TSTP Solution File: GRP389-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP389-1 : 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 : n013.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 16:21:31 EDT 2022
% Result : Unsatisfiable 2.49s 0.67s
% Output : Refutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 66
% Syntax : Number of formulae : 264 ( 7 unt; 0 def)
% Number of atoms : 865 ( 334 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1160 ( 559 ~; 568 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 34 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 82 ( 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1167,plain,
$false,
inference(avatar_sat_refutation,[],[f79,f96,f106,f125,f149,f151,f154,f155,f163,f164,f172,f173,f174,f175,f181,f182,f183,f184,f185,f187,f200,f201,f202,f203,f205,f206,f208,f209,f210,f212,f213,f215,f216,f218,f221,f241,f408,f424,f636,f639,f641,f681,f701,f739,f870,f875,f1009,f1061,f1064,f1166]) ).
fof(f1166,plain,
( spl5_37
| ~ spl5_1
| ~ spl5_14 ),
inference(avatar_split_clause,[],[f1165,f134,f72,f621]) ).
fof(f621,plain,
( spl5_37
<=> identity = sk_c10 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).
fof(f72,plain,
( spl5_1
<=> sk_c10 = multiply(sk_c2,sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f134,plain,
( spl5_14
<=> sk_c3 = inverse(sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f1165,plain,
( identity = sk_c10
| ~ spl5_1
| ~ spl5_14 ),
inference(forward_demodulation,[],[f1154,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f1154,plain,
( sk_c10 = multiply(inverse(sk_c3),sk_c3)
| ~ spl5_1
| ~ spl5_14 ),
inference(superposition,[],[f266,f578]) ).
fof(f578,plain,
( sk_c3 = multiply(sk_c3,sk_c10)
| ~ spl5_1
| ~ spl5_14 ),
inference(forward_demodulation,[],[f576,f136]) ).
fof(f136,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f576,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c10)
| ~ spl5_1 ),
inference(superposition,[],[f266,f74]) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c2,sk_c3)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f266,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
inference(forward_demodulation,[],[f259,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f259,plain,
! [X6,X7] : multiply(identity,X7) = multiply(inverse(X6),multiply(X6,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(f1064,plain,
( spl5_37
| ~ spl5_16
| ~ spl5_42 ),
inference(avatar_split_clause,[],[f1063,f674,f145,f621]) ).
fof(f145,plain,
( spl5_16
<=> inverse(sk_c10) = sk_c9 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).
fof(f674,plain,
( spl5_42
<=> identity = sk_c9 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).
fof(f1063,plain,
( identity = sk_c10
| ~ spl5_16
| ~ spl5_42 ),
inference(forward_demodulation,[],[f1062,f2]) ).
fof(f1062,plain,
( sk_c10 = multiply(inverse(identity),identity)
| ~ spl5_16
| ~ spl5_42 ),
inference(forward_demodulation,[],[f733,f675]) ).
fof(f675,plain,
( identity = sk_c9
| ~ spl5_42 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f733,plain,
( sk_c10 = multiply(inverse(sk_c9),identity)
| ~ spl5_16 ),
inference(superposition,[],[f266,f575]) ).
fof(f575,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl5_16 ),
inference(superposition,[],[f2,f147]) ).
fof(f147,plain,
( inverse(sk_c10) = sk_c9
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f1061,plain,
( ~ spl5_16
| ~ spl5_37
| ~ spl5_42
| spl5_43 ),
inference(avatar_contradiction_clause,[],[f1060]) ).
fof(f1060,plain,
( $false
| ~ spl5_16
| ~ spl5_37
| ~ spl5_42
| spl5_43 ),
inference(trivial_inequality_removal,[],[f1059]) ).
fof(f1059,plain,
( identity != identity
| ~ spl5_16
| ~ spl5_37
| ~ spl5_42
| spl5_43 ),
inference(superposition,[],[f1019,f1045]) ).
fof(f1045,plain,
( identity = inverse(identity)
| ~ spl5_16
| ~ spl5_37
| ~ spl5_42 ),
inference(forward_demodulation,[],[f783,f675]) ).
fof(f783,plain,
( sk_c9 = inverse(identity)
| ~ spl5_16
| ~ spl5_37 ),
inference(backward_demodulation,[],[f147,f622]) ).
fof(f622,plain,
( identity = sk_c10
| ~ spl5_37 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f1019,plain,
( identity != inverse(identity)
| ~ spl5_37
| ~ spl5_42
| spl5_43 ),
inference(forward_demodulation,[],[f1018,f622]) ).
fof(f1018,plain,
( sk_c10 != inverse(identity)
| ~ spl5_42
| spl5_43 ),
inference(forward_demodulation,[],[f680,f675]) ).
fof(f680,plain,
( sk_c10 != inverse(sk_c9)
| spl5_43 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f678,plain,
( spl5_43
<=> sk_c10 = inverse(sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).
fof(f1009,plain,
( ~ spl5_9
| ~ spl5_12
| ~ spl5_18
| ~ spl5_37 ),
inference(avatar_contradiction_clause,[],[f1008]) ).
fof(f1008,plain,
( $false
| ~ spl5_9
| ~ spl5_12
| ~ spl5_18
| ~ spl5_37 ),
inference(trivial_inequality_removal,[],[f1007]) ).
fof(f1007,plain,
( sk_c11 != sk_c11
| ~ spl5_9
| ~ spl5_12
| ~ spl5_18
| ~ spl5_37 ),
inference(superposition,[],[f995,f998]) ).
