TSTP Solution File: GRP175-4 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP175-4 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n149.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Tue Jun 10 00:22:31 EDT 2014
% Result : Unsatisfiable 54.94s
% Output : Refutation 54.94s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP175-4 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n149.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun 6 06:17:13 CDT 2014
% % CPUTime : 54.94
% Processing problem /tmp/CiME_15856_n149.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; a,b,identity : constant; inverse : 1; multiply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z));
% multiply(identity,X) = X;
% multiply(inverse(X),X) = identity;
% X least_upper_bound X = X;
% X greatest_lower_bound X = X;
% X least_upper_bound (X greatest_lower_bound Y) = X;
% X greatest_lower_bound (X least_upper_bound Y) = X;
% multiply(X,Y least_upper_bound Z) = multiply(X,Y) least_upper_bound multiply(X,Z);
% multiply(X,Y greatest_lower_bound Z) = multiply(X,Y) greatest_lower_bound multiply(X,Z);
% multiply(Y least_upper_bound Z,X) = multiply(Y,X) least_upper_bound multiply(Z,X);
% multiply(Y greatest_lower_bound Z,X) = multiply(Y,X) greatest_lower_bound multiply(Z,X);
% identity greatest_lower_bound b = identity;
% ";
%
% let s1 = status F "
% a lr_lex;
% b lr_lex;
% inverse lr_lex;
% identity lr_lex;
% least_upper_bound mul;
% greatest_lower_bound mul;
% multiply mul;
% ";
%
% let p1 = precedence F "
% inverse > multiply > greatest_lower_bound > least_upper_bound > identity > b > a";
%
% let s2 = status F "
% a mul;
% b mul;
% least_upper_bound mul;
% greatest_lower_bound mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% inverse > multiply > greatest_lower_bound > least_upper_bound > identity = b = a";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " identity least_upper_bound multiply(inverse(a),multiply(b,a)) = multiply(inverse(a),multiply(b,a));"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
%
% let Red_Conjectures = normalize_equations Defining_rules Conjectures;
% *)
% #time on;
%
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
%
% #time off;
%
%
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
%
% F : signature = <signature>
% X : variable_set = <variable set>
%
% Axioms : (F,X) equations = { multiply(multiply(X,Y),Z) =
% multiply(X,multiply(Y,Z)),
% multiply(identity,X) = X,
% multiply(inverse(X),X) = identity,
% X least_upper_bound X = X,
% X greatest_lower_bound X = X,
% (X greatest_lower_bound Y) least_upper_bound X =
% X,
% (X least_upper_bound Y) greatest_lower_bound X =
% X,
% multiply(X,Y least_upper_bound Z) =
% multiply(X,Y) least_upper_bound multiply(X,Z),
% multiply(X,Y greatest_lower_bound Z) =
% multiply(X,Y) greatest_lower_bound multiply(X,Z),
% multiply(Y least_upper_bound Z,X) =
% multiply(Y,X) least_upper_bound multiply(Z,X),
% multiply(Y greatest_lower_bound Z,X) =
% multiply(Y,X) greatest_lower_bound multiply(Z,X),
% b greatest_lower_bound identity = identity }
% (12 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { identity least_upper_bound multiply(
% inverse(a),
% multiply(b,a)) =
% multiply(inverse(a),multiply(b,a)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] X least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 1
% New rule produced : [2] X greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 2
% New rule produced : [3] b greatest_lower_bound identity -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 3
% New rule produced : [4] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 4
% New rule produced : [5] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 5
% New rule produced : [6] (X greatest_lower_bound Y) least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 6
% New rule produced : [7] (X least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 7
% New rule produced :
% [8] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 8
% New rule produced :
% [9]
% multiply(X,Y least_upper_bound Z) ->
% multiply(X,Y) least_upper_bound multiply(X,Z)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 9
% New rule produced :
% [10]
% multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 10
% New rule produced :
% [11]
% multiply(Y least_upper_bound Z,X) ->
% multiply(Y,X) least_upper_bound multiply(Z,X)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced :
% [12]
% multiply(Y greatest_lower_bound Z,X) ->
% multiply(Y,X) greatest_lower_bound multiply(Z,X)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] b least_upper_bound identity -> b
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] (identity greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] (b least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% (b greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> b greatest_lower_bound X
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% multiply(X,b) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] multiply(b,X) greatest_lower_bound X -> X
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] multiply(b,X) least_upper_bound X -> multiply(b,X)
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [21] multiply(inverse(identity),X) -> X
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [23] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Rule [22] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [24] multiply(X,identity) -> X
% Rule
% [18]
% multiply(X,b) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity) collapsed.
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [25] multiply(X,b) greatest_lower_bound X -> X
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [26]
% (b least_upper_bound X) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [27] multiply(X,b) least_upper_bound X -> multiply(X,b)
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [28] identity greatest_lower_bound multiply(b,b) -> identity
% Current number of equations to process: 135
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [29] (multiply(b,X) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [30] multiply(b,multiply(b,X)) greatest_lower_bound X -> X
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [31] identity least_upper_bound multiply(b,b) -> multiply(b,b)
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [32] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 160
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [33]
% (multiply(b,b) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [34] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [35] inverse(identity) -> identity
% Rule [21] multiply(inverse(identity),X) -> X collapsed.
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [36] inverse(inverse(X)) -> X
% Rule [23] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [37] identity greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 160
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [38] (multiply(X,b) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [39] multiply(b,multiply(X,b)) greatest_lower_bound X -> X
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [40]
% (X greatest_lower_bound Y) least_upper_bound multiply(b,X) -> multiply(b,X)
% Current number of equations to process: 200
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [41]
% (identity greatest_lower_bound X) least_upper_bound multiply(b,b) ->
% multiply(b,b)
% Current number of equations to process: 199
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [42]
% (X greatest_lower_bound Y) least_upper_bound multiply(X,b) -> multiply(X,b)
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [43] identity least_upper_bound inverse(b) -> identity
% Current number of equations to process: 205
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [44] multiply(X,multiply(b,b)) greatest_lower_bound X -> X
% Current number of equations to process: 231
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [45] identity greatest_lower_bound multiply(b,multiply(b,b)) -> identity
% Current number of equations to process: 230
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [46] b greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 296
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [47]
% (identity least_upper_bound X) greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 295
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [48] multiply(inverse(b),X) least_upper_bound X -> X
% Current number of equations to process: 314
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [49]
% (inverse(b) greatest_lower_bound X) least_upper_bound identity -> identity
% Current number of equations to process: 325
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [50] b least_upper_bound inverse(b) -> b
% Current number of equations to process: 334
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [51] (inverse(b) greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 335
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [52] (b least_upper_bound X) greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 338
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [53] inverse(b) greatest_lower_bound multiply(b,b) -> inverse(b)
% Current number of equations to process: 337
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [54] multiply(inverse(b),X) greatest_lower_bound X -> multiply(inverse(b),X)
% Current number of equations to process: 345
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [55] multiply(X,inverse(b)) greatest_lower_bound X -> multiply(X,inverse(b))
% Current number of equations to process: 344
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [56] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% Current number of equations to process: 417
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [57] (multiply(inverse(b),X) greatest_lower_bound Y) least_upper_bound X -> X
% Current number of equations to process: 453
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [58] inverse(b) least_upper_bound multiply(b,b) -> multiply(b,b)
% Current number of equations to process: 462
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced : [59] multiply(X,inverse(b)) least_upper_bound X -> X
% Current number of equations to process: 519
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [60]
% identity greatest_lower_bound inverse(multiply(b,b)) ->
% inverse(multiply(b,b))
% Current number of equations to process: 534
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [61] identity least_upper_bound multiply(inverse(b),inverse(b)) -> identity
% Current number of equations to process: 643
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [62] b least_upper_bound multiply(inverse(b),inverse(b)) -> b
% Current number of equations to process: 668
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [63] (multiply(X,inverse(b)) greatest_lower_bound Y) least_upper_bound X -> X
% Current number of equations to process: 773
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [64]
% identity least_upper_bound multiply(X,inverse(multiply(b,X))) -> identity
% Current number of equations to process: 821
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced : [65] multiply(Y,inverse(multiply(X,Y))) -> inverse(X)
% Rule [56] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% collapsed.
% Rule
% [64]
% identity least_upper_bound multiply(X,inverse(multiply(b,X))) -> identity
% collapsed.
% Current number of equations to process: 827
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [66] identity least_upper_bound inverse(multiply(b,b)) -> identity
% Current number of equations to process: 913
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [67] b greatest_lower_bound inverse(multiply(b,b)) -> inverse(multiply(b,b))
% Current number of equations to process: 916
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [68]
% (inverse(multiply(b,b)) greatest_lower_bound X) least_upper_bound identity ->
% identity
% Current number of equations to process: 915
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced : [69] b least_upper_bound inverse(multiply(b,b)) -> b
% Current number of equations to process: 924
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [70] inverse(b) least_upper_bound inverse(multiply(b,b)) -> inverse(b)
% Current number of equations to process: 933
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [71] (inverse(multiply(b,b)) greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 1001
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [72]
% (multiply(b,b) least_upper_bound X) greatest_lower_bound inverse(b) ->
% inverse(b)
% Current number of equations to process: 1000
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced : [73] multiply(inverse(multiply(X,Y)),X) -> inverse(Y)
% Current number of equations to process: 1022
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [74] inverse(multiply(X,b)) least_upper_bound inverse(X) -> inverse(X)
% Rule [70] inverse(b) least_upper_bound inverse(multiply(b,b)) -> inverse(b)
% collapsed.
% Current number of equations to process: 1026
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [75] inverse(multiply(Y,X)) -> multiply(inverse(X),inverse(Y))
% Rule
% [60]
% identity greatest_lower_bound inverse(multiply(b,b)) ->
% inverse(multiply(b,b)) collapsed.
% Rule [65] multiply(Y,inverse(multiply(X,Y))) -> inverse(X) collapsed.
% Rule [66] identity least_upper_bound inverse(multiply(b,b)) -> identity
% collapsed.
% Rule
% [67] b greatest_lower_bound inverse(multiply(b,b)) -> inverse(multiply(b,b))
% collapsed.
% Rule
% [68]
% (inverse(multiply(b,b)) greatest_lower_bound X) least_upper_bound identity ->
% identity collapsed.
% Rule [69] b least_upper_bound inverse(multiply(b,b)) -> b collapsed.
% Rule
% [71] (inverse(multiply(b,b)) greatest_lower_bound X) least_upper_bound b -> b
% collapsed.
% Rule [73] multiply(inverse(multiply(X,Y)),X) -> inverse(Y) collapsed.
% Rule [74] inverse(multiply(X,b)) least_upper_bound inverse(X) -> inverse(X)
% collapsed.
% Current number of equations to process: 1034
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [76] inverse(b) greatest_lower_bound multiply(b,multiply(b,b)) -> inverse(b)
% Current number of equations to process: 1047
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [77]
% ((identity least_upper_bound X) greatest_lower_bound b) least_upper_bound identity
% -> (identity least_upper_bound X) greatest_lower_bound b
% Current number of equations to process: 1077
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [78]
% ((identity least_upper_bound X) greatest_lower_bound b) least_upper_bound X
% -> identity least_upper_bound X
% Current number of equations to process: 1090
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [79]
% multiply(b,multiply(b,X)) least_upper_bound X -> multiply(b,multiply(b,X))
% Current number of equations to process: 1176
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [80]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound b
% -> (b greatest_lower_bound X) least_upper_bound identity
% Current number of equations to process: 1254
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [81]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound X
% -> b greatest_lower_bound X
% Current number of equations to process: 1269
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [82]
% multiply(b,multiply(X,b)) least_upper_bound X -> multiply(b,multiply(X,b))
% Current number of equations to process: 1362
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [83]
% (multiply(b,multiply(b,X)) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1411
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [84]
% (multiply(b,multiply(X,b)) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1469
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [85]
% (multiply(b,multiply(b,b)) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 1513
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [86] multiply(b,multiply(b,multiply(b,X))) greatest_lower_bound X -> X
% Current number of equations to process: 1535
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [87] multiply(b,multiply(b,multiply(X,b))) greatest_lower_bound X -> X
% Current number of equations to process: 1596
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [88]
% identity greatest_lower_bound multiply(b,multiply(b,multiply(b,b))) ->
% identity
% Current number of equations to process: 1645
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [89]
% multiply(X,multiply(b,b)) least_upper_bound X -> multiply(X,multiply(b,b))
% Current number of equations to process: 1677
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [90]
% identity least_upper_bound multiply(b,multiply(b,b)) ->
% multiply(b,multiply(b,b))
% Current number of equations to process: 1722
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [91]
% (identity greatest_lower_bound X) least_upper_bound (inverse(b) greatest_lower_bound X)
% -> identity greatest_lower_bound X
% Current number of equations to process: 1740
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [92]
% (inverse(b) greatest_lower_bound X) least_upper_bound multiply(b,b) ->
% multiply(b,b)
% Current number of equations to process: 1774
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [93]
% identity greatest_lower_bound multiply(inverse(b),inverse(b)) ->
% multiply(inverse(b),inverse(b))
% Current number of equations to process: 1793
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [94]
% (multiply(X,multiply(b,b)) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1830
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [95] multiply(b,multiply(X,multiply(b,b))) greatest_lower_bound X -> X
% Current number of equations to process: 1868
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [96] multiply(X,multiply(b,multiply(b,b))) greatest_lower_bound X -> X
% Current number of equations to process: 1912
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [97]
% (b greatest_lower_bound X) least_upper_bound (inverse(b) greatest_lower_bound X)
% -> b greatest_lower_bound X
% Current number of equations to process: 1955
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [98] multiply(b,X) least_upper_bound multiply(inverse(b),X) -> multiply(b,X)
% Current number of equations to process: 2000
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [99] multiply(inverse(b),multiply(inverse(b),X)) least_upper_bound X -> X
% Current number of equations to process: 2030
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [100] multiply(inverse(b),X) least_upper_bound multiply(X,b) -> multiply(X,b)
% Current number of equations to process: 2079
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [101] multiply(X,b) least_upper_bound multiply(X,inverse(b)) -> multiply(X,b)
% Current number of equations to process: 2113
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [102]
% b greatest_lower_bound multiply(inverse(b),inverse(b)) ->
% multiply(inverse(b),inverse(b))
% Current number of equations to process: 2142
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [103]
% (multiply(inverse(b),inverse(b)) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 2184
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [104]
% (multiply(inverse(b),inverse(b)) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 2207
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [105] multiply(b,X) least_upper_bound multiply(X,inverse(b)) -> multiply(b,X)
% Current number of equations to process: 2226
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [106] multiply(inverse(b),multiply(X,inverse(b))) least_upper_bound X -> X
% Current number of equations to process: 2251
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [107]
% multiply(b,b) least_upper_bound multiply(inverse(b),inverse(b)) