TSTP Solution File: GRP227-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP227-1 : 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 : n017.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 16:20:57 EDT 2022
% Result : Unsatisfiable 0.11s 0.51s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 42
% Syntax : Number of formulae : 168 ( 7 unt; 0 def)
% Number of atoms : 515 ( 200 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 677 ( 330 ~; 324 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f731,plain,
$false,
inference(avatar_sat_refutation,[],[f51,f59,f76,f82,f87,f97,f102,f110,f111,f119,f126,f127,f128,f129,f132,f133,f136,f138,f144,f185,f239,f265,f285,f287,f300,f555,f565,f575,f608,f613,f617,f621,f710,f728]) ).
fof(f728,plain,
( ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_20
| spl3_21 ),
inference(avatar_contradiction_clause,[],[f727]) ).
fof(f727,plain,
( $false
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_20
| spl3_21 ),
inference(subsumption_resolution,[],[f721,f170]) ).
fof(f170,plain,
( sk_c8 != sk_c7
| spl3_21 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f168,plain,
( spl3_21
<=> sk_c8 = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f721,plain,
( sk_c8 = sk_c7
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12
| ~ spl3_20 ),
inference(backward_demodulation,[],[f703,f714]) ).
fof(f714,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl3_20 ),
inference(backward_demodulation,[],[f1,f164]) ).
fof(f164,plain,
( identity = sk_c7
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f163,plain,
( spl3_20
<=> identity = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f703,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12 ),
inference(forward_demodulation,[],[f701,f46]) ).
fof(f46,plain,
( inverse(sk_c8) = sk_c7
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f44,plain,
( spl3_1
<=> inverse(sk_c8) = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f701,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl3_10
| ~ spl3_12 ),
inference(superposition,[],[f211,f678]) ).
fof(f678,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl3_10
| ~ spl3_12 ),
inference(forward_demodulation,[],[f676,f86]) ).
fof(f86,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f84,plain,
( spl3_10
<=> sk_c8 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f676,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c7)
| ~ spl3_12 ),
inference(superposition,[],[f211,f96]) ).
fof(f96,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f94,plain,
( spl3_12
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f211,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
inference(forward_demodulation,[],[f203,f1]) ).
fof(f203,plain,
! [X6,X7] : multiply(identity,X7) = multiply(inverse(X6),multiply(X6,X7)),
inference(superposition,[],[f3,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f710,plain,
( spl3_20
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f707,f94,f84,f44,f163]) ).
fof(f707,plain,
( identity = sk_c7
| ~ spl3_1
| ~ spl3_10
| ~ spl3_12 ),
inference(backward_demodulation,[],[f146,f703]) ).
fof(f146,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl3_1 ),
inference(superposition,[],[f2,f46]) ).
fof(f621,plain,
( ~ spl3_25
| spl3_20
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f620,f168,f163,f195]) ).
fof(f195,plain,
( spl3_25
<=> identity = sk_c8 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f620,plain,
( identity != sk_c8
| spl3_20
| ~ spl3_21 ),
inference(forward_demodulation,[],[f165,f169]) ).
fof(f169,plain,
( sk_c8 = sk_c7
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f165,plain,
( identity != sk_c7
| spl3_20 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f617,plain,
( ~ spl3_5
| ~ spl3_9
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f609,f113,f79,f61]) ).
fof(f61,plain,
( spl3_5
<=> inverse(sk_c1) = sk_c8 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f79,plain,
( spl3_9
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f113,plain,
( spl3_15
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f609,plain,
( inverse(sk_c1) != sk_c8
| ~ spl3_9
| ~ spl3_15 ),
inference(trivial_inequality_removal,[],[f188]) ).
fof(f188,plain,
( sk_c8 != sk_c8
| inverse(sk_c1) != sk_c8
| ~ spl3_9
| ~ spl3_15 ),
inference(superposition,[],[f114,f81]) ).
fof(f81,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f114,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f613,plain,
( spl3_23
| ~ spl3_21
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f597,f191,f168,f182]) ).
