ).
fof(f333,plain,
( ! [X0] :
( identity != multiply(identity,inverse(identity))
| inverse(X0) != multiply(X0,inverse(identity))
| inverse(inverse(X0)) != inverse(identity)
| identity != identity )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(superposition,[],[f320,f2]) ).
fof(f320,plain,
( ! [X9,X7] :
( identity != multiply(inverse(X7),identity)
| inverse(X9) != multiply(X9,inverse(X7))
| inverse(X7) != inverse(inverse(X9))
| identity != multiply(X7,inverse(X7)) )
| ~ spl3_6
| ~ spl3_10
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f319,f290]) ).
fof(f319,plain,
( ! [X9,X7] :
( inverse(X9) != multiply(X9,inverse(X7))
| identity != multiply(inverse(X7),sk_c10)
| inverse(X7) != inverse(inverse(X9))
| identity != multiply(X7,inverse(X7)) )
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f274,f225]) ).
fof(f274,plain,
( ! [X9,X7] :
( sk_c11 != multiply(X7,inverse(X7))
| identity != multiply(inverse(X7),sk_c10)
| inverse(X7) != inverse(inverse(X9))
| inverse(X9) != multiply(X9,inverse(X7)) )
| ~ spl3_19
| ~ spl3_23 ),
inference(backward_demodulation,[],[f159,f225]) ).
fof(f159,plain,
( ! [X9,X7] :
( inverse(X9) != multiply(X9,inverse(X7))
| sk_c11 != multiply(inverse(X7),sk_c10)
| inverse(X7) != inverse(inverse(X9))
| sk_c11 != multiply(X7,inverse(X7)) )
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f158,plain,
( spl3_19
<=> ! [X9,X7] :
( inverse(X7) != inverse(inverse(X9))
| sk_c11 != multiply(inverse(X7),sk_c10)
| inverse(X9) != multiply(X9,inverse(X7))
| sk_c11 != multiply(X7,inverse(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f268,plain,
( spl3_23
| ~ spl3_2
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f267,f119,f69,f224]) ).
fof(f69,plain,
( spl3_2
<=> sk_c11 = multiply(sk_c1,sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f119,plain,
( spl3_12
<=> sk_c2 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f267,plain,
( identity = sk_c11
| ~ spl3_2
| ~ spl3_12 ),
inference(forward_demodulation,[],[f261,f2]) ).
fof(f261,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c2)
| ~ spl3_2
| ~ spl3_12 ),
inference(superposition,[],[f216,f245]) ).
fof(f245,plain,
( sk_c2 = multiply(sk_c2,sk_c11)
| ~ spl3_2
| ~ spl3_12 ),
inference(superposition,[],[f215,f71]) ).
fof(f71,plain,
( sk_c11 = multiply(sk_c1,sk_c2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f215,plain,
( ! [X12] : multiply(sk_c2,multiply(sk_c1,X12)) = X12
| ~ spl3_12 ),
inference(forward_demodulation,[],[f211,f1]) ).
fof(f211,plain,
( ! [X12] : multiply(sk_c2,multiply(sk_c1,X12)) = multiply(identity,X12)
| ~ spl3_12 ),
inference(superposition,[],[f3,f203]) ).
fof(f203,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl3_12 ),
inference(superposition,[],[f2,f121]) ).
fof(f121,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f243,plain,
( ~ spl3_2
| ~ spl3_4
| ~ spl3_8
| ~ spl3_12 ),
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f242,plain,
( $false
| ~ spl3_2
| ~ spl3_4
| ~ spl3_8
| ~ spl3_12 ),
inference(subsumption_resolution,[],[f241,f71]) ).
fof(f241,plain,
( sk_c11 != multiply(sk_c1,sk_c2)
| ~ spl3_4
| ~ spl3_8
| ~ spl3_12 ),
inference(subsumption_resolution,[],[f221,f80]) ).
fof(f80,plain,
( sk_c11 = multiply(sk_c2,sk_c10)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f78,plain,
( spl3_4
<=> sk_c11 = multiply(sk_c2,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f221,plain,
( sk_c11 != multiply(sk_c2,sk_c10)
| sk_c11 != multiply(sk_c1,sk_c2)
| ~ spl3_8
| ~ spl3_12 ),
inference(superposition,[],[f98,f121]) ).
fof(f98,plain,
( ! [X3] :
( sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c11 != multiply(X3,inverse(X3)) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f97,plain,
( spl3_8
<=> ! [X3] :
( sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c11 != multiply(X3,inverse(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f231,plain,
( ~ spl3_23
| ~ spl3_24
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f222,f97,f228,f224]) ).
fof(f222,plain,
( sk_c11 != multiply(sk_c10,inverse(sk_c10))
| identity != sk_c11
| ~ spl3_8 ),
inference(superposition,[],[f98,f2]) ).
fof(f201,plain,
( spl3_10
| spl3_11 ),
inference(avatar_split_clause,[],[f19,f113,f107]) ).
fof(f19,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c10 = multiply(sk_c11,sk_c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f200,plain,
( spl3_1
| spl3_12 ),
inference(avatar_split_clause,[],[f40,f119,f65]) ).
fof(f40,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c11 = multiply(sk_c8,sk_c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f198,plain,
( spl3_12
| spl3_5 ),
inference(avatar_split_clause,[],[f42,f83,f119]) ).
fof(f42,axiom,
( sk_c8 = inverse(sk_c6)
| sk_c2 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f197,plain,
( spl3_10
| spl3_15 ),
inference(avatar_split_clause,[],[f21,f134,f107]) ).
fof(f21,axiom,
( inverse(sk_c7) = sk_c6
| sk_c10 = multiply(sk_c11,sk_c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f196,plain,
( spl3_3
| spl3_12 ),
inference(avatar_split_clause,[],[f34,f119,f74]) ).
fof(f34,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f195,plain,
( spl3_17
| spl3_2 ),
inference(avatar_split_clause,[],[f28,f69,f144]) ).
fof(f28,axiom,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f191,plain,
( spl3_11
| spl3_2 ),
inference(avatar_split_clause,[],[f29,f69,f113]) ).
fof(f29,axiom,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f189,plain,
( spl3_18
| spl3_22 ),
inference(avatar_split_clause,[],[f62,f187,f154]) ).
fof(f154,plain,
( spl3_18
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f62,plain,
! [X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(X5,sk_c11)
| sP2 ),
inference(cnf_transformation,[],[f62_D]) ).
fof(f62_D,plain,
( ! [X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(X5,sk_c11) )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f185,plain,
( spl3_10
| spl3_17 ),
inference(avatar_split_clause,[],[f18,f144,f107]) ).
fof(f18,axiom,
( sk_c11 = multiply(sk_c5,sk_c8)
| sk_c10 = multiply(sk_c11,sk_c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f181,plain,
( spl3_20
| spl3_21 ),
inference(avatar_split_clause,[],[f60,f179,f161]) ).
fof(f161,plain,
( spl3_20
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f60,plain,
! [X6] :
( sk_c10 != inverse(X6)
| sk_c9 != multiply(X6,sk_c10)
| sP1 ),
inference(cnf_transformation,[],[f60_D]) ).
fof(f60_D,plain,
( ! [X6] :
( sk_c10 != inverse(X6)
| sk_c9 != multiply(X6,sk_c10) )
<=> ~ sP1 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f177,plain,
( spl3_2
| spl3_15 ),
inference(avatar_split_clause,[],[f31,f134,f69]) ).
fof(f31,axiom,
( inverse(sk_c7) = sk_c6
| sk_c11 = multiply(sk_c1,sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f176,plain,
( spl3_16
| spl3_12 ),
inference(avatar_split_clause,[],[f35,f119,f139]) ).
fof(f35,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f173,plain,
( spl3_16
| spl3_4 ),
inference(avatar_split_clause,[],[f45,f78,f139]) ).
fof(f45,axiom,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c11 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f172,plain,
( spl3_17
| spl3_12 ),
inference(avatar_split_clause,[],[f38,f119,f144]) ).
fof(f38,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f170,plain,
( spl3_13
| spl3_10 ),
inference(avatar_split_clause,[],[f17,f107,f124]) ).
