TSTP Solution File: GRP244-1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP244-1 : 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 : n022.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 16:21:01 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 56
% Syntax : Number of formulae : 204 ( 6 unt; 0 def)
% Number of atoms : 620 ( 255 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 809 ( 393 ~; 379 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 38 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f895,plain,
$false,
inference(avatar_sat_refutation,[],[f93,f126,f137,f138,f163,f166,f178,f187,f190,f191,f192,f199,f203,f206,f210,f213,f218,f219,f221,f225,f227,f228,f245,f257,f273,f304,f313,f315,f367,f370,f387,f433,f488,f502,f583,f682,f773,f849,f893]) ).
fof(f893,plain,
( ~ spl6_5
| ~ spl6_18
| ~ spl6_26
| ~ spl6_36
| ~ spl6_40 ),
inference(avatar_contradiction_clause,[],[f892]) ).
fof(f892,plain,
( $false
| ~ spl6_5
| ~ spl6_18
| ~ spl6_26
| ~ spl6_36
| ~ spl6_40 ),
inference(subsumption_resolution,[],[f891,f851]) ).
fof(f851,plain,
( identity = multiply(sk_c5,identity)
| ~ spl6_36
| ~ spl6_40 ),
inference(forward_demodulation,[],[f360,f318]) ).
fof(f318,plain,
( identity = sk_c10
| ~ spl6_36 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f317,plain,
( spl6_36
<=> identity = sk_c10 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_36])]) ).
fof(f360,plain,
( sk_c10 = multiply(sk_c5,sk_c10)
| ~ spl6_40 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f359,plain,
( spl6_40
<=> sk_c10 = multiply(sk_c5,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_40])]) ).
fof(f891,plain,
( identity != multiply(sk_c5,identity)
| ~ spl6_5
| ~ spl6_18
| ~ spl6_26
| ~ spl6_36 ),
inference(trivial_inequality_removal,[],[f889]) ).
fof(f889,plain,
( identity != identity
| identity != multiply(sk_c5,identity)
| ~ spl6_5
| ~ spl6_18
| ~ spl6_26
| ~ spl6_36 ),
inference(superposition,[],[f863,f777]) ).
fof(f777,plain,
( identity = inverse(sk_c5)
| ~ spl6_18
| ~ spl6_36 ),
inference(forward_demodulation,[],[f151,f318]) ).
fof(f151,plain,
( sk_c10 = inverse(sk_c5)
| ~ spl6_18 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f149,plain,
( spl6_18
<=> sk_c10 = inverse(sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
fof(f863,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != multiply(X4,identity) )
| ~ spl6_5
| ~ spl6_26
| ~ spl6_36 ),
inference(backward_demodulation,[],[f757,f239]) ).
fof(f239,plain,
( identity = sk_c9
| ~ spl6_26 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f238,plain,
( spl6_26
<=> identity = sk_c9 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).
fof(f757,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c9 != multiply(X4,identity) )
| ~ spl6_5
| ~ spl6_36 ),
inference(forward_demodulation,[],[f756,f318]) ).
fof(f756,plain,
( ! [X4] :
( sk_c10 != inverse(X4)
| sk_c9 != multiply(X4,identity) )
| ~ spl6_5
| ~ spl6_36 ),
inference(forward_demodulation,[],[f92,f318]) ).
fof(f92,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f91,plain,
( spl6_5
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
fof(f849,plain,
( ~ spl6_1
| ~ spl6_18
| ~ spl6_36
| spl6_39 ),
inference(avatar_contradiction_clause,[],[f848]) ).
fof(f848,plain,
( $false
| ~ spl6_1
| ~ spl6_18
| ~ spl6_36
| spl6_39 ),
inference(subsumption_resolution,[],[f847,f792]) ).
fof(f792,plain,
( identity != multiply(identity,sk_c9)
| ~ spl6_36
| spl6_39 ),
inference(forward_demodulation,[],[f357,f318]) ).
fof(f357,plain,
( sk_c10 != multiply(sk_c10,sk_c9)
| spl6_39 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f355,plain,
( spl6_39
<=> sk_c10 = multiply(sk_c10,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_39])]) ).