fof(f182,plain,
( spl3_23
<=> sk_c8 = inverse(inverse(sk_c8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f191,plain,
( spl3_24
<=> sk_c8 = inverse(inverse(sk_c7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f597,plain,
( sk_c8 = inverse(inverse(sk_c8))
| ~ spl3_21
| ~ spl3_24 ),
inference(forward_demodulation,[],[f192,f169]) ).
fof(f192,plain,
( sk_c8 = inverse(inverse(sk_c7))
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f608,plain,
( ~ spl3_18
| ~ spl3_21
| ~ spl3_25 ),
inference(avatar_contradiction_clause,[],[f607]) ).
fof(f607,plain,
( $false
| ~ spl3_18
| ~ spl3_21
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f606,f399]) ).
fof(f399,plain,
( ! [X3] : inverse(inverse(X3)) = X3
| ~ spl3_25 ),
inference(superposition,[],[f357,f313]) ).
fof(f313,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c8) = X0
| ~ spl3_25 ),
inference(superposition,[],[f211,f289]) ).
fof(f289,plain,
( ! [X0] : multiply(inverse(X0),X0) = sk_c8
| ~ spl3_25 ),
inference(backward_demodulation,[],[f2,f196]) ).
fof(f196,plain,
( identity = sk_c8
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f357,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl3_25 ),
inference(superposition,[],[f223,f313]) ).
fof(f223,plain,
! [X6,X5] : multiply(X5,X6) = multiply(inverse(inverse(X5)),X6),
inference(superposition,[],[f211,f211]) ).
fof(f606,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl3_18
| ~ spl3_21
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f371,f288]) ).
fof(f288,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl3_25 ),
inference(backward_demodulation,[],[f1,f196]) ).
fof(f371,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl3_18
| ~ spl3_21
| ~ spl3_25 ),
inference(superposition,[],[f303,f289]) ).
fof(f303,plain,
( ! [X5] :
( sk_c8 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) )
| ~ spl3_18
| ~ spl3_21 ),
inference(forward_demodulation,[],[f143,f169]) ).
fof(f143,plain,
( ! [X5] :
( sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) )
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f142,plain,
( spl3_18
<=> ! [X5] :
( sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f575,plain,
( ~ spl3_21
| spl3_24
| ~ spl3_25 ),
inference(avatar_contradiction_clause,[],[f574]) ).
fof(f574,plain,
( $false
| ~ spl3_21
| spl3_24
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f573,f399]) ).
fof(f573,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl3_21
| spl3_24 ),
inference(forward_demodulation,[],[f193,f169]) ).
fof(f193,plain,
( sk_c8 != inverse(inverse(sk_c7))
| spl3_24 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f565,plain,
( ~ spl3_15
| ~ spl3_21
| ~ spl3_25 ),
inference(avatar_contradiction_clause,[],[f564]) ).
fof(f564,plain,
( $false
| ~ spl3_15
| ~ spl3_21
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f563,f399]) ).
fof(f563,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl3_15
| ~ spl3_21
| ~ spl3_25 ),
inference(forward_demodulation,[],[f562,f169]) ).
fof(f562,plain,
( sk_c8 != inverse(inverse(sk_c7))
| ~ spl3_15
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f187,f196]) ).
fof(f187,plain,
( sk_c8 != inverse(inverse(sk_c7))
| identity != sk_c8
| ~ spl3_15 ),
inference(superposition,[],[f114,f2]) ).
fof(f555,plain,
( ~ spl3_8
| ~ spl3_21
| ~ spl3_25 ),
inference(avatar_contradiction_clause,[],[f554]) ).
fof(f554,plain,
( $false
| ~ spl3_8
| ~ spl3_21
| ~ spl3_25 ),
inference(trivial_inequality_removal,[],[f552]) ).
fof(f552,plain,
( sk_c8 != sk_c8
| ~ spl3_8
| ~ spl3_21
| ~ spl3_25 ),
inference(superposition,[],[f549,f289]) ).
