TSTP Solution File: GRP310-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP310-1 : 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 : n027.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 16:21:15 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 43
% Syntax : Number of formulae : 196 ( 15 unt; 0 def)
% Number of atoms : 695 ( 224 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 957 ( 458 ~; 483 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f610,plain,
$false,
inference(avatar_sat_refutation,[],[f46,f55,f60,f65,f70,f75,f76,f81,f82,f83,f84,f86,f94,f95,f96,f98,f99,f100,f101,f102,f103,f104,f105,f129,f132,f216,f238,f280,f284,f305,f320,f340,f345,f441,f509,f609]) ).
fof(f609,plain,
( ~ spl0_12
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f608]) ).
fof(f608,plain,
( $false
| ~ spl0_12
| ~ spl0_14
| ~ spl0_16 ),
inference(subsumption_resolution,[],[f600,f389]) ).
fof(f389,plain,
! [X2] : inverse(inverse(X2)) = X2,
inference(forward_demodulation,[],[f380,f367]) ).
fof(f367,plain,
! [X4] : multiply(X4,identity) = X4,
inference(superposition,[],[f266,f264]) ).
fof(f264,plain,
! [X1] : multiply(inverse(inverse(X1)),identity) = X1,
inference(superposition,[],[f145,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f145,plain,
! [X2,X3] : multiply(inverse(X2),multiply(X2,X3)) = X3,
inference(forward_demodulation,[],[f134,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f134,plain,
! [X2,X3] : multiply(inverse(X2),multiply(X2,X3)) = multiply(identity,X3),
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(f266,plain,
! [X6,X5] : multiply(X5,X6) = multiply(inverse(inverse(X5)),X6),
inference(superposition,[],[f145,f145]) ).
fof(f380,plain,
! [X2] : multiply(X2,identity) = inverse(inverse(X2)),
inference(superposition,[],[f367,f266]) ).
fof(f600,plain,
( identity != inverse(inverse(identity))
| ~ spl0_12
| ~ spl0_14
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f598]) ).
fof(f598,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_12
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f492,f370]) ).
fof(f370,plain,
! [X1] : identity = multiply(X1,inverse(X1)),
inference(superposition,[],[f2,f266]) ).
fof(f492,plain,
( ! [X4] :
( identity != multiply(identity,X4)
| identity != inverse(X4) )
| ~ spl0_12
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f491,f367]) ).
fof(f491,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != multiply(identity,multiply(X4,identity)) )
| ~ spl0_12
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f483,f479]) ).
fof(f479,plain,
( identity = sk_c8
| ~ spl0_16 ),
inference(forward_demodulation,[],[f127,f378]) ).
fof(f378,plain,
identity = inverse(identity),
inference(superposition,[],[f367,f2]) ).
fof(f127,plain,
( sk_c8 = inverse(identity)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f126,plain,
( spl0_16
<=> sk_c8 = inverse(identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f483,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_12
| ~ spl0_14
| ~ spl0_16 ),
inference(backward_demodulation,[],[f450,f479]) ).
fof(f450,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| identity != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f93,f118]) ).
fof(f118,plain,
( identity = sk_c7
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f117,plain,
( spl0_14
<=> identity = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f93,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f92,plain,
( spl0_12
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f509,plain,
( spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f508,plain,
( $false
| spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(subsumption_resolution,[],[f507,f479]) ).
fof(f507,plain,
( identity != sk_c8
| spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f506,f378]) ).
fof(f506,plain,
( sk_c8 != inverse(identity)
| spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f115,f482]) ).
fof(f482,plain,
( identity = sk_c6
| ~ spl0_14
| ~ spl0_16 ),
inference(backward_demodulation,[],[f449,f479]) ).
fof(f449,plain,
( sk_c8 = sk_c6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f448,f367]) ).
fof(f448,plain,
( sk_c6 = multiply(sk_c8,identity)
| ~ spl0_14 ),
inference(forward_demodulation,[],[f4,f118]) ).
fof(f4,axiom,
multiply(sk_c8,sk_c7) = sk_c6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f115,plain,
( sk_c8 != inverse(sk_c6)
| spl0_13 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f113,plain,
( spl0_13
<=> sk_c8 = inverse(sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f441,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f440,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_14 ),
inference(subsumption_resolution,[],[f433,f389]) ).