fof(f17,axiom,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f168,plain,
( spl3_16
| spl3_2 ),
inference(avatar_split_clause,[],[f25,f69,f139]) ).
fof(f25,axiom,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c11 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f164,plain,
( ~ spl3_6
| ~ spl3_7
| ~ spl3_18
| ~ spl3_10
| spl3_19
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f63,f161,f158,f107,f154,f93,f87]) ).
fof(f93,plain,
( spl3_7
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f63,plain,
! [X9,X7] :
( ~ sP1
| inverse(X7) != inverse(inverse(X9))
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c11 != multiply(X7,inverse(X7))
| ~ sP2
| ~ sP0
| inverse(sk_c11) != sk_c10
| inverse(X9) != multiply(X9,inverse(X7))
| sk_c11 != multiply(inverse(X7),sk_c10) ),
inference(general_splitting,[],[f61,f62_D]) ).
fof(f61,plain,
! [X9,X7,X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(sk_c11,sk_c9)
| inverse(X7) != inverse(inverse(X9))
| sk_c11 != multiply(X7,inverse(X7))
| sk_c11 != multiply(inverse(X7),sk_c10)
| inverse(X9) != multiply(X9,inverse(X7))
| sk_c10 != multiply(X5,sk_c11)
| inverse(sk_c11) != sk_c10
| ~ sP0
| ~ sP1 ),
inference(general_splitting,[],[f59,f60_D]) ).
fof(f59,plain,
! [X6,X9,X7,X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(sk_c11,sk_c9)
| inverse(X7) != inverse(inverse(X9))
| sk_c9 != multiply(X6,sk_c10)
| sk_c10 != inverse(X6)
| sk_c11 != multiply(X7,inverse(X7))
| sk_c11 != multiply(inverse(X7),sk_c10)
| inverse(X9) != multiply(X9,inverse(X7))
| sk_c10 != multiply(X5,sk_c11)
| inverse(sk_c11) != sk_c10
| ~ sP0 ),
inference(general_splitting,[],[f57,f58_D]) ).
fof(f58,plain,
! [X3] :
( sk_c11 != multiply(inverse(X3),sk_c10)
| sP0
| sk_c11 != multiply(X3,inverse(X3)) ),
inference(cnf_transformation,[],[f58_D]) ).
fof(f58_D,plain,
( ! [X3] :
( sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c11 != multiply(X3,inverse(X3)) )
<=> ~ sP0 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f57,plain,
! [X3,X6,X9,X7,X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(sk_c11,sk_c9)
| inverse(X7) != inverse(inverse(X9))
| sk_c9 != multiply(X6,sk_c10)
| sk_c10 != inverse(X6)
| sk_c11 != multiply(X7,inverse(X7))
| sk_c11 != multiply(X3,inverse(X3))
| sk_c11 != multiply(inverse(X7),sk_c10)
| inverse(X9) != multiply(X9,inverse(X7))
| sk_c11 != multiply(inverse(X3),sk_c10)
| sk_c10 != multiply(X5,sk_c11)
| inverse(sk_c11) != sk_c10 ),
inference(equality_resolution,[],[f56]) ).
fof(f56,plain,
! [X3,X6,X9,X7,X4,X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(sk_c11,sk_c9)
| inverse(X7) != inverse(inverse(X9))
| sk_c9 != multiply(X6,sk_c10)
| sk_c10 != inverse(X6)
| sk_c11 != multiply(X7,inverse(X7))
| sk_c11 != multiply(X3,X4)
| sk_c11 != multiply(inverse(X7),sk_c10)
| inverse(X9) != multiply(X9,inverse(X7))
| sk_c11 != multiply(X4,sk_c10)
| inverse(X3) != X4
| sk_c10 != multiply(X5,sk_c11)
| inverse(sk_c11) != sk_c10 ),
inference(equality_resolution,[],[f55]) ).