fof(f998,plain,
( sk_c11 = inverse(sk_c11)
| ~ spl5_9
| ~ spl5_12
| ~ spl5_37 ),
inference(backward_demodulation,[],[f124,f997]) ).
fof(f997,plain,
( sk_c11 = sk_c1
| ~ spl5_9
| ~ spl5_12
| ~ spl5_37 ),
inference(backward_demodulation,[],[f729,f993]) ).
fof(f993,plain,
( sk_c11 = multiply(inverse(sk_c11),identity)
| ~ spl5_9
| ~ spl5_12
| ~ spl5_37 ),
inference(superposition,[],[f266,f797]) ).
fof(f797,plain,
( identity = multiply(sk_c11,sk_c11)
| ~ spl5_9
| ~ spl5_12
| ~ spl5_37 ),
inference(backward_demodulation,[],[f586,f622]) ).
fof(f586,plain,
( sk_c10 = multiply(sk_c11,sk_c11)
| ~ spl5_9
| ~ spl5_12 ),
inference(forward_demodulation,[],[f584,f124]) ).
fof(f584,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c11)
| ~ spl5_9 ),
inference(superposition,[],[f266,f110]) ).
fof(f110,plain,
( sk_c11 = multiply(sk_c1,sk_c10)
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f108,plain,
( spl5_9
<=> sk_c11 = multiply(sk_c1,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f729,plain,
( sk_c1 = multiply(inverse(sk_c11),identity)
| ~ spl5_12 ),
inference(superposition,[],[f266,f571]) ).
fof(f571,plain,
( identity = multiply(sk_c11,sk_c1)
| ~ spl5_12 ),
inference(superposition,[],[f2,f124]) ).
fof(f124,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f122,plain,
( spl5_12
<=> sk_c11 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f995,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl5_9
| ~ spl5_12
| ~ spl5_18
| ~ spl5_37 ),
inference(trivial_inequality_removal,[],[f992]) ).
fof(f992,plain,
( identity != identity
| sk_c11 != inverse(sk_c11)
| ~ spl5_9
| ~ spl5_12
| ~ spl5_18
| ~ spl5_37 ),
inference(superposition,[],[f893,f797]) ).
fof(f893,plain,
( ! [X6] :
( identity != multiply(X6,sk_c11)
| sk_c11 != inverse(X6) )
| ~ spl5_18
| ~ spl5_37 ),
inference(forward_demodulation,[],[f162,f622]) ).
fof(f162,plain,
( ! [X6] :
( sk_c10 != multiply(X6,sk_c11)
| sk_c11 != inverse(X6) )
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f161,plain,
( spl5_18
<=> ! [X6] :
( sk_c10 != multiply(X6,sk_c11)
| sk_c11 != inverse(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
fof(f875,plain,
( spl5_42
| ~ spl5_1
| ~ spl5_4
| ~ spl5_14
| ~ spl5_16
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f874,f621,f145,f134,f85,f72,f674]) ).
fof(f85,plain,
( spl5_4
<=> sk_c10 = multiply(sk_c3,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f874,plain,
( identity = sk_c9
| ~ spl5_1
| ~ spl5_4
| ~ spl5_14
| ~ spl5_16
| ~ spl5_37 ),
inference(forward_demodulation,[],[f873,f2]) ).
fof(f873,plain,
( sk_c9 = multiply(inverse(identity),identity)
| ~ spl5_1
| ~ spl5_4
| ~ spl5_14
| ~ spl5_16
| ~ spl5_37 ),
inference(forward_demodulation,[],[f803,f856]) ).
fof(f856,plain,
( identity = sk_c3
| ~ spl5_1
| ~ spl5_4
| ~ spl5_14
| ~ spl5_16
| ~ spl5_37 ),
inference(backward_demodulation,[],[f796,f854]) ).
fof(f854,plain,
( ! [X0] : multiply(sk_c3,X0) = X0
| ~ spl5_4
| ~ spl5_16
| ~ spl5_37 ),
inference(forward_demodulation,[],[f853,f1]) ).
fof(f853,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c3,X0)
| ~ spl5_4
| ~ spl5_16
| ~ spl5_37 ),
inference(forward_demodulation,[],[f804,f814]) ).
fof(f814,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl5_16
| ~ spl5_37 ),
inference(backward_demodulation,[],[f279,f783]) ).
fof(f279,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f266,f1]) ).
fof(f804,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c3,multiply(sk_c9,X0))
| ~ spl5_4
| ~ spl5_37 ),
inference(backward_demodulation,[],[f692,f622]) ).
fof(f692,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c9,X0)) = multiply(sk_c10,X0)
| ~ spl5_4 ),
inference(superposition,[],[f3,f87]) ).
fof(f87,plain,
( sk_c10 = multiply(sk_c3,sk_c9)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f796,plain,
( sk_c3 = multiply(sk_c3,identity)
| ~ spl5_1
| ~ spl5_14
| ~ spl5_37 ),
inference(backward_demodulation,[],[f578,f622]) ).
fof(f803,plain,
( sk_c9 = multiply(inverse(sk_c3),identity)
| ~ spl5_4
| ~ spl5_37 ),
inference(backward_demodulation,[],[f691,f622]) ).
fof(f691,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c10)
| ~ spl5_4 ),
inference(superposition,[],[f266,f87]) ).
fof(f870,plain,
( spl5_42
| ~ spl5_16
| ~ spl5_21
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f869,f621,f177,f145,f674]) ).