fof(f433,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f432]) ).
fof(f432,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_14 ),
inference(superposition,[],[f375,f370]) ).
fof(f375,plain,
( ! [X4] :
( identity != multiply(identity,X4)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_14 ),
inference(backward_demodulation,[],[f350,f367]) ).
fof(f350,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != multiply(identity,multiply(X4,identity)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f349,f118]) ).
fof(f349,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c7 != multiply(identity,multiply(X4,identity)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f348,f322]) ).
fof(f322,plain,
( identity = sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f307,f317]) ).
fof(f317,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f314,f1]) ).
fof(f314,plain,
( ! [X0] : multiply(sk_c8,multiply(identity,X0)) = X0
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f258,f311]) ).
fof(f311,plain,
( identity = sk_c3
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f270,f310]) ).
fof(f310,plain,
( identity = multiply(inverse(sk_c8),identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f303,f118]) ).
fof(f303,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(backward_demodulation,[],[f271,f301]) ).
fof(f301,plain,
( sk_c7 = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f294,f80]) ).
fof(f80,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f78,plain,
( spl0_10
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f294,plain,
( multiply(sk_c3,sk_c8) = sk_c5
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f74,f289]) ).
fof(f289,plain,
( sk_c3 = sk_c4
| ~ spl0_5
| ~ spl0_7 ),
inference(backward_demodulation,[],[f272,f270]) ).
fof(f272,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_7 ),
inference(superposition,[],[f145,f252]) ).
fof(f252,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f2,f64]) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f62,plain,
( spl0_7
<=> sk_c8 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f74,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f72,plain,
( spl0_9
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f271,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_2 ),
inference(superposition,[],[f145,f40]) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f38,plain,
( spl0_2
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f270,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_5 ),
inference(superposition,[],[f145,f251]) ).
fof(f251,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_5 ),
inference(superposition,[],[f2,f54]) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f52,plain,
( spl0_5
<=> sk_c8 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f258,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c3,X0)) = X0
| ~ spl0_5 ),
inference(forward_demodulation,[],[f257,f1]) ).
fof(f257,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c3,X0))
| ~ spl0_5 ),
inference(superposition,[],[f3,f251]) ).
fof(f307,plain,
( sk_c8 = multiply(sk_c8,identity)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f274,f118]) ).
fof(f274,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[],[f268,f54]) ).
fof(f268,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f145,f80]) ).
fof(f348,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f93,f322]) ).
fof(f345,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f344]) ).
fof(f344,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(subsumption_resolution,[],[f330,f342]) ).
fof(f342,plain,
( identity = inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f341,f322]) ).
fof(f341,plain,
( sk_c8 = inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f114,f324]) ).
fof(f324,plain,
( identity = sk_c6
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f275,f322]) ).
fof(f275,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_10 ),
inference(backward_demodulation,[],[f4,f274]) ).
fof(f114,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f330,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f329,f324]) ).
fof(f329,plain,
( sk_c6 != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f68,f322]) ).
fof(f68,plain,
( sk_c6 != inverse(sk_c8)
| spl0_8 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl0_8
<=> sk_c6 = inverse(sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f340,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f339,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| spl0_13
| ~ spl0_14 ),
inference(subsumption_resolution,[],[f338,f325]) ).
fof(f325,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| spl0_13
| ~ spl0_14 ),
inference(backward_demodulation,[],[f278,f322]) ).
fof(f278,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_5
| ~ spl0_10
| spl0_13 ),
inference(backward_demodulation,[],[f115,f275]) ).
fof(f338,plain,
( identity = inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f312,f322]) ).
fof(f312,plain,
( sk_c8 = inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f54,f311]) ).
fof(f320,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f319,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| spl0_16 ),
inference(subsumption_resolution,[],[f312,f128]) ).
fof(f128,plain,
( sk_c8 != inverse(identity)
| spl0_16 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f305,plain,
( spl0_15
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f286,f72,f62,f38,f122]) ).
fof(f122,plain,
( spl0_15
<=> sk_c8 = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f286,plain,
( sk_c8 = sk_c7
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f40,f285]) ).
fof(f285,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f267,f64]) ).
fof(f267,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f145,f74]) ).
fof(f284,plain,
( spl0_14
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f283,f78,f52,f117]) ).
fof(f283,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[],[f282,f2]) ).
fof(f282,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[],[f269,f275]) ).
fof(f269,plain,
sk_c7 = multiply(inverse(sk_c8),sk_c6),
inference(superposition,[],[f145,f4]) ).
fof(f280,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f279,plain,
( $false
| spl0_1
| ~ spl0_5
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f277,f274]) ).
fof(f277,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| spl0_1
| ~ spl0_5
| ~ spl0_10 ),
inference(backward_demodulation,[],[f35,f275]) ).
fof(f35,plain,
( sk_c8 != multiply(sk_c6,sk_c7)
| spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f34,plain,
( spl0_1
<=> sk_c8 = multiply(sk_c6,sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f238,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| spl0_16 ),
inference(avatar_contradiction_clause,[],[f237]) ).
fof(f237,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| spl0_16 ),
inference(subsumption_resolution,[],[f236,f192]) ).
fof(f192,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| spl0_16 ),
inference(backward_demodulation,[],[f128,f182]) ).
fof(f182,plain,
( identity = sk_c8
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f178,f107]) ).
fof(f107,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f2,f69]) ).
fof(f69,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f178,plain,
( sk_c8 = multiply(sk_c6,sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f168,f156]) ).
fof(f156,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f45,f152]) ).
fof(f152,plain,
( sk_c8 = sk_c2
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f148,f36]) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f148,plain,
( multiply(sk_c6,sk_c7) = sk_c2
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f144,f50]) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl0_4
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f144,plain,
( ! [X9] : multiply(sk_c6,multiply(sk_c8,X9)) = X9
| ~ spl0_8 ),
inference(forward_demodulation,[],[f137,f1]) ).
fof(f137,plain,
( ! [X9] : multiply(identity,X9) = multiply(sk_c6,multiply(sk_c8,X9))
| ~ spl0_8 ),
inference(superposition,[],[f3,f107]) ).
fof(f45,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f43,plain,
( spl0_3
<=> sk_c2 = multiply(sk_c1,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(sk_c6,X0)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f167,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(sk_c6,multiply(identity,X0))
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f3,f149]) ).
fof(f149,plain,
( sk_c1 = multiply(sk_c6,identity)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f144,f106]) ).
fof(f106,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_6 ),
inference(superposition,[],[f2,f59]) ).
fof(f59,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f57,plain,
( spl0_6
<=> sk_c8 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f236,plain,
( identity = inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f185,f206]) ).
fof(f206,plain,
( identity = sk_c1
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[],[f149,f189]) ).
fof(f189,plain,
( identity = multiply(sk_c6,identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[],[f107,f182]) ).
fof(f185,plain,
( identity = inverse(sk_c1)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[],[f59,f182]) ).
fof(f216,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f215,f67,f57,f48,f43,f34,f117]) ).
fof(f215,plain,
( identity = sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f201,f1]) ).
fof(f201,plain,
( sk_c7 = multiply(identity,identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[],[f157,f182]) ).
fof(f157,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[],[f50,f152]) ).
fof(f132,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f131,f89,f67,f113,f117]) ).
fof(f89,plain,
( spl0_11
<=> ! [X5] :
( sk_c7 != multiply(X5,sk_c8)
| sk_c8 != inverse(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f131,plain,
( sk_c8 != inverse(sk_c6)
| identity != sk_c7
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f111,f69]) ).
fof(f111,plain,
( identity != sk_c7
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_11 ),
inference(superposition,[],[f90,f2]) ).
fof(f90,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c8)
| sk_c8 != inverse(X5) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f129,plain,
( ~ spl0_15
| ~ spl0_16
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f110,f89,f126,f122]) ).
fof(f110,plain,
( sk_c8 != inverse(identity)
| sk_c8 != sk_c7
| ~ spl0_11 ),
inference(superposition,[],[f90,f1]) ).
fof(f105,plain,
( spl0_1
| spl0_10 ),
inference(avatar_split_clause,[],[f10,f78,f34]) ).
fof(f10,axiom,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c6,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f104,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f52,f67]) ).
fof(f6,axiom,
( sk_c8 = inverse(sk_c3)
| sk_c6 = inverse(sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f103,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f15,f78,f48]) ).
fof(f15,axiom,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f102,plain,
( spl0_6
| spl0_10 ),
inference(avatar_split_clause,[],[f25,f78,f57]) ).