fof(f55,plain,
! [X3,X10,X6,X9,X7,X4,X5] :
( sk_c11 != inverse(X5)
| sk_c10 != multiply(sk_c11,sk_c9)
| inverse(X9) != X10
| inverse(X7) != inverse(X10)
| sk_c9 != multiply(X6,sk_c10)
| sk_c10 != inverse(X6)
| sk_c11 != multiply(X7,inverse(X7))
| sk_c11 != multiply(X3,X4)
| sk_c11 != multiply(inverse(X7),sk_c10)
| multiply(X9,inverse(X7)) != X10
| sk_c11 != multiply(X4,sk_c10)
| inverse(X3) != X4
| sk_c10 != multiply(X5,sk_c11)
| inverse(sk_c11) != sk_c10 ),
inference(equality_resolution,[],[f54]) ).
fof(f54,axiom,
! [X3,X10,X8,X6,X9,X7,X4,X5] :
( inverse(X7) != X8
| sk_c11 != inverse(X5)
| sk_c10 != multiply(sk_c11,sk_c9)
| inverse(X9) != X10
| inverse(X10) != X8
| sk_c9 != multiply(X6,sk_c10)
| sk_c10 != inverse(X6)
| sk_c11 != multiply(X7,X8)
| sk_c11 != multiply(X3,X4)
| sk_c11 != multiply(X8,sk_c10)
| multiply(X9,X8) != X10
| sk_c11 != multiply(X4,sk_c10)
| inverse(X3) != X4
| sk_c10 != multiply(X5,sk_c11)
| inverse(sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f152,plain,
( spl3_6
| spl3_3 ),
inference(avatar_split_clause,[],[f4,f74,f87]) ).
fof(f4,axiom,
( sk_c10 = multiply(sk_c3,sk_c11)
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f150,plain,
( spl3_1
| spl3_10 ),
inference(avatar_split_clause,[],[f20,f107,f65]) ).
fof(f20,axiom,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = multiply(sk_c8,sk_c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f149,plain,
( spl3_16
| spl3_6 ),
inference(avatar_split_clause,[],[f5,f87,f139]) ).
fof(f5,axiom,
( inverse(sk_c11) = sk_c10
| sk_c11 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f142,plain,
( spl3_16
| spl3_10 ),
inference(avatar_split_clause,[],[f15,f107,f139]) ).
fof(f15,axiom,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f137,plain,
( spl3_12
| spl3_15 ),
inference(avatar_split_clause,[],[f41,f134,f119]) ).
fof(f41,axiom,
( inverse(sk_c7) = sk_c6
| sk_c2 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f132,plain,
( spl3_12
| spl3_14 ),
inference(avatar_split_clause,[],[f43,f129,f119]) ).
fof(f43,axiom,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c2 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f122,plain,
( spl3_12
| spl3_11 ),
inference(avatar_split_clause,[],[f39,f113,f119]) ).
fof(f39,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c2 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f117,plain,
( spl3_9
| spl3_10 ),
inference(avatar_split_clause,[],[f16,f107,f102]) ).
fof(f16,axiom,
( sk_c10 = multiply(sk_c11,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f111,plain,
( spl3_10
| spl3_3 ),
inference(avatar_split_clause,[],[f14,f74,f107]) ).
fof(f14,axiom,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c10 = multiply(sk_c11,sk_c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f110,plain,
( spl3_5
| spl3_10 ),
inference(avatar_split_clause,[],[f22,f107,f83]) ).
fof(f22,axiom,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c8 = inverse(sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f100,plain,
( spl3_2
| spl3_5 ),
inference(avatar_split_clause,[],[f32,f83,f69]) ).
fof(f32,axiom,
( sk_c8 = inverse(sk_c6)
| sk_c11 = multiply(sk_c1,sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f99,plain,
( spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f58,f97,f93]) ).
fof(f91,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f24,f74,f69]) ).
fof(f24,axiom,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c11 = multiply(sk_c1,sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f81,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f44,f78,f74]) ).
fof(f44,axiom,
( sk_c11 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f72,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f30,f69,f65]) ).