fof(f549,plain,
( ! [X7] : sk_c8 != multiply(inverse(X7),sk_c8)
| ~ spl3_8
| ~ spl3_21
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f396,f360]) ).
fof(f360,plain,
( ! [X6] : sk_c8 = multiply(X6,inverse(X6))
| ~ spl3_25 ),
inference(superposition,[],[f223,f289]) ).
fof(f396,plain,
( ! [X7] :
( sk_c8 != multiply(inverse(X7),sk_c8)
| sk_c8 != multiply(X7,inverse(X7)) )
| ~ spl3_8
| ~ spl3_21 ),
inference(forward_demodulation,[],[f395,f169]) ).
fof(f395,plain,
( ! [X7] :
( sk_c7 != multiply(inverse(X7),sk_c8)
| sk_c8 != multiply(X7,inverse(X7)) )
| ~ spl3_8
| ~ spl3_21 ),
inference(forward_demodulation,[],[f75,f169]) ).
fof(f75,plain,
( ! [X7] :
( sk_c7 != multiply(X7,inverse(X7))
| sk_c7 != multiply(inverse(X7),sk_c8) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f74,plain,
( spl3_8
<=> ! [X7] :
( sk_c7 != multiply(inverse(X7),sk_c8)
| sk_c7 != multiply(X7,inverse(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f300,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_5
| ~ spl3_9
| ~ spl3_13
| ~ spl3_17
| ~ spl3_21
| ~ spl3_25 ),
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f299,plain,
( $false
| spl3_1
| ~ spl3_2
| ~ spl3_5
| ~ spl3_9
| ~ spl3_13
| ~ spl3_17
| ~ spl3_21
| ~ spl3_25 ),
inference(subsumption_resolution,[],[f298,f240]) ).
fof(f240,plain,
( sk_c8 != inverse(sk_c8)
| spl3_1
| ~ spl3_21 ),
inference(backward_demodulation,[],[f45,f169]) ).
fof(f45,plain,
( inverse(sk_c8) != sk_c7
| spl3_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f298,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl3_2
| ~ spl3_5
| ~ spl3_9
| ~ spl3_13
| ~ spl3_17
| ~ spl3_21
| ~ spl3_25 ),
inference(backward_demodulation,[],[f63,f293]) ).
fof(f293,plain,
( sk_c1 = sk_c8
| ~ spl3_2
| ~ spl3_5
| ~ spl3_9
| ~ spl3_13
| ~ spl3_17
| ~ spl3_21
| ~ spl3_25 ),
inference(forward_demodulation,[],[f292,f274]) ).
fof(f274,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl3_2
| ~ spl3_5
| ~ spl3_9
| ~ spl3_13
| ~ spl3_17
| ~ spl3_21 ),
inference(forward_demodulation,[],[f266,f272]) ).
fof(f272,plain,
( sk_c8 = sk_c3
| ~ spl3_2
| ~ spl3_5
| ~ spl3_9
| ~ spl3_13
| ~ spl3_21 ),
inference(forward_demodulation,[],[f270,f242]) ).
fof(f242,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl3_9
| ~ spl3_21 ),
inference(backward_demodulation,[],[f81,f169]) ).
fof(f270,plain,
( sk_c3 = multiply(sk_c1,sk_c8)
| ~ spl3_2
| ~ spl3_5
| ~ spl3_13 ),
inference(backward_demodulation,[],[f50,f267]) ).
fof(f267,plain,
( sk_c1 = sk_c2
| ~ spl3_5
| ~ spl3_13 ),
inference(forward_demodulation,[],[f228,f226]) ).
fof(f226,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl3_5 ),
inference(superposition,[],[f211,f145]) ).
fof(f145,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl3_5 ),
inference(superposition,[],[f2,f63]) ).
fof(f228,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl3_13 ),
inference(superposition,[],[f211,f149]) ).
fof(f149,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl3_13 ),
inference(superposition,[],[f2,f101]) ).
fof(f101,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f99,plain,
( spl3_13
<=> sk_c8 = inverse(sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl3_2
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f266,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c8)
| ~ spl3_17
| ~ spl3_21 ),
inference(forward_demodulation,[],[f227,f169]) ).