fof(f847,plain,
( identity = multiply(identity,sk_c9)
| ~ spl6_1
| ~ spl6_18
| ~ spl6_36 ),
inference(forward_demodulation,[],[f843,f777]) ).
fof(f843,plain,
( identity = multiply(inverse(sk_c5),sk_c9)
| ~ spl6_1
| ~ spl6_36 ),
inference(superposition,[],[f337,f814]) ).
fof(f814,plain,
( sk_c9 = multiply(sk_c5,identity)
| ~ spl6_1
| ~ spl6_36 ),
inference(forward_demodulation,[],[f75,f318]) ).
fof(f75,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f73,plain,
( spl6_1
<=> multiply(sk_c5,sk_c10) = sk_c9 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f337,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
inference(forward_demodulation,[],[f327,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f327,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = multiply(identity,X7),
inference(superposition,[],[f3,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f773,plain,
( ~ spl6_16
| spl6_27
| ~ spl6_36 ),
inference(avatar_contradiction_clause,[],[f772]) ).
fof(f772,plain,
( $false
| ~ spl6_16
| spl6_27
| ~ spl6_36 ),
inference(subsumption_resolution,[],[f771,f734]) ).
fof(f734,plain,
( identity = inverse(identity)
| ~ spl6_16
| ~ spl6_36 ),
inference(backward_demodulation,[],[f684,f733]) ).
fof(f733,plain,
( identity = sk_c2
| ~ spl6_16
| ~ spl6_36 ),
inference(forward_demodulation,[],[f694,f2]) ).
fof(f694,plain,
( sk_c2 = multiply(inverse(identity),identity)
| ~ spl6_16
| ~ spl6_36 ),
inference(backward_demodulation,[],[f409,f318]) ).
fof(f409,plain,
( sk_c2 = multiply(inverse(sk_c10),identity)
| ~ spl6_16 ),
inference(superposition,[],[f337,f230]) ).
fof(f230,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl6_16 ),
inference(superposition,[],[f2,f142]) ).
fof(f142,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl6_16
<=> sk_c10 = inverse(sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
fof(f684,plain,
( identity = inverse(sk_c2)
| ~ spl6_16
| ~ spl6_36 ),
inference(backward_demodulation,[],[f142,f318]) ).
fof(f771,plain,
( identity != inverse(identity)
| ~ spl6_16
| spl6_27
| ~ spl6_36 ),
inference(forward_demodulation,[],[f770,f734]) ).
fof(f770,plain,
( identity != inverse(inverse(identity))
| spl6_27
| ~ spl6_36 ),
inference(forward_demodulation,[],[f244,f318]) ).
fof(f244,plain,
( sk_c10 != inverse(inverse(sk_c10))
| spl6_27 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f242,plain,
( spl6_27
<=> sk_c10 = inverse(inverse(sk_c10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).
fof(f682,plain,
( ~ spl6_2
| ~ spl6_17
| spl6_36 ),
inference(avatar_contradiction_clause,[],[f681]) ).
fof(f681,plain,
( $false
| ~ spl6_2
| ~ spl6_17
| spl6_36 ),
inference(subsumption_resolution,[],[f680,f319]) ).
fof(f319,plain,
( identity != sk_c10
| spl6_36 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f680,plain,
( identity = sk_c10
| ~ spl6_2
| ~ spl6_17 ),
inference(forward_demodulation,[],[f678,f2]) ).
fof(f678,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl6_2
| ~ spl6_17 ),
inference(superposition,[],[f337,f441]) ).
fof(f441,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl6_2
| ~ spl6_17 ),
inference(forward_demodulation,[],[f402,f147]) ).
fof(f147,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl6_17 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f145,plain,
( spl6_17
<=> sk_c11 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).
fof(f402,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c10)
| ~ spl6_2 ),
inference(superposition,[],[f337,f79]) ).
fof(f79,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f77,plain,
( spl6_2
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f583,plain,
( ~ spl6_16
| ~ spl6_36
| spl6_41 ),
inference(avatar_contradiction_clause,[],[f582]) ).
fof(f582,plain,
( $false
| ~ spl6_16
| ~ spl6_36
| spl6_41 ),
inference(subsumption_resolution,[],[f578,f1]) ).
fof(f578,plain,
( identity != multiply(identity,identity)
| ~ spl6_16
| ~ spl6_36
| spl6_41 ),
inference(backward_demodulation,[],[f573,f577]) ).
fof(f577,plain,
( identity = sk_c2
| ~ spl6_16
| ~ spl6_36 ),
inference(forward_demodulation,[],[f576,f2]) ).
fof(f576,plain,
( sk_c2 = multiply(inverse(identity),identity)
| ~ spl6_16
| ~ spl6_36 ),
inference(forward_demodulation,[],[f409,f318]) ).
fof(f573,plain,
( identity != multiply(sk_c2,identity)
| ~ spl6_36
| spl6_41 ),
inference(forward_demodulation,[],[f366,f318]) ).
fof(f366,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| spl6_41 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f364,plain,
( spl6_41
<=> sk_c10 = multiply(sk_c2,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_41])]) ).
fof(f502,plain,
( ~ spl6_36
| ~ spl6_1
| ~ spl6_26
| spl6_40 ),
inference(avatar_split_clause,[],[f462,f359,f238,f73,f317]) ).
fof(f462,plain,
( identity != sk_c10
| ~ spl6_1
| ~ spl6_26
| spl6_40 ),
inference(backward_demodulation,[],[f361,f451]) ).
fof(f451,plain,
( identity = multiply(sk_c5,sk_c10)
| ~ spl6_1
| ~ spl6_26 ),
inference(backward_demodulation,[],[f75,f239]) ).
fof(f361,plain,
( sk_c10 != multiply(sk_c5,sk_c10)
| spl6_40 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f488,plain,
( ~ spl6_19
| ~ spl6_20
| spl6_36 ),
inference(avatar_contradiction_clause,[],[f487]) ).
fof(f487,plain,
( $false
| ~ spl6_19
| ~ spl6_20
| spl6_36 ),
inference(subsumption_resolution,[],[f486,f319]) ).
fof(f486,plain,
( identity = sk_c10
| ~ spl6_19
| ~ spl6_20 ),
inference(forward_demodulation,[],[f484,f2]) ).
fof(f484,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl6_19
| ~ spl6_20 ),
inference(superposition,[],[f337,f418]) ).
fof(f418,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl6_19
| ~ spl6_20 ),
inference(forward_demodulation,[],[f410,f161]) ).
fof(f161,plain,
( sk_c11 = inverse(sk_c4)
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f159,plain,
( spl6_20
<=> sk_c11 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).
fof(f410,plain,
( sk_c11 = multiply(inverse(sk_c4),sk_c10)
| ~ spl6_19 ),
inference(superposition,[],[f337,f156]) ).
fof(f156,plain,
( sk_c10 = multiply(sk_c4,sk_c11)
| ~ spl6_19 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f154,plain,
( spl6_19
<=> sk_c10 = multiply(sk_c4,sk_c11) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).
fof(f433,plain,
( spl6_26
| ~ spl6_39 ),
inference(avatar_split_clause,[],[f432,f355,f238]) ).
fof(f432,plain,
( identity = sk_c9
| ~ spl6_39 ),
inference(forward_demodulation,[],[f408,f2]) ).
fof(f408,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl6_39 ),
inference(superposition,[],[f337,f356]) ).
fof(f356,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl6_39 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f387,plain,
( ~ spl6_7
| ~ spl6_16
| spl6_39 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f386,plain,
( $false
| ~ spl6_7
| ~ spl6_16
| spl6_39 ),
inference(subsumption_resolution,[],[f383,f357]) ).
fof(f383,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl6_7
| ~ spl6_16 ),
inference(superposition,[],[f338,f101]) ).
fof(f101,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f99,plain,
( spl6_7
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
fof(f338,plain,
( ! [X9] : multiply(sk_c10,multiply(sk_c2,X9)) = X9
| ~ spl6_16 ),
inference(forward_demodulation,[],[f329,f1]) ).
fof(f329,plain,
( ! [X9] : multiply(identity,X9) = multiply(sk_c10,multiply(sk_c2,X9))
| ~ spl6_16 ),
inference(superposition,[],[f3,f230]) ).
fof(f370,plain,
( ~ spl6_3
| ~ spl6_6
| ~ spl6_22
| ~ spl6_25 ),
inference(avatar_contradiction_clause,[],[f369]) ).
fof(f369,plain,
( $false
| ~ spl6_3
| ~ spl6_6
| ~ spl6_22
| ~ spl6_25 ),
inference(subsumption_resolution,[],[f368,f177]) ).
fof(f177,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| ~ spl6_22 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f175,plain,
( spl6_22
<=> sk_c10 = multiply(sk_c7,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).
fof(f368,plain,
( sk_c10 != multiply(sk_c7,sk_c8)
| ~ spl6_3
| ~ spl6_6
| ~ spl6_25 ),
inference(subsumption_resolution,[],[f344,f84]) ).
fof(f84,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f82,plain,
( spl6_3
<=> sk_c10 = multiply(sk_c8,sk_c9) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f344,plain,
( sk_c10 != multiply(sk_c8,sk_c9)
| sk_c10 != multiply(sk_c7,sk_c8)
| ~ spl6_6
| ~ spl6_25 ),
inference(superposition,[],[f202,f97]) ).
fof(f97,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f95,plain,
( spl6_6
<=> sk_c8 = inverse(sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
fof(f202,plain,
( ! [X9] :
( sk_c10 != multiply(inverse(X9),sk_c9)
| sk_c10 != multiply(X9,inverse(X9)) )
| ~ spl6_25 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f201,plain,
( spl6_25
<=> ! [X9] :
( sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != multiply(inverse(X9),sk_c9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).
fof(f367,plain,
( ~ spl6_41
| ~ spl6_39
| ~ spl6_16
| ~ spl6_25 ),
inference(avatar_split_clause,[],[f345,f201,f140,f355,f364]) ).
fof(f345,plain,
( sk_c10 != multiply(sk_c10,sk_c9)
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl6_16
| ~ spl6_25 ),
inference(superposition,[],[f202,f142]) ).
fof(f315,plain,
( ~ spl6_2
| ~ spl6_17
| ~ spl6_24 ),
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f314,plain,
( $false
| ~ spl6_2
| ~ spl6_17
| ~ spl6_24 ),
inference(subsumption_resolution,[],[f310,f147]) ).
fof(f310,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl6_2
| ~ spl6_24 ),
inference(trivial_inequality_removal,[],[f308]) ).
fof(f308,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c1)
| ~ spl6_2
| ~ spl6_24 ),
inference(superposition,[],[f198,f79]) ).
fof(f198,plain,
( ! [X6] :
( sk_c10 != multiply(X6,sk_c11)
| sk_c11 != inverse(X6) )
| ~ spl6_24 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f197,plain,
( spl6_24
<=> ! [X6] :
( sk_c10 != multiply(X6,sk_c11)
| sk_c11 != inverse(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).
fof(f313,plain,
( ~ spl6_19
| ~ spl6_20
| ~ spl6_24 ),
inference(avatar_contradiction_clause,[],[f312]) ).
fof(f312,plain,
( $false
| ~ spl6_19
| ~ spl6_20
| ~ spl6_24 ),
inference(subsumption_resolution,[],[f311,f161]) ).
fof(f311,plain,
( sk_c11 != inverse(sk_c4)
| ~ spl6_19
| ~ spl6_24 ),
inference(trivial_inequality_removal,[],[f309]) ).
fof(f309,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c4)
| ~ spl6_19
| ~ spl6_24 ),
inference(superposition,[],[f198,f156]) ).
fof(f304,plain,
( ~ spl6_10
| ~ spl6_15
| ~ spl6_23 ),
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f303,plain,
( $false
| ~ spl6_10
| ~ spl6_15
| ~ spl6_23 ),
inference(subsumption_resolution,[],[f302,f136]) ).
fof(f136,plain,
( sk_c11 = multiply(sk_c6,sk_c10)
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f134,plain,
( spl6_15
<=> sk_c11 = multiply(sk_c6,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
fof(f302,plain,
( sk_c11 != multiply(sk_c6,sk_c10)
| ~ spl6_10
| ~ spl6_23 ),
inference(trivial_inequality_removal,[],[f300]) ).
