TSTP Solution File: GRP174-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP174-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 : Tue Apr 30 11:52:01 EDT 2024
% Result : Unsatisfiable 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 64
% Syntax : Number of formulae : 166 ( 37 unt; 0 def)
% Number of atoms : 369 ( 118 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 362 ( 159 ~; 157 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 48 ( 46 usr; 47 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 213 ( 213 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1308,plain,
$false,
inference(avatar_sat_refutation,[],[f23,f28,f32,f36,f40,f44,f49,f53,f57,f61,f65,f79,f84,f88,f92,f136,f140,f144,f148,f235,f241,f245,f277,f282,f300,f313,f317,f361,f376,f389,f393,f398,f402,f406,f410,f415,f419,f423,f427,f431,f435,f1123,f1127,f1131,f1135,f1306,f1307]) ).
fof(f1307,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_13
| ~ spl0_20
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1205,f1125,f232,f81,f30,f20]) ).
fof(f20,plain,
( spl0_1
<=> identity = a ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f30,plain,
( spl0_3
<=> ! [X0] : multiply(identity,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f81,plain,
( spl0_13
<=> identity = least_upper_bound(identity,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f232,plain,
( spl0_20
<=> identity = least_upper_bound(identity,inverse(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1125,plain,
( spl0_43
<=> ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1205,plain,
( identity = a
| ~ spl0_3
| ~ spl0_13
| ~ spl0_20
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1204,f83]) ).
fof(f83,plain,
( identity = least_upper_bound(identity,a)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f1204,plain,
( a = least_upper_bound(identity,a)
| ~ spl0_3
| ~ spl0_20
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1183,f31]) ).
fof(f31,plain,
( ! [X0] : multiply(identity,X0) = X0
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f1183,plain,
( multiply(identity,a) = least_upper_bound(identity,multiply(identity,a))
| ~ spl0_20
| ~ spl0_43 ),
inference(superposition,[],[f1126,f234]) ).
fof(f234,plain,
( identity = least_upper_bound(identity,inverse(a))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f1126,plain,
( ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1125]) ).
fof(f1306,plain,
( spl0_46
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f109,f86,f63,f1304]) ).
fof(f1304,plain,
( spl0_46
<=> ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X0,X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f63,plain,
( spl0_11
<=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f86,plain,
( spl0_14
<=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f109,plain,
( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X0,X1),X2)))
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f87,f64]) ).
fof(f64,plain,
( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f87,plain,
( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f1135,plain,
( spl0_45
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f228,f146,f51,f42,f1133]) ).
fof(f1133,plain,
( spl0_45
<=> ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f42,plain,
( spl0_6
<=> ! [X0] : identity = multiply(inverse(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f51,plain,
( spl0_8
<=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f146,plain,
( spl0_19
<=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f228,plain,
( ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_19 ),
inference(forward_demodulation,[],[f216,f52]) ).
fof(f52,plain,
( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f216,plain,
( ! [X0,X1] : multiply(greatest_lower_bound(X1,inverse(X0)),X0) = greatest_lower_bound(multiply(X1,X0),identity)
| ~ spl0_6
| ~ spl0_19 ),
inference(superposition,[],[f147,f43]) ).
fof(f43,plain,
( ! [X0] : identity = multiply(inverse(X0),X0)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f147,plain,
( ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f1131,plain,
( spl0_44
| ~ spl0_6
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f213,f146,f42,f1129]) ).
fof(f1129,plain,
( spl0_44
<=> ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f213,plain,
( ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0))
| ~ spl0_6
| ~ spl0_19 ),
inference(superposition,[],[f147,f43]) ).
fof(f1127,plain,
( spl0_43
| ~ spl0_6
| ~ spl0_9
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f209,f142,f55,f42,f1125]) ).
fof(f55,plain,
( spl0_9
<=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f142,plain,
( spl0_18
<=> ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f209,plain,
( ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_18 ),
inference(forward_demodulation,[],[f197,f56]) ).
fof(f56,plain,
( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f197,plain,
( ! [X0,X1] : multiply(least_upper_bound(X1,inverse(X0)),X0) = least_upper_bound(multiply(X1,X0),identity)
| ~ spl0_6
| ~ spl0_18 ),
inference(superposition,[],[f143,f43]) ).
fof(f143,plain,
( ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f1123,plain,
( spl0_42
| ~ spl0_6
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f194,f142,f42,f1121]) ).
fof(f1121,plain,
( spl0_42
<=> ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f194,plain,
( ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0))
| ~ spl0_6
| ~ spl0_18 ),
inference(superposition,[],[f143,f43]) ).
fof(f435,plain,
( spl0_41
| ~ spl0_3
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f215,f146,f30,f433]) ).
fof(f433,plain,
( spl0_41
<=> ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f215,plain,
( ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0)
| ~ spl0_3
| ~ spl0_19 ),
inference(superposition,[],[f147,f31]) ).
fof(f431,plain,
( spl0_40
| ~ spl0_3
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f283,f275,f30,f429]) ).
fof(f429,plain,
( spl0_40
<=> ! [X0] : multiply(inverse(identity),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f275,plain,
( spl0_23
<=> ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f283,plain,
( ! [X0] : multiply(inverse(identity),X0) = X0
| ~ spl0_3
| ~ spl0_23 ),
inference(superposition,[],[f276,f31]) ).
fof(f276,plain,
( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f427,plain,
( spl0_39
| ~ spl0_3
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f212,f146,f30,f425]) ).
fof(f425,plain,
( spl0_39
<=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f212,plain,
( ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0))
| ~ spl0_3
| ~ spl0_19 ),
inference(superposition,[],[f147,f31]) ).
fof(f423,plain,
( spl0_38
| ~ spl0_3
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f196,f142,f30,f421]) ).
fof(f421,plain,
( spl0_38
<=> ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f196,plain,
( ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f143,f31]) ).
fof(f419,plain,
( spl0_37
| ~ spl0_3
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f193,f142,f30,f417]) ).
fof(f417,plain,
( spl0_37
<=> ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f193,plain,
( ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0))
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f143,f31]) ).
fof(f415,plain,
( spl0_36
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f123,f90,f55,f413]) ).
fof(f413,plain,
( spl0_36
<=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f90,plain,
( spl0_15
<=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f123,plain,
( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1))
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f91,f56]) ).
fof(f91,plain,
( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f410,plain,
( spl0_35
| ~ spl0_4
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f122,f90,f34,f408]) ).
fof(f408,plain,
( spl0_35
<=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f34,plain,
( spl0_4
<=> ! [X0] : least_upper_bound(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f122,plain,
( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X1)))
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f91,f35]) ).
fof(f35,plain,
( ! [X0] : least_upper_bound(X0,X0) = X0
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f406,plain,
( spl0_34
| ~ spl0_10
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f120,f90,f59,f404]) ).
fof(f404,plain,
( spl0_34
<=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f59,plain,
( spl0_10
<=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f120,plain,
( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2)
| ~ spl0_10
| ~ spl0_15 ),
inference(superposition,[],[f91,f60]) ).
fof(f60,plain,
( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f402,plain,
( spl0_33
| ~ spl0_9
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f118,f90,f55,f400]) ).
fof(f400,plain,
( spl0_33
<=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f118,plain,
( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2)
| ~ spl0_9
| ~ spl0_15 ),
inference(superposition,[],[f91,f56]) ).
fof(f398,plain,
( spl0_32
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f107,f86,f51,f396]) ).
fof(f396,plain,
( spl0_32
<=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f107,plain,
( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1))
| ~ spl0_8
| ~ spl0_14 ),
inference(superposition,[],[f87,f52]) ).
fof(f393,plain,
( spl0_31
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f106,f86,f38,f391]) ).
fof(f391,plain,
( spl0_31
<=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f38,plain,
( spl0_5
<=> ! [X0] : greatest_lower_bound(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f106,plain,
( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X1)))
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[],[f87,f39]) ).
fof(f39,plain,
( ! [X0] : greatest_lower_bound(X0,X0) = X0
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f389,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f104,f86,f63,f387]) ).
fof(f387,plain,
( spl0_30
<=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f104,plain,
( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2)
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f87,f64]) ).
fof(f376,plain,
( spl0_29
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f102,f86,f51,f374]) ).
fof(f374,plain,
( spl0_29
<=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X1,X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f102,plain,
( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X1,X0),X2)
| ~ spl0_8
| ~ spl0_14 ),
inference(superposition,[],[f87,f52]) ).
fof(f361,plain,
( spl0_28
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f100,f86,f46,f359]) ).
fof(f359,plain,
( spl0_28
<=> ! [X0] : greatest_lower_bound(inverse(a),X0) = greatest_lower_bound(identity,greatest_lower_bound(inverse(a),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f46,plain,
( spl0_7
<=> inverse(a) = greatest_lower_bound(identity,inverse(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f100,plain,
( ! [X0] : greatest_lower_bound(inverse(a),X0) = greatest_lower_bound(identity,greatest_lower_bound(inverse(a),X0))
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f87,f48]) ).
fof(f48,plain,
( inverse(a) = greatest_lower_bound(identity,inverse(a))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f317,plain,
( spl0_27
| ~ spl0_4
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f117,f90,f34,f315]) ).
fof(f315,plain,
( spl0_27
<=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f117,plain,
( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1))
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f91,f35]) ).
fof(f313,plain,
( spl0_26
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f101,f86,f38,f311]) ).
fof(f311,plain,
( spl0_26
<=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f101,plain,
( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1))
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[],[f87,f39]) ).
fof(f300,plain,
( spl0_25
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f99,f86,f25,f298]) ).