fof(f25,axiom,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f101,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f29,f57,f62]) ).
fof(f29,axiom,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f100,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f18,f72,f48]) ).
fof(f18,axiom,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f99,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f19,f48,f62]) ).
fof(f19,axiom,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f98,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f28,f57,f72]) ).
fof(f28,axiom,
( sk_c8 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f96,plain,
( spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f17,f38,f48]) ).
fof(f17,axiom,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = multiply(sk_c8,sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f95,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f9,f62,f67]) ).
fof(f9,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c6 = inverse(sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f94,plain,
( ~ spl0_8
| ~ spl0_1
| spl0_11
| spl0_12
| spl0_12 ),
inference(avatar_split_clause,[],[f87,f92,f92,f89,f34,f67]) ).
fof(f87,plain,
! [X7,X4,X5] :
( sk_c8 != inverse(X7)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c7 != multiply(sk_c8,multiply(X7,sk_c8))
| sk_c7 != multiply(X5,sk_c8)
| sk_c8 != inverse(X5)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c8 != inverse(X4)
| sk_c6 != inverse(sk_c8) ),
inference(subsumption_resolution,[],[f32,f4]) ).
fof(f32,plain,
! [X7,X4,X5] :
( sk_c7 != multiply(sk_c8,multiply(X7,sk_c8))
| sk_c7 != multiply(X5,sk_c8)
| sk_c8 != inverse(X5)
| sk_c6 != inverse(sk_c8)
| sk_c8 != inverse(X7)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f31]) ).
fof(f31,plain,
! [X6,X7,X4,X5] :
( sk_c6 != inverse(sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c8 != inverse(X4)
| sk_c7 != multiply(X5,sk_c8)
| multiply(X7,sk_c8) != X6
| sk_c8 != inverse(X7)
| sk_c7 != multiply(sk_c8,X6)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f30]) ).
fof(f30,axiom,
! [X3,X6,X7,X4,X5] :
( sk_c6 != inverse(sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(X5,sk_c8)
| multiply(X7,sk_c8) != X6
| sk_c8 != inverse(X7)
| sk_c7 != multiply(sk_c8,X6)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,X3)
| sk_c8 != inverse(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f86,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f5,f67,f78]) ).
fof(f5,axiom,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f84,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f8,f67,f72]) ).
fof(f8,axiom,
( sk_c6 = inverse(sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f83,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f21,f52,f43]) ).
fof(f21,axiom,
( sk_c8 = inverse(sk_c3)
| sk_c2 = multiply(sk_c1,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f82,plain,
( spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f11,f34,f52]) ).
fof(f11,axiom,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f81,plain,
( spl0_10
| spl0_3 ),
inference(avatar_split_clause,[],[f20,f43,f78]) ).
fof(f20,axiom,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f76,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f26,f57,f52]) ).
fof(f26,axiom,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f75,plain,
( spl0_9
| spl0_3 ),
inference(avatar_split_clause,[],[f23,f43,f72]) ).
fof(f23,axiom,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f70,plain,
( spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f7,f67,f38]) ).
fof(f7,axiom,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f65,plain,
( spl0_7
| spl0_3 ),
inference(avatar_split_clause,[],[f24,f43,f62]) ).
fof(f24,axiom,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f60,plain,
( spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f27,f38,f57]) ).
fof(f27,axiom,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f55,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f52,f48]) ).
fof(f16,axiom,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f46,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f22,f38,f43]) ).
fof(f22,axiom,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c2 = multiply(sk_c1,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP310-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 22:46:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44 % (21140)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.48 % (21160)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.50 % (21140)First to succeed.
% 0.19/0.50 % (21143)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (21163)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.50 % (21153)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.50 % (21154)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.50 % (21141)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.50 % (21151)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.51 % (21142)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (21146)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51 % (21166)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)
% 0.19/0.51 % (21140)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (21140)------------------------------
% 0.19/0.52 % (21140)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (21140)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (21140)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (21140)Memory used [KB]: 5756
% 0.19/0.52 % (21140)Time elapsed: 0.106 s
% 0.19/0.52 % (21140)Instructions burned: 19 (million)
% 0.19/0.52 % (21140)------------------------------
% 0.19/0.52 % (21140)------------------------------
% 0.19/0.52 % (21135)Success in time 0.17 s
%------------------------------------------------------------------------------