fof(f177,plain,
( spl5_21
<=> sk_c9 = multiply(sk_c5,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).
fof(f869,plain,
( identity = sk_c9
| ~ spl5_16
| ~ spl5_21
| ~ spl5_37 ),
inference(forward_demodulation,[],[f784,f816]) ).
fof(f816,plain,
( ! [X9] : multiply(sk_c5,X9) = X9
| ~ spl5_16
| ~ spl5_21
| ~ spl5_37 ),
inference(forward_demodulation,[],[f815,f1]) ).
fof(f815,plain,
( ! [X9] : multiply(sk_c5,multiply(identity,X9)) = X9
| ~ spl5_16
| ~ spl5_21
| ~ spl5_37 ),
inference(forward_demodulation,[],[f787,f814]) ).
fof(f787,plain,
( ! [X9] : multiply(sk_c5,multiply(identity,X9)) = multiply(sk_c9,X9)
| ~ spl5_21
| ~ spl5_37 ),
inference(backward_demodulation,[],[f261,f622]) ).
fof(f261,plain,
( ! [X9] : multiply(sk_c5,multiply(sk_c10,X9)) = multiply(sk_c9,X9)
| ~ spl5_21 ),
inference(superposition,[],[f3,f179]) ).
fof(f179,plain,
( sk_c9 = multiply(sk_c5,sk_c10)
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f784,plain,
( sk_c9 = multiply(sk_c5,identity)
| ~ spl5_21
| ~ spl5_37 ),
inference(backward_demodulation,[],[f179,f622]) ).
fof(f739,plain,
( spl5_42
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f738,f607,f674]) ).
fof(f607,plain,
( spl5_34
<=> sk_c10 = multiply(sk_c10,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).
fof(f738,plain,
( identity = sk_c9
| ~ spl5_34 ),
inference(forward_demodulation,[],[f736,f2]) ).
fof(f736,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl5_34 ),
inference(superposition,[],[f266,f608]) ).
fof(f608,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl5_34 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f701,plain,
( ~ spl5_12
| ~ spl5_9
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f700,f166,f108,f122]) ).
fof(f166,plain,
( spl5_19
<=> ! [X3] :
( sk_c11 != multiply(X3,sk_c10)
| sk_c11 != inverse(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).
fof(f700,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl5_9
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f698]) ).
fof(f698,plain,
( sk_c11 != inverse(sk_c1)
| sk_c11 != sk_c11
| ~ spl5_9
| ~ spl5_19 ),
inference(superposition,[],[f167,f110]) ).
fof(f167,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c10)
| sk_c11 != inverse(X3) )
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f681,plain,
( ~ spl5_42
| ~ spl5_43
| ~ spl5_6
| ~ spl5_16 ),
inference(avatar_split_clause,[],[f672,f145,f94,f678,f674]) ).
fof(f94,plain,
( spl5_6
<=> ! [X7] :
( sk_c9 != multiply(X7,sk_c10)
| sk_c10 != inverse(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f672,plain,
( sk_c10 != inverse(sk_c9)
| identity != sk_c9
| ~ spl5_6
| ~ spl5_16 ),
inference(forward_demodulation,[],[f656,f147]) ).
fof(f656,plain,
( sk_c10 != inverse(inverse(sk_c10))
| identity != sk_c9
| ~ spl5_6 ),
inference(superposition,[],[f95,f2]) ).
fof(f95,plain,
( ! [X7] :
( sk_c9 != multiply(X7,sk_c10)
| sk_c10 != inverse(X7) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f641,plain,
( spl5_34
| ~ spl5_10
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f640,f177,f113,f607]) ).
fof(f113,plain,
( spl5_10
<=> sk_c10 = inverse(sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f640,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl5_10
| ~ spl5_21 ),
inference(backward_demodulation,[],[f287,f115]) ).
fof(f115,plain,
( sk_c10 = inverse(sk_c5)
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f287,plain,
( sk_c10 = multiply(inverse(sk_c5),sk_c9)
| ~ spl5_21 ),
inference(superposition,[],[f266,f179]) ).
fof(f639,plain,
( ~ spl5_15
| ~ spl5_2
| ~ spl5_8
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f638,f198,f103,f76,f140]) ).
fof(f140,plain,
( spl5_15
<=> sk_c10 = multiply(sk_c8,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
fof(f76,plain,
( spl5_2
<=> sk_c10 = multiply(sk_c7,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f103,plain,
( spl5_8
<=> sk_c8 = inverse(sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f198,plain,
( spl5_24
<=> ! [X4] :
( sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X4),sk_c9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).
fof(f638,plain,
( sk_c10 != multiply(sk_c8,sk_c9)
| ~ spl5_2
| ~ spl5_8
| ~ spl5_24 ),
inference(trivial_inequality_removal,[],[f637]) ).
fof(f637,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c8,sk_c9)
| ~ spl5_2
| ~ spl5_8
| ~ spl5_24 ),
inference(forward_demodulation,[],[f598,f78]) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f598,plain,
( sk_c10 != multiply(sk_c8,sk_c9)
| sk_c10 != multiply(sk_c7,sk_c8)
| ~ spl5_8
| ~ spl5_24 ),
inference(superposition,[],[f199,f105]) ).
fof(f105,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f199,plain,
( ! [X4] :
( sk_c10 != multiply(inverse(X4),sk_c9)
| sk_c10 != multiply(X4,inverse(X4)) )
| ~ spl5_24 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f636,plain,
( ~ spl5_4
| ~ spl5_1
| ~ spl5_14
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f635,f198,f134,f72,f85]) ).