fof(f227,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c7)
| ~ spl3_17 ),
inference(superposition,[],[f211,f124]) ).
fof(f124,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f122,plain,
( spl3_17
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f292,plain,
( sk_c1 = multiply(inverse(sk_c8),sk_c8)
| ~ spl3_5
| ~ spl3_25 ),
inference(backward_demodulation,[],[f226,f196]) ).
fof(f63,plain,
( inverse(sk_c1) = sk_c8
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f287,plain,
( spl3_25
| ~ spl3_2
| ~ spl3_5
| ~ spl3_9
| ~ spl3_13
| ~ spl3_17
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f276,f168,f122,f99,f79,f61,f48,f195]) ).
fof(f276,plain,
( identity = sk_c8
| ~ spl3_2
| ~ spl3_5
| ~ spl3_9
| ~ spl3_13
| ~ spl3_17
| ~ spl3_21 ),
inference(superposition,[],[f2,f274]) ).
fof(f285,plain,
( spl3_25
| ~ spl3_20
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f284,f168,f163,f195]) ).
fof(f284,plain,
( identity = sk_c8
| ~ spl3_20
| ~ spl3_21 ),
inference(forward_demodulation,[],[f164,f169]) ).
fof(f265,plain,
( ~ spl3_3
| ~ spl3_5
| ~ spl3_9
| ~ spl3_21 ),
inference(avatar_contradiction_clause,[],[f264]) ).
fof(f264,plain,
( $false
| ~ spl3_3
| ~ spl3_5
| ~ spl3_9
| ~ spl3_21 ),
inference(subsumption_resolution,[],[f263,f63]) ).
fof(f263,plain,
( inverse(sk_c1) != sk_c8
| ~ spl3_3
| ~ spl3_9
| ~ spl3_21 ),
inference(trivial_inequality_removal,[],[f258]) ).
fof(f258,plain,
( sk_c8 != sk_c8
| inverse(sk_c1) != sk_c8
| ~ spl3_3
| ~ spl3_9
| ~ spl3_21 ),
inference(superposition,[],[f241,f242]) ).
fof(f241,plain,
( ! [X6] :
( sk_c8 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6) )
| ~ spl3_3
| ~ spl3_21 ),
inference(backward_demodulation,[],[f54,f169]) ).
fof(f54,plain,
( ! [X6] :
( sk_c7 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl3_3
<=> ! [X6] :
( sk_c8 != inverse(X6)
| sk_c7 != multiply(X6,sk_c8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f239,plain,
( spl3_21
| ~ spl3_2
| ~ spl3_13
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f234,f122,f99,f48,f168]) ).
fof(f234,plain,
( sk_c8 = sk_c7
| ~ spl3_2
| ~ spl3_13
| ~ spl3_17 ),
inference(backward_demodulation,[],[f124,f231]) ).
fof(f231,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl3_2
| ~ spl3_13 ),
inference(forward_demodulation,[],[f229,f101]) ).
fof(f229,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl3_2 ),
inference(superposition,[],[f211,f50]) ).
fof(f185,plain,
( ~ spl3_20
| ~ spl3_23
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f151,f53,f182,f163]) ).
fof(f151,plain,
( sk_c8 != inverse(inverse(sk_c8))
| identity != sk_c7
| ~ spl3_3 ),
inference(superposition,[],[f54,f2]) ).
fof(f144,plain,
( ~ spl3_4
| ~ spl3_1
| ~ spl3_7
| spl3_18
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f42,f116,f142,f70,f44,f56]) ).
fof(f56,plain,
( spl3_4
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f70,plain,
( spl3_7
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f116,plain,
( spl3_16
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f42,plain,
! [X5] :
( ~ sP0
| sk_c8 != inverse(X5)
| ~ sP2
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| ~ sP1 ),
inference(general_splitting,[],[f40,f41_D]) ).