fof(f300,plain,
( sk_c11 != multiply(sk_c6,sk_c10)
| sk_c11 != sk_c11
| ~ spl6_10
| ~ spl6_23 ),
inference(superposition,[],[f113,f182]) ).
fof(f182,plain,
( sk_c11 = inverse(sk_c6)
| ~ spl6_23 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f180,plain,
( spl6_23
<=> sk_c11 = inverse(sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).
fof(f113,plain,
( ! [X5] :
( sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f112,plain,
( spl6_10
<=> ! [X5] :
( sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
fof(f273,plain,
( ~ spl6_10
| ~ spl6_14
| ~ spl6_21 ),
inference(avatar_contradiction_clause,[],[f272]) ).
fof(f272,plain,
( $false
| ~ spl6_10
| ~ spl6_14
| ~ spl6_21 ),
inference(subsumption_resolution,[],[f271,f172]) ).
fof(f172,plain,
( sk_c11 = multiply(sk_c3,sk_c10)
| ~ spl6_21 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f170,plain,
( spl6_21
<=> sk_c11 = multiply(sk_c3,sk_c10) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).
fof(f271,plain,
( sk_c11 != multiply(sk_c3,sk_c10)
| ~ spl6_10
| ~ spl6_14 ),
inference(trivial_inequality_removal,[],[f267]) ).
fof(f267,plain,
( sk_c11 != sk_c11
| sk_c11 != multiply(sk_c3,sk_c10)
| ~ spl6_10
| ~ spl6_14 ),
inference(superposition,[],[f113,f131]) ).
fof(f131,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f129,plain,
( spl6_14
<=> sk_c11 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
fof(f257,plain,
( ~ spl6_5
| ~ spl6_7
| ~ spl6_16 ),
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f256,plain,
( $false
| ~ spl6_5
| ~ spl6_7
| ~ spl6_16 ),
inference(subsumption_resolution,[],[f236,f142]) ).
fof(f236,plain,
( sk_c10 != inverse(sk_c2)
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f234]) ).
fof(f234,plain,
( sk_c10 != inverse(sk_c2)
| sk_c9 != sk_c9
| ~ spl6_5
| ~ spl6_7 ),
inference(superposition,[],[f92,f101]) ).
fof(f245,plain,
( ~ spl6_26
| ~ spl6_27
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f233,f91,f242,f238]) ).
fof(f233,plain,
( sk_c10 != inverse(inverse(sk_c10))
| identity != sk_c9
| ~ spl6_5 ),
inference(superposition,[],[f92,f2]) ).
fof(f228,plain,
( spl6_23
| spl6_14 ),
inference(avatar_split_clause,[],[f44,f129,f180]) ).
fof(f44,axiom,
( sk_c11 = inverse(sk_c3)
| sk_c11 = inverse(sk_c6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f227,plain,
( spl6_20
| spl6_2 ),
inference(avatar_split_clause,[],[f5,f77,f159]) ).
fof(f5,axiom,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f225,plain,
( spl6_18
| spl6_16 ),
inference(avatar_split_clause,[],[f34,f140,f149]) ).
fof(f34,axiom,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f221,plain,
( spl6_24
| spl6_13 ),
inference(avatar_split_clause,[],[f60,f123,f197]) ).
fof(f123,plain,
( spl6_13
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
fof(f60,plain,
! [X3] :
( sP0
| sk_c11 != inverse(X3)
| sk_c10 != multiply(X3,sk_c11) ),
inference(cnf_transformation,[],[f60_D]) ).
fof(f60_D,plain,
( ! [X3] :
( sk_c11 != inverse(X3)
| sk_c10 != multiply(X3,sk_c11) )
<=> ~ sP0 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f219,plain,
( spl6_6
| spl6_16 ),
inference(avatar_split_clause,[],[f38,f140,f95]) ).
fof(f38,axiom,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f218,plain,
( spl6_17
| spl6_19 ),
inference(avatar_split_clause,[],[f13,f154,f145]) ).
fof(f13,axiom,
( sk_c10 = multiply(sk_c4,sk_c11)
| sk_c11 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f213,plain,
( spl6_18
| spl6_7 ),
inference(avatar_split_clause,[],[f25,f99,f149]) ).