fof(f635,plain,
( sk_c10 != multiply(sk_c3,sk_c9)
| ~ spl5_1
| ~ spl5_14
| ~ spl5_24 ),
inference(trivial_inequality_removal,[],[f634]) ).
fof(f634,plain,
( sk_c10 != multiply(sk_c3,sk_c9)
| sk_c10 != sk_c10
| ~ spl5_1
| ~ spl5_14
| ~ spl5_24 ),
inference(forward_demodulation,[],[f600,f74]) ).
fof(f600,plain,
( sk_c10 != multiply(sk_c3,sk_c9)
| sk_c10 != multiply(sk_c2,sk_c3)
| ~ spl5_14
| ~ spl5_24 ),
inference(superposition,[],[f199,f136]) ).
fof(f424,plain,
( ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(avatar_contradiction_clause,[],[f423]) ).
fof(f423,plain,
( $false
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(trivial_inequality_removal,[],[f422]) ).
fof(f422,plain,
( sk_c4 != sk_c4
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(superposition,[],[f419,f369]) ).
fof(f369,plain,
( sk_c4 = inverse(sk_c4)
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13 ),
inference(backward_demodulation,[],[f100,f368]) ).
fof(f368,plain,
( sk_c4 = sk_c11
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13 ),
inference(forward_demodulation,[],[f367,f1]) ).
fof(f367,plain,
( sk_c11 = multiply(identity,sk_c4)
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13 ),
inference(forward_demodulation,[],[f350,f349]) ).
fof(f349,plain,
( sk_c11 = multiply(sk_c4,identity)
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13 ),
inference(backward_demodulation,[],[f302,f337]) ).
fof(f337,plain,
( identity = sk_c10
| ~ spl5_7
| ~ spl5_11 ),
inference(forward_demodulation,[],[f335,f2]) ).
fof(f335,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl5_7
| ~ spl5_11 ),
inference(superposition,[],[f266,f295]) ).
fof(f295,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl5_7
| ~ spl5_11 ),
inference(forward_demodulation,[],[f284,f100]) ).
fof(f284,plain,
( sk_c11 = multiply(inverse(sk_c4),sk_c10)
| ~ spl5_11 ),
inference(superposition,[],[f266,f120]) ).
fof(f120,plain,
( sk_c10 = multiply(sk_c4,sk_c11)
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f118,plain,
( spl5_11
<=> sk_c10 = multiply(sk_c4,sk_c11) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f302,plain,
( sk_c11 = multiply(sk_c4,sk_c10)
| ~ spl5_3
| ~ spl5_7
| ~ spl5_13 ),
inference(backward_demodulation,[],[f131,f298]) ).
fof(f298,plain,
( sk_c4 = sk_c6
| ~ spl5_3
| ~ spl5_7 ),
inference(forward_demodulation,[],[f286,f285]) ).
fof(f285,plain,
( sk_c4 = multiply(inverse(sk_c11),identity)
| ~ spl5_7 ),
inference(superposition,[],[f266,f223]) ).
fof(f223,plain,
( identity = multiply(sk_c11,sk_c4)
| ~ spl5_7 ),
inference(superposition,[],[f2,f100]) ).
fof(f286,plain,
( sk_c6 = multiply(inverse(sk_c11),identity)
| ~ spl5_3 ),
inference(superposition,[],[f266,f225]) ).
fof(f225,plain,
( identity = multiply(sk_c11,sk_c6)
| ~ spl5_3 ),
inference(superposition,[],[f2,f83]) ).
fof(f83,plain,
( sk_c11 = inverse(sk_c6)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f81,plain,
( spl5_3
<=> sk_c11 = inverse(sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f131,plain,
( sk_c11 = multiply(sk_c6,sk_c10)
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f129,plain,
( spl5_13
<=> sk_c11 = multiply(sk_c6,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f350,plain,
( multiply(identity,sk_c4) = multiply(sk_c4,identity)
| ~ spl5_7
| ~ spl5_11 ),
inference(backward_demodulation,[],[f307,f337]) ).
fof(f307,plain,
( multiply(sk_c10,sk_c4) = multiply(sk_c4,identity)
| ~ spl5_7
| ~ spl5_11 ),
inference(superposition,[],[f260,f223]) ).
fof(f260,plain,
( ! [X8] : multiply(sk_c10,X8) = multiply(sk_c4,multiply(sk_c11,X8))
| ~ spl5_11 ),
inference(superposition,[],[f3,f120]) ).
fof(f100,plain,
( sk_c11 = inverse(sk_c4)
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f98,plain,
( spl5_7
<=> sk_c11 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f419,plain,
( sk_c4 != inverse(sk_c4)
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(forward_demodulation,[],[f418,f369]) ).
fof(f418,plain,
( sk_c4 != inverse(inverse(sk_c4))
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(trivial_inequality_removal,[],[f417]) ).
fof(f417,plain,
( sk_c4 != inverse(inverse(sk_c4))
| identity != identity
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(superposition,[],[f414,f2]) ).
fof(f414,plain,
( ! [X6] :
( identity != multiply(X6,sk_c4)
| sk_c4 != inverse(X6) )
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(forward_demodulation,[],[f413,f337]) ).
fof(f413,plain,
( ! [X6] :
( sk_c10 != multiply(X6,sk_c4)
| sk_c4 != inverse(X6) )
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(forward_demodulation,[],[f412,f368]) ).
fof(f412,plain,
( ! [X6] :
( sk_c10 != multiply(X6,sk_c11)
| sk_c4 != inverse(X6) )
| ~ spl5_3
| ~ spl5_7
| ~ spl5_11
| ~ spl5_13
| ~ spl5_18 ),
inference(forward_demodulation,[],[f162,f368]) ).
fof(f408,plain,
( ~ spl5_2
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| spl5_16
| ~ spl5_21 ),
inference(avatar_contradiction_clause,[],[f407]) ).
fof(f407,plain,
( $false
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| spl5_16
| ~ spl5_21 ),
inference(trivial_inequality_removal,[],[f404]) ).
fof(f404,plain,
( identity != identity
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| spl5_16
| ~ spl5_21 ),
inference(superposition,[],[f353,f385]) ).
fof(f385,plain,
( identity = inverse(identity)
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| ~ spl5_21 ),
inference(backward_demodulation,[],[f363,f383]) ).
fof(f383,plain,
( identity = sk_c8
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| ~ spl5_21 ),
inference(forward_demodulation,[],[f346,f364]) ).
fof(f364,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| ~ spl5_21 ),
inference(forward_demodulation,[],[f361,f1]) ).
fof(f361,plain,
( ! [X0] : multiply(sk_c8,multiply(identity,X0)) = X0
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| ~ spl5_21 ),
inference(backward_demodulation,[],[f274,f360]) ).
fof(f360,plain,
( identity = sk_c7
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| ~ spl5_21 ),
inference(backward_demodulation,[],[f291,f355]) ).
fof(f355,plain,
( identity = multiply(inverse(sk_c8),identity)
| ~ spl5_7
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| ~ spl5_21 ),
inference(backward_demodulation,[],[f321,f337]) ).
fof(f321,plain,
( identity = multiply(inverse(sk_c8),sk_c10)
| ~ spl5_10
| ~ spl5_15
| ~ spl5_21 ),
inference(backward_demodulation,[],[f290,f315]) ).
fof(f315,plain,
( identity = sk_c9
| ~ spl5_10
| ~ spl5_21 ),
inference(forward_demodulation,[],[f313,f2]) ).
fof(f313,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl5_10
| ~ spl5_21 ),
inference(superposition,[],[f266,f294]) ).
fof(f294,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl5_10
| ~ spl5_21 ),
inference(forward_demodulation,[],[f287,f115]) ).
fof(f290,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c10)
| ~ spl5_15 ),
inference(superposition,[],[f266,f142]) ).
fof(f142,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f291,plain,
( sk_c7 = multiply(inverse(sk_c8),identity)
| ~ spl5_8 ),
inference(superposition,[],[f266,f226]) ).
fof(f226,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl5_8 ),
inference(superposition,[],[f2,f105]) ).
fof(f274,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl5_8 ),
inference(forward_demodulation,[],[f273,f1]) ).
fof(f273,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c7,X0))
| ~ spl5_8 ),
inference(superposition,[],[f3,f226]) ).
fof(f346,plain,
( sk_c8 = multiply(sk_c8,identity)
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8
| ~ spl5_11 ),
inference(backward_demodulation,[],[f296,f337]) ).
fof(f296,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl5_2
| ~ spl5_8 ),
inference(forward_demodulation,[],[f289,f105]) ).
fof(f289,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c10)
| ~ spl5_2 ),
inference(superposition,[],[f266,f78]) ).
fof(f363,plain,
( sk_c8 = inverse(identity)
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10
| ~ spl5_11
| ~ spl5_15
| ~ spl5_21 ),
inference(backward_demodulation,[],[f105,f360]) ).
fof(f353,plain,
( identity != inverse(identity)
| ~ spl5_7
| ~ spl5_10
| ~ spl5_11
| spl5_16
| ~ spl5_21 ),
inference(backward_demodulation,[],[f317,f337]) ).
fof(f317,plain,
( identity != inverse(sk_c10)
| ~ spl5_10
| spl5_16
| ~ spl5_21 ),
inference(backward_demodulation,[],[f146,f315]) ).
fof(f146,plain,
( inverse(sk_c10) != sk_c9
| spl5_16 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f241,plain,
( ~ spl5_3
| ~ spl5_13
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f231,f166,f129,f81]) ).
fof(f231,plain,
( sk_c11 != inverse(sk_c6)
| ~ spl5_13
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f230]) ).
fof(f230,plain,
( sk_c11 != sk_c11
| sk_c11 != inverse(sk_c6)
| ~ spl5_13
| ~ spl5_19 ),
inference(superposition,[],[f167,f131]) ).
fof(f221,plain,
( spl5_14
| spl5_15 ),
inference(avatar_split_clause,[],[f48,f140,f134]) ).
fof(f48,axiom,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c3 = inverse(sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f218,plain,
( spl5_14
| spl5_8 ),
inference(avatar_split_clause,[],[f47,f103,f134]) ).
fof(f47,axiom,
( sk_c8 = inverse(sk_c7)
| sk_c3 = inverse(sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f216,plain,
( spl5_16
| spl5_10 ),
inference(avatar_split_clause,[],[f7,f113,f145]) ).
fof(f7,axiom,
( sk_c10 = inverse(sk_c5)
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f215,plain,
( spl5_15
| spl5_16 ),
inference(avatar_split_clause,[],[f12,f145,f140]) ).