fof(f41,plain,
! [X7] :
( sk_c7 != multiply(inverse(X7),sk_c8)
| sk_c7 != multiply(X7,inverse(X7))
| sP2 ),
inference(cnf_transformation,[],[f41_D]) ).
fof(f41_D,plain,
( ! [X7] :
( sk_c7 != multiply(inverse(X7),sk_c8)
| sk_c7 != multiply(X7,inverse(X7)) )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f40,plain,
! [X7,X5] :
( sk_c7 != multiply(X7,inverse(X7))
| sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(inverse(X7),sk_c8)
| ~ sP0
| ~ sP1 ),
inference(general_splitting,[],[f38,f39_D]) ).
fof(f39,plain,
! [X6] :
( sP1
| sk_c8 != inverse(X6)
| sk_c7 != multiply(X6,sk_c8) ),
inference(cnf_transformation,[],[f39_D]) ).
fof(f39_D,plain,
( ! [X6] :
( sk_c8 != inverse(X6)
| sk_c7 != multiply(X6,sk_c8) )
<=> ~ sP1 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f38,plain,
! [X6,X7,X5] :
( sk_c7 != multiply(X7,inverse(X7))
| sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6)
| sk_c7 != multiply(inverse(X7),sk_c8)
| ~ sP0 ),
inference(general_splitting,[],[f36,f37_D]) ).
fof(f37,plain,
! [X3] :
( sP0
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ),
inference(cnf_transformation,[],[f37_D]) ).
fof(f37_D,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
<=> ~ sP0 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f36,plain,
! [X3,X6,X7,X5] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(X7,inverse(X7))
| sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(inverse(X7),sk_c8) ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X3,X8,X6,X7,X5] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(X7,X8)
| sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| inverse(sk_c8) != sk_c7
| inverse(X7) != X8
| sk_c7 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X8,sk_c8) ),
inference(equality_resolution,[],[f34]) ).
fof(f34,axiom,
! [X3,X8,X6,X7,X4,X5] :
( multiply(X5,sk_c8) != X4
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(X7,X8)
| sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,X4)
| inverse(sk_c8) != sk_c7
| inverse(X7) != X8
| sk_c7 != multiply(X6,sk_c8)
| sk_c8 != inverse(X6)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X8,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f138,plain,
( spl3_1
| spl3_13 ),
inference(avatar_split_clause,[],[f28,f99,f44]) ).
fof(f28,axiom,
( sk_c8 = inverse(sk_c2)
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f136,plain,
( spl3_2
| spl3_10 ),
inference(avatar_split_clause,[],[f24,f84,f48]) ).
fof(f24,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f133,plain,
( spl3_17
| spl3_12 ),
inference(avatar_split_clause,[],[f17,f94,f122]) ).
fof(f17,axiom,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f132,plain,
( spl3_10
| spl3_5 ),
inference(avatar_split_clause,[],[f6,f61,f84]) ).
fof(f6,axiom,
( inverse(sk_c1) = sk_c8
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f129,plain,
( spl3_10
| spl3_17 ),
inference(avatar_split_clause,[],[f18,f122,f84]) ).
fof(f18,axiom,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f128,plain,
( spl3_10
| spl3_13 ),
inference(avatar_split_clause,[],[f30,f99,f84]) ).
fof(f30,axiom,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f127,plain,
( spl3_9
| spl3_12 ),
inference(avatar_split_clause,[],[f11,f94,f79]) ).
fof(f11,axiom,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f126,plain,
( spl3_1
| spl3_17 ),
inference(avatar_split_clause,[],[f16,f122,f44]) ).
fof(f16,axiom,
( sk_c7 = multiply(sk_c8,sk_c3)
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f119,plain,
( spl3_15
| spl3_16 ),
inference(avatar_split_clause,[],[f37,f116,f113]) ).
fof(f111,plain,
( spl3_2
| spl3_12 ),
inference(avatar_split_clause,[],[f23,f94,f48]) ).
fof(f23,axiom,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f110,plain,
( spl3_5
| spl3_1 ),
inference(avatar_split_clause,[],[f4,f44,f61]) ).