fof(f30,axiom,
( sk_c11 = multiply(sk_c1,sk_c2)
| sk_c11 = multiply(sk_c8,sk_c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP378-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 22:11:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (12470)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)
% 0.20/0.51 % (12483)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51 % (12478)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52 TRYING [1]
% 0.20/0.52 % (12487)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.52 % (12482)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.52 % (12474)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 TRYING [1]
% 0.20/0.52 % (12471)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)
% 0.20/0.52 % (12472)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)
% 0.20/0.53 TRYING [2]
% 0.20/0.53 % (12486)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)
% 0.20/0.53 TRYING [3]
% 0.20/0.53 % (12491)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.53 % (12492)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)
% 0.20/0.53 % (12480)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (12479)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)
% 0.20/0.53 % (12475)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)
% 0.20/0.53 TRYING [2]
% 0.20/0.53 % (12484)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)
% 0.20/0.53 % (12493)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)
% 0.20/0.53 % (12481)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)
% 0.20/0.53 % (12495)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.53 % (12478)Instruction limit reached!
% 0.20/0.53 % (12478)------------------------------
% 0.20/0.53 % (12478)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (12478)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (12478)Termination reason: Unknown
% 0.20/0.53 % (12478)Termination phase: Saturation
% 0.20/0.53
% 0.20/0.53 % (12478)Memory used [KB]: 895
% 0.20/0.53 % (12478)Time elapsed: 0.003 s
% 0.20/0.53 % (12478)Instructions burned: 2 (million)
% 0.20/0.53 % (12478)------------------------------
% 0.20/0.53 % (12478)------------------------------
% 0.20/0.53 % (12477)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.54 TRYING [3]
% 0.20/0.54 % (12499)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)
% 0.20/0.54 % (12477)Instruction limit reached!
% 0.20/0.54 % (12477)------------------------------
% 0.20/0.54 % (12477)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (12477)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (12477)Termination reason: Unknown
% 0.20/0.54 % (12477)Termination phase: Saturation
% 0.20/0.54
% 0.20/0.54 % (12477)Memory used [KB]: 5628
% 0.20/0.54 % (12477)Time elapsed: 0.135 s
% 0.20/0.54 % (12485)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)
% 0.20/0.54 % (12494)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.54 TRYING [4]
% 0.20/0.54 % (12497)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)
% 0.20/0.54 % (12496)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)
% 0.20/0.54 % (12488)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54 % (12473)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)
% 0.20/0.54 % (12498)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54 % (12477)Instructions burned: 9 (million)
% 0.20/0.54 % (12477)------------------------------
% 0.20/0.54 % (12477)------------------------------
% 0.20/0.54 % (12476)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)
% 0.20/0.55 % (12489)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)
% 0.20/0.56 % (12490)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)
% 0.20/0.56 TRYING [1]
% 0.20/0.56 TRYING [2]
% 0.20/0.57 TRYING [3]
% 0.20/0.58 % (12491)First to succeed.
% 0.20/0.58 % (12472)Instruction limit reached!
% 0.20/0.58 % (12472)------------------------------
% 0.20/0.58 % (12472)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58 % (12472)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58 % (12472)Termination reason: Unknown
% 0.20/0.58 % (12472)Termination phase: Saturation
% 0.20/0.58
% 0.20/0.58 % (12472)Memory used [KB]: 1279
% 0.20/0.58 % (12472)Time elapsed: 0.174 s
% 0.20/0.58 % (12472)Instructions burned: 38 (million)
% 0.20/0.58 % (12472)------------------------------
% 0.20/0.58 % (12472)------------------------------
% 0.20/0.58 % (12491)Refutation found. Thanks to Tanya!
% 0.20/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.58 % (12491)------------------------------
% 0.20/0.58 % (12491)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58 % (12491)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58 % (12491)Termination reason: Refutation
% 0.20/0.58
% 0.20/0.58 % (12491)Memory used [KB]: 5756
% 0.20/0.58 % (12491)Time elapsed: 0.170 s
% 0.20/0.58 % (12491)Instructions burned: 18 (million)
% 0.20/0.58 % (12491)------------------------------
% 0.20/0.58 % (12491)------------------------------
% 0.20/0.58 % (12469)Success in time 0.228 s
%------------------------------------------------------------------------------