fof(f12,axiom,
( inverse(sk_c10) = sk_c9
| sk_c10 = multiply(sk_c8,sk_c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f213,plain,
( spl5_13
| spl5_12 ),
inference(avatar_split_clause,[],[f18,f122,f129]) ).
fof(f18,axiom,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c6,sk_c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f212,plain,
( spl5_9
| spl5_7 ),
inference(avatar_split_clause,[],[f23,f98,f108]) ).
fof(f23,axiom,
( sk_c11 = inverse(sk_c4)
| sk_c11 = multiply(sk_c1,sk_c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f210,plain,
( spl5_23
| spl5_24 ),
inference(avatar_split_clause,[],[f67,f198,f194]) ).
fof(f194,plain,
( spl5_23
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).
fof(f67,plain,
! [X9] :
( sk_c10 != multiply(X9,inverse(X9))
| sP3
| sk_c10 != multiply(inverse(X9),sk_c9) ),
inference(cnf_transformation,[],[f67_D]) ).
fof(f67_D,plain,
( ! [X9] :
( sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != multiply(inverse(X9),sk_c9) )
<=> ~ sP3 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f209,plain,
( spl5_13
| spl5_9 ),
inference(avatar_split_clause,[],[f27,f108,f129]) ).
fof(f27,axiom,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c11 = multiply(sk_c6,sk_c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f208,plain,
( spl5_19
| spl5_22 ),
inference(avatar_split_clause,[],[f63,f190,f166]) ).
fof(f190,plain,
( spl5_22
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).
fof(f63,plain,
! [X8] :
( sP1
| sk_c11 != multiply(X8,sk_c10)
| sk_c11 != inverse(X8) ),
inference(cnf_transformation,[],[f63_D]) ).
fof(f63_D,plain,
( ! [X8] :
( sk_c11 != multiply(X8,sk_c10)
| sk_c11 != inverse(X8) )
<=> ~ sP1 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f206,plain,
( spl5_7
| spl5_12 ),
inference(avatar_split_clause,[],[f14,f122,f98]) ).
fof(f14,axiom,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f205,plain,
( spl5_9
| spl5_3 ),
inference(avatar_split_clause,[],[f26,f81,f108]) ).
fof(f26,axiom,
( sk_c11 = inverse(sk_c6)
| sk_c11 = multiply(sk_c1,sk_c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f203,plain,
( spl5_2
| spl5_16 ),
inference(avatar_split_clause,[],[f10,f145,f76]) ).
fof(f10,axiom,
( inverse(sk_c10) = sk_c9
| sk_c10 = multiply(sk_c7,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f202,plain,
( spl5_1
| spl5_21 ),
inference(avatar_split_clause,[],[f33,f177,f72]) ).
fof(f33,axiom,
( sk_c9 = multiply(sk_c5,sk_c10)
| sk_c10 = multiply(sk_c2,sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f201,plain,
( spl5_14
| spl5_21 ),
inference(avatar_split_clause,[],[f42,f177,f134]) ).
fof(f42,axiom,
( sk_c9 = multiply(sk_c5,sk_c10)
| sk_c3 = inverse(sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f200,plain,
( ~ spl5_22
| ~ spl5_23
| spl5_24
| ~ spl5_17
| ~ spl5_20
| ~ spl5_16
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f70,f90,f145,f169,f157,f198,f194,f190]) ).
fof(f157,plain,
( spl5_17
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).
fof(f169,plain,
( spl5_20
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).
fof(f90,plain,
( spl5_5
<=> sP4 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f70,plain,
! [X4] :
( ~ sP4
| inverse(sk_c10) != sk_c9
| ~ sP0
| ~ sP2
| sk_c10 != multiply(X4,inverse(X4))
| ~ sP3
| sk_c10 != multiply(inverse(X4),sk_c9)
| ~ sP1 ),
inference(general_splitting,[],[f68,f69_D]) ).
fof(f69,plain,
! [X7] :
( sk_c9 != multiply(X7,sk_c10)
| sk_c10 != inverse(X7)
| sP4 ),
inference(cnf_transformation,[],[f69_D]) ).
fof(f69_D,plain,
( ! [X7] :
( sk_c9 != multiply(X7,sk_c10)
| sk_c10 != inverse(X7) )
<=> ~ sP4 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).
fof(f68,plain,
! [X7,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| inverse(sk_c10) != sk_c9
| sk_c10 != multiply(inverse(X4),sk_c9)
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| ~ sP0
| ~ sP1
| ~ sP2
| ~ sP3 ),
inference(general_splitting,[],[f66,f67_D]) ).
fof(f66,plain,
! [X9,X7,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X9),sk_c9)
| inverse(sk_c10) != sk_c9
| sk_c10 != multiply(inverse(X4),sk_c9)
| sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| ~ sP0
| ~ sP1
| ~ sP2 ),
inference(general_splitting,[],[f64,f65_D]) ).
fof(f65,plain,
! [X6] :
( sk_c10 != multiply(X6,sk_c11)
| sP2
| sk_c11 != inverse(X6) ),
inference(cnf_transformation,[],[f65_D]) ).
fof(f65_D,plain,
( ! [X6] :
( sk_c10 != multiply(X6,sk_c11)
| sk_c11 != inverse(X6) )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f64,plain,
! [X6,X9,X7,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X9),sk_c9)
| inverse(sk_c10) != sk_c9
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(inverse(X4),sk_c9)
| sk_c11 != inverse(X6)
| sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| ~ sP0
| ~ sP1 ),
inference(general_splitting,[],[f62,f63_D]) ).