fof(f4,axiom,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f102,plain,
( spl3_12
| spl3_13 ),
inference(avatar_split_clause,[],[f29,f99,f94]) ).
fof(f29,axiom,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f97,plain,
( spl3_5
| spl3_12 ),
inference(avatar_split_clause,[],[f5,f94,f61]) ).
fof(f5,axiom,
( sk_c7 = multiply(sk_c4,sk_c8)
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f87,plain,
( spl3_9
| spl3_10 ),
inference(avatar_split_clause,[],[f12,f84,f79]) ).
fof(f12,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f82,plain,
( spl3_1
| spl3_9 ),
inference(avatar_split_clause,[],[f10,f79,f44]) ).
fof(f10,axiom,
( sk_c8 = multiply(sk_c1,sk_c7)
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f76,plain,
( spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f41,f74,f70]) ).
fof(f59,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f39,f56,f53]) ).
fof(f51,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f22,f48,f44]) ).
fof(f22,axiom,
( sk_c3 = multiply(sk_c2,sk_c8)
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.07 % Problem : GRP227-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.07 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.07/0.26 % Computer : n017.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Aug 29 21:45:34 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.11/0.43 % (20205)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.11/0.44 % (20222)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.11/0.45 % (20213)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)
% 0.11/0.45 % (20214)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)
% 0.11/0.45 % (20206)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.45 % (20206)Instruction limit reached!
% 0.11/0.45 % (20206)------------------------------
% 0.11/0.45 % (20206)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.11/0.45 % (20206)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.11/0.45 % (20206)Termination reason: Unknown
% 0.11/0.45 % (20206)Termination phase: Saturation
% 0.11/0.45
% 0.11/0.45 % (20206)Memory used [KB]: 5373
% 0.11/0.45 % (20206)Time elapsed: 0.004 s
% 0.11/0.45 % (20206)Instructions burned: 2 (million)
% 0.11/0.45 % (20206)------------------------------
% 0.11/0.45 % (20206)------------------------------
% 0.11/0.45 % (20205)Instruction limit reached!
% 0.11/0.45 % (20205)------------------------------
% 0.11/0.45 % (20205)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.11/0.46 % (20221)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)
% 0.11/0.47 % (20205)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.11/0.47 % (20205)Termination reason: Unknown
% 0.11/0.47 % (20205)Termination phase: Saturation
% 0.11/0.47
% 0.11/0.47 % (20205)Memory used [KB]: 5500
% 0.11/0.47 % (20205)Time elapsed: 0.126 s
% 0.11/0.47 % (20205)Instructions burned: 7 (million)
% 0.11/0.47 % (20205)------------------------------
% 0.11/0.47 % (20205)------------------------------
% 0.11/0.50 % (20203)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)
% 0.11/0.50 % (20200)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)
% 0.11/0.50 % (20198)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)
% 0.11/0.50 % (20202)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.11/0.50 % (20201)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)
% 0.11/0.50 % (20214)First to succeed.
% 0.11/0.50 % (20227)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)
% 0.11/0.51 % (20224)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)
% 0.11/0.51 % (20220)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)
% 0.11/0.51 % (20218)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)
% 0.11/0.51 % (20223)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.11/0.51 % (20204)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)
% 0.11/0.51 % (20219)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.11/0.51 % (20207)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)
% 0.11/0.51 % (20214)Refutation found. Thanks to Tanya!
% 0.11/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.52 % (20214)------------------------------
% 0.11/0.52 % (20214)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.11/0.52 % (20214)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.11/0.52 % (20214)Termination reason: Refutation
% 0.11/0.52
% 0.11/0.52 % (20214)Memory used [KB]: 5756
% 0.11/0.52 % (20214)Time elapsed: 0.180 s
% 0.11/0.52 % (20214)Instructions burned: 24 (million)
% 0.11/0.52 % (20214)------------------------------
% 0.11/0.52 % (20214)------------------------------
% 0.11/0.52 % (20197)Success in time 0.246 s
%------------------------------------------------------------------------------