fof(f25,axiom,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f210,plain,
( spl6_21
| spl6_23 ),
inference(avatar_split_clause,[],[f53,f180,f170]) ).
fof(f53,axiom,
( sk_c11 = inverse(sk_c6)
| sk_c11 = multiply(sk_c3,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
fof(f206,plain,
( spl6_9
| spl6_10 ),
inference(avatar_split_clause,[],[f62,f112,f108]) ).
fof(f108,plain,
( spl6_9
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
fof(f62,plain,
! [X8] :
( sk_c11 != multiply(X8,sk_c10)
| sk_c11 != inverse(X8)
| sP1 ),
inference(cnf_transformation,[],[f62_D]) ).
fof(f62_D,plain,
( ! [X8] :
( sk_c11 != multiply(X8,sk_c10)
| sk_c11 != inverse(X8) )
<=> ~ sP1 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f203,plain,
( spl6_8
| spl6_25 ),
inference(avatar_split_clause,[],[f66,f201,f104]) ).
fof(f104,plain,
( spl6_8
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
fof(f66,plain,
! [X9] :
( sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != multiply(inverse(X9),sk_c9)
| sP3 ),
inference(cnf_transformation,[],[f66_D]) ).
fof(f66_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(f199,plain,
( spl6_24
| spl6_12 ),
inference(avatar_split_clause,[],[f64,f119,f197]) ).
fof(f119,plain,
( spl6_12
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
fof(f64,plain,
! [X6] :
( sP2
| sk_c10 != multiply(X6,sk_c11)
| sk_c11 != inverse(X6) ),
inference(cnf_transformation,[],[f64_D]) ).
fof(f64_D,plain,
( ! [X6] :
( sk_c10 != multiply(X6,sk_c11)
| sk_c11 != inverse(X6) )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f192,plain,
( spl6_11
| spl6_5 ),
inference(avatar_split_clause,[],[f68,f91,f115]) ).
fof(f115,plain,
( spl6_11
<=> sP4 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
fof(f68,plain,
! [X7] :
( sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| sP4 ),
inference(cnf_transformation,[],[f68_D]) ).
fof(f68_D,plain,
( ! [X7] :
( sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10) )
<=> ~ sP4 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).
fof(f191,plain,
( spl6_16
| spl6_3 ),
inference(avatar_split_clause,[],[f39,f82,f140]) ).
fof(f39,axiom,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c10 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f190,plain,
( spl6_15
| spl6_21 ),
inference(avatar_split_clause,[],[f54,f170,f134]) ).
fof(f54,axiom,
( sk_c11 = multiply(sk_c3,sk_c10)
| sk_c11 = multiply(sk_c6,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f187,plain,
( spl6_2
| spl6_19 ),
inference(avatar_split_clause,[],[f4,f154,f77]) ).
fof(f4,axiom,
( sk_c10 = multiply(sk_c4,sk_c11)
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f178,plain,
( spl6_22
| spl6_16 ),
inference(avatar_split_clause,[],[f37,f140,f175]) ).
fof(f37,axiom,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c7,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f166,plain,
( spl6_16
| spl6_1 ),
inference(avatar_split_clause,[],[f33,f73,f140]) ).
fof(f33,axiom,
( multiply(sk_c5,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f163,plain,
( spl6_17
| spl6_20 ),
inference(avatar_split_clause,[],[f14,f159,f145]) ).
fof(f14,axiom,
( sk_c11 = inverse(sk_c4)
| sk_c11 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f138,plain,
( spl6_7
| spl6_1 ),
inference(avatar_split_clause,[],[f24,f73,f99]) ).
fof(f24,axiom,
( multiply(sk_c5,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c2,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f137,plain,
( spl6_14
| spl6_15 ),
inference(avatar_split_clause,[],[f45,f134,f129]) ).
fof(f45,axiom,
( sk_c11 = multiply(sk_c6,sk_c10)
| sk_c11 = inverse(sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f126,plain,
( ~ spl6_8
| ~ spl6_9
| ~ spl6_4
| spl6_10
| ~ spl6_11
| ~ spl6_12
| ~ spl6_13 ),
inference(avatar_split_clause,[],[f71,f123,f119,f115,f112,f87,f108,f104]) ).