fof(f62,plain,
! [X8,X6,X9,X7,X4] :
( sk_c11 != multiply(X8,sk_c10)
| sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X9),sk_c9)
| inverse(sk_c10) != sk_c9
| sk_c11 != inverse(X8)
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(inverse(X4),sk_c9)
| sk_c11 != inverse(X6)
| sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| ~ sP0 ),
inference(general_splitting,[],[f60,f61_D]) ).
fof(f61,plain,
! [X3] :
( sP0
| sk_c11 != multiply(X3,sk_c10)
| sk_c11 != inverse(X3) ),
inference(cnf_transformation,[],[f61_D]) ).
fof(f61_D,plain,
( ! [X3] :
( sk_c11 != multiply(X3,sk_c10)
| sk_c11 != inverse(X3) )
<=> ~ sP0 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f60,plain,
! [X3,X8,X6,X9,X7,X4] :
( sk_c11 != multiply(X3,sk_c10)
| sk_c11 != inverse(X3)
| sk_c11 != multiply(X8,sk_c10)
| sk_c10 != multiply(X4,inverse(X4))
| sk_c10 != multiply(inverse(X9),sk_c9)
| inverse(sk_c10) != sk_c9
| sk_c11 != inverse(X8)
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(inverse(X4),sk_c9)
| sk_c11 != inverse(X6)
| sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10) ),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X3,X8,X6,X9,X7,X4,X5] :
( sk_c11 != multiply(X3,sk_c10)
| sk_c11 != inverse(X3)
| sk_c11 != multiply(X8,sk_c10)
| sk_c10 != multiply(X4,X5)
| sk_c10 != multiply(inverse(X9),sk_c9)
| inverse(sk_c10) != sk_c9
| sk_c11 != inverse(X8)
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(X5,sk_c9)
| sk_c11 != inverse(X6)
| inverse(X4) != X5
| sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10) ),
inference(equality_resolution,[],[f58]) ).
fof(f58,axiom,
! [X3,X10,X8,X6,X9,X7,X4,X5] :
( sk_c11 != multiply(X3,sk_c10)
| sk_c11 != inverse(X3)
| sk_c11 != multiply(X8,sk_c10)
| sk_c10 != multiply(X4,X5)
| sk_c10 != multiply(X10,sk_c9)
| inverse(sk_c10) != sk_c9
| sk_c11 != inverse(X8)
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(X5,sk_c9)
| inverse(X9) != X10
| sk_c11 != inverse(X6)
| inverse(X4) != X5
| sk_c10 != multiply(X9,X10)
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f187,plain,
( spl5_4
| spl5_21 ),
inference(avatar_split_clause,[],[f51,f177,f85]) ).
fof(f51,axiom,
( sk_c9 = multiply(sk_c5,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f185,plain,
( spl5_16
| spl5_8 ),
inference(avatar_split_clause,[],[f11,f103,f145]) ).
fof(f11,axiom,
( sk_c8 = inverse(sk_c7)
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f184,plain,
( spl5_16
| spl5_7 ),
inference(avatar_split_clause,[],[f5,f98,f145]) ).
fof(f5,axiom,
( sk_c11 = inverse(sk_c4)
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f183,plain,
( spl5_15
| spl5_1 ),
inference(avatar_split_clause,[],[f39,f72,f140]) ).
fof(f39,axiom,
( sk_c10 = multiply(sk_c2,sk_c3)
| sk_c10 = multiply(sk_c8,sk_c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f182,plain,
( spl5_16
| spl5_11 ),
inference(avatar_split_clause,[],[f4,f118,f145]) ).
fof(f4,axiom,
( sk_c10 = multiply(sk_c4,sk_c11)
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f181,plain,
( spl5_16
| spl5_21 ),
inference(avatar_split_clause,[],[f6,f177,f145]) ).
fof(f6,axiom,
( sk_c9 = multiply(sk_c5,sk_c10)
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f175,plain,
( spl5_3
| spl5_12 ),
inference(avatar_split_clause,[],[f17,f122,f81]) ).
fof(f17,axiom,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f174,plain,
( spl5_1
| spl5_8 ),
inference(avatar_split_clause,[],[f38,f103,f72]) ).
fof(f38,axiom,
( sk_c8 = inverse(sk_c7)
| sk_c10 = multiply(sk_c2,sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f173,plain,
( spl5_4
| spl5_15 ),
inference(avatar_split_clause,[],[f57,f140,f85]) ).
fof(f57,axiom,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_54) ).
fof(f172,plain,
( spl5_19
| spl5_20 ),
inference(avatar_split_clause,[],[f61,f169,f166]) ).
fof(f164,plain,
( spl5_10
| spl5_14 ),
inference(avatar_split_clause,[],[f43,f134,f113]) ).
fof(f43,axiom,
( sk_c3 = inverse(sk_c2)
| sk_c10 = inverse(sk_c5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f163,plain,
( spl5_17
| spl5_18 ),
inference(avatar_split_clause,[],[f65,f161,f157]) ).
fof(f155,plain,
( spl5_1
| spl5_10 ),
inference(avatar_split_clause,[],[f34,f113,f72]) ).
fof(f34,axiom,
( sk_c10 = inverse(sk_c5)
| sk_c10 = multiply(sk_c2,sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f154,plain,
( spl5_2
| spl5_4 ),
inference(avatar_split_clause,[],[f55,f85,f76]) ).
fof(f55,axiom,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c10 = multiply(sk_c7,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f151,plain,
( spl5_11
| spl5_9 ),
inference(avatar_split_clause,[],[f22,f108,f118]) ).
fof(f22,axiom,
( sk_c11 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f149,plain,
( spl5_14
| spl5_2 ),
inference(avatar_split_clause,[],[f46,f76,f134]) ).
fof(f46,axiom,
( sk_c10 = multiply(sk_c7,sk_c8)
| sk_c3 = inverse(sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f125,plain,
( spl5_11
| spl5_12 ),
inference(avatar_split_clause,[],[f13,f122,f118]) ).
fof(f13,axiom,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f106,plain,
( spl5_8
| spl5_4 ),
inference(avatar_split_clause,[],[f56,f85,f103]) ).
fof(f56,axiom,
( sk_c10 = multiply(sk_c3,sk_c9)
| sk_c8 = inverse(sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
fof(f96,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f69,f94,f90]) ).
fof(f79,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f37,f76,f72]) ).
fof(f37,axiom,
( sk_c10 = multiply(sk_c7,sk_c8)
| sk_c10 = multiply(sk_c2,sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP389-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % 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 : n013.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 22:23:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.54 % (2307)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.56 % (2325)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)
% 0.19/0.57 % (2329)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)
% 0.19/0.57 % (2317)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)
% 0.19/0.57 % (2313)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.61/0.58 % (2321)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.61/0.58 % (2309)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)
% 1.61/0.59 % (2316)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.61/0.59 % (2315)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.92/0.60 % (2306)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.92/0.60 % (2303)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)
% 1.92/0.60 % (2326)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.92/0.60 % (2330)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)
% 1.92/0.60 TRYING [1]
% 1.92/0.61 % (2318)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.92/0.61 % (2327)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.92/0.61 TRYING [1]
% 1.92/0.61 TRYING [2]
% 1.92/0.61 % (2305)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)
% 1.92/0.61 % (2322)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)
% 1.92/0.61 % (2308)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)
% 1.92/0.61 % (2304)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)
% 1.92/0.62 % (2324)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.92/0.62 % (2332)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)
% 1.92/0.62 % (2310)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.92/0.62 % (2319)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.92/0.62 % (2314)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)
% 1.92/0.62 % (2331)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.92/0.63 TRYING [2]
% 1.92/0.63 % (2311)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.92/0.63 % (2311)Instruction limit reached!
% 1.92/0.63 % (2311)------------------------------
% 1.92/0.63 % (2311)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.92/0.63 % (2311)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.92/0.63 % (2311)Termination reason: Unknown
% 1.92/0.63 % (2311)Termination phase: Property scanning
% 1.92/0.63
% 1.92/0.63 % (2311)Memory used [KB]: 895
% 1.92/0.63 % (2311)Time elapsed: 0.002 s
% 1.92/0.63 % (2311)Instructions burned: 2 (million)
% 1.92/0.63 % (2311)------------------------------
% 1.92/0.63 % (2311)------------------------------
% 1.92/0.63 TRYING [3]
% 1.92/0.63 % (2323)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.92/0.63 TRYING [3]
% 1.92/0.64 % (2307)Instruction limit reached!
% 1.92/0.64 % (2307)------------------------------
% 1.92/0.64 % (2307)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.92/0.65 % (2320)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.92/0.65 % (2310)Instruction limit reached!
% 1.92/0.65 % (2310)------------------------------
% 1.92/0.65 % (2310)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.92/0.65 % (2310)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.92/0.65 % (2310)Termination reason: Unknown
% 1.92/0.65 % (2310)Termination phase: Saturation
% 1.92/0.65
% 1.92/0.65 % (2310)Memory used [KB]: 5628
% 1.92/0.65 % (2310)Time elapsed: 0.152 s
% 1.92/0.65 % (2310)Instructions burned: 7 (million)
% 1.92/0.65 % (2310)------------------------------
% 1.92/0.65 % (2310)------------------------------
% 1.92/0.65 % (2307)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.92/0.65 % (2307)Termination reason: Unknown
% 1.92/0.65 % (2307)Termination phase: Saturation
% 1.92/0.65
% 1.92/0.65 % (2307)Memory used [KB]: 6140
% 1.92/0.65 % (2307)Time elapsed: 0.221 s
% 1.92/0.65 % (2307)Instructions burned: 51 (million)
% 1.92/0.65 % (2307)------------------------------
% 1.92/0.65 % (2307)------------------------------
% 1.92/0.65 % (2328)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.92/0.65 % (2313)First to succeed.
% 1.92/0.66 % (2312)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)
% 1.92/0.66 % (2321)Also succeeded, but the first one will report.
% 2.47/0.66 TRYING [4]
% 2.49/0.67 % (2313)Refutation found. Thanks to Tanya!
% 2.49/0.67 % SZS status Unsatisfiable for theBenchmark
% 2.49/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 2.49/0.67 % (2313)------------------------------
% 2.49/0.67 % (2313)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.49/0.67 % (2313)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.49/0.67 % (2313)Termination reason: Refutation
% 2.49/0.67
% 2.49/0.67 % (2313)Memory used [KB]: 6012
% 2.49/0.67 % (2313)Time elapsed: 0.225 s
% 2.49/0.67 % (2313)Instructions burned: 34 (million)
% 2.49/0.67 % (2313)------------------------------
% 2.49/0.67 % (2313)------------------------------
% 2.49/0.67 % (2302)Success in time 0.314 s
%------------------------------------------------------------------------------