fof(f298,plain,
( spl0_25
<=> ! [X0] : greatest_lower_bound(a,X0) = greatest_lower_bound(identity,greatest_lower_bound(a,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f25,plain,
( spl0_2
<=> a = greatest_lower_bound(identity,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f99,plain,
( ! [X0] : greatest_lower_bound(a,X0) = greatest_lower_bound(identity,greatest_lower_bound(a,X0))
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f87,f27]) ).
fof(f27,plain,
( a = greatest_lower_bound(identity,a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f282,plain,
( spl0_24
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f264,f243,f81,f279]) ).
fof(f279,plain,
( spl0_24
<=> a = greatest_lower_bound(a,identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f243,plain,
( spl0_22
<=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f264,plain,
( a = greatest_lower_bound(a,identity)
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f244,f83]) ).
fof(f244,plain,
( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f277,plain,
( spl0_23
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f96,f77,f42,f30,f275]) ).
fof(f77,plain,
( spl0_12
<=> ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f96,plain,
( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f94,f31]) ).
fof(f94,plain,
( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1)
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[],[f78,f43]) ).
fof(f78,plain,
( ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f245,plain,
( spl0_22
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f72,f63,f55,f243]) ).
fof(f72,plain,
( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f64,f56]) ).
fof(f241,plain,
( spl0_21
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f69,f59,f51,f239]) ).
fof(f239,plain,
( spl0_21
<=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f69,plain,
( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f60,f52]) ).
fof(f235,plain,
( spl0_20
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f67,f59,f46,f232]) ).
fof(f67,plain,
( identity = least_upper_bound(identity,inverse(a))
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f60,f48]) ).
fof(f148,plain,
spl0_19,
inference(avatar_split_clause,[],[f15,f146]) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f144,plain,
spl0_18,
inference(avatar_split_clause,[],[f14,f142]) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f140,plain,
spl0_17,
inference(avatar_split_clause,[],[f13,f138]) ).
fof(f138,plain,
( spl0_17
<=> ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
fof(f136,plain,
spl0_16,
inference(avatar_split_clause,[],[f12,f134]) ).
fof(f134,plain,
( spl0_16
<=> ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f92,plain,
spl0_15,
inference(avatar_split_clause,[],[f7,f90]) ).
fof(f7,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f88,plain,
spl0_14,
inference(avatar_split_clause,[],[f6,f86]) ).
fof(f6,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
fof(f84,plain,
( spl0_13
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f66,f59,f25,f81]) ).
fof(f66,plain,
( identity = least_upper_bound(identity,a)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f60,f27]) ).
fof(f79,plain,
spl0_12,
inference(avatar_split_clause,[],[f3,f77]) ).
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(f65,plain,
spl0_11,
inference(avatar_split_clause,[],[f11,f63]) ).
fof(f11,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
fof(f61,plain,
spl0_10,
inference(avatar_split_clause,[],[f10,f59]) ).
fof(f10,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f57,plain,
spl0_9,
inference(avatar_split_clause,[],[f5,f55]) ).
fof(f5,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f53,plain,
spl0_8,
inference(avatar_split_clause,[],[f4,f51]) ).
fof(f4,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f49,plain,
spl0_7,
inference(avatar_split_clause,[],[f17,f46]) ).
fof(f17,axiom,
inverse(a) = greatest_lower_bound(identity,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p05b_2) ).
fof(f44,plain,
spl0_6,
inference(avatar_split_clause,[],[f2,f42]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f40,plain,
spl0_5,
inference(avatar_split_clause,[],[f9,f38]) ).
fof(f9,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_gld) ).
fof(f36,plain,
spl0_4,
inference(avatar_split_clause,[],[f8,f34]) ).
fof(f8,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_lub) ).
fof(f32,plain,
spl0_3,
inference(avatar_split_clause,[],[f1,f30]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f28,plain,
spl0_2,
inference(avatar_split_clause,[],[f16,f25]) ).
fof(f16,axiom,
a = greatest_lower_bound(identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p05b_1) ).
fof(f23,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f18,f20]) ).
fof(f18,axiom,
identity != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p05b) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP174-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 04:51:25 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (19660)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (19665)WARNING: value z3 for option sas not known
% 0.21/0.37 % (19666)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (19664)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (19663)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (19665)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37 % (19667)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.37 % (19668)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.37 % (19669)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.37 TRYING [1]
% 0.21/0.37 TRYING [2]
% 0.21/0.37 TRYING [3]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [4]
% 0.21/0.43 % (19667)First to succeed.
% 0.21/0.43 % (19667)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.43 % (19667)------------------------------
% 0.21/0.43 % (19667)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.43 % (19667)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (19667)Memory used [KB]: 1634
% 0.21/0.43 % (19667)Time elapsed: 0.063 s
% 0.21/0.43 % (19667)Instructions burned: 106 (million)
% 0.21/0.43 % (19667)------------------------------
% 0.21/0.43 % (19667)------------------------------
% 0.21/0.43 % (19660)Success in time 0.079 s
%------------------------------------------------------------------------------