fof(f87,plain,
( spl6_4
<=> sP5 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f71,plain,
! [X5] :
( ~ sP0
| ~ sP2
| ~ sP4
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| ~ sP5
| ~ sP1
| ~ sP3 ),
inference(general_splitting,[],[f69,f70_D]) ).
fof(f70,plain,
! [X4] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4)
| sP5 ),
inference(cnf_transformation,[],[f70_D]) ).
fof(f70_D,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4) )
<=> ~ sP5 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).
fof(f69,plain,
! [X4,X5] :
( sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| ~ sP0
| ~ sP1
| ~ sP2
| ~ sP3
| ~ sP4 ),
inference(general_splitting,[],[f67,f68_D]) ).
fof(f67,plain,
! [X7,X4,X5] :
( sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| ~ sP0
| ~ sP1
| ~ sP2
| ~ sP3 ),
inference(general_splitting,[],[f65,f66_D]) ).
fof(f65,plain,
! [X9,X7,X4,X5] :
( sk_c10 != multiply(inverse(X9),sk_c9)
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| ~ sP0
| ~ sP1
| ~ sP2 ),
inference(general_splitting,[],[f63,f64_D]) ).
fof(f63,plain,
! [X6,X9,X7,X4,X5] :
( sk_c11 != inverse(X6)
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(inverse(X9),sk_c9)
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != multiply(X9,inverse(X9))
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| ~ sP0
| ~ sP1 ),
inference(general_splitting,[],[f61,f62_D]) ).
fof(f61,plain,
! [X8,X6,X9,X7,X4,X5] :
( sk_c11 != inverse(X6)
| sk_c11 != multiply(X8,sk_c10)
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(inverse(X9),sk_c9)
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != multiply(X9,inverse(X9))
| sk_c11 != inverse(X8)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10)
| ~ sP0 ),
inference(general_splitting,[],[f59,f60_D]) ).
fof(f59,plain,
! [X3,X8,X6,X9,X7,X4,X5] :
( sk_c11 != inverse(X6)
| sk_c11 != multiply(X8,sk_c10)
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(inverse(X9),sk_c9)
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != multiply(X9,inverse(X9))
| sk_c11 != inverse(X8)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| sk_c11 != multiply(X5,sk_c10) ),
inference(equality_resolution,[],[f58]) ).
fof(f58,axiom,
! [X3,X10,X8,X6,X9,X7,X4,X5] :
( sk_c11 != inverse(X6)
| sk_c11 != multiply(X8,sk_c10)
| sk_c10 != multiply(X6,sk_c11)
| sk_c10 != multiply(X10,sk_c9)
| sk_c10 != inverse(X7)
| sk_c9 != multiply(X7,sk_c10)
| sk_c10 != multiply(X3,sk_c11)
| sk_c11 != inverse(X3)
| sk_c9 != multiply(X4,sk_c10)
| sk_c10 != multiply(X9,X10)
| sk_c11 != inverse(X8)
| sk_c10 != inverse(X4)
| sk_c11 != inverse(X5)
| inverse(X9) != X10
| sk_c11 != multiply(X5,sk_c10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_55) ).
fof(f93,plain,
( spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f70,f91,f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP244-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % 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 : n022.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 22:23:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 % (11280)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.47 % (11280)First to succeed.
% 0.20/0.47 % (11280)Refutation found. Thanks to Tanya!
% 0.20/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.47 % (11280)------------------------------
% 0.20/0.47 % (11280)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.47 % (11280)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.47 % (11280)Termination reason: Refutation
% 0.20/0.47
% 0.20/0.47 % (11280)Memory used [KB]: 5884
% 0.20/0.47 % (11280)Time elapsed: 0.069 s
% 0.20/0.47 % (11280)Instructions burned: 26 (million)
% 0.20/0.47 % (11280)------------------------------
% 0.20/0.47 % (11280)------------------------------
% 0.20/0.47 % (11253)Success in time 0.122 s
%------------------------------------------------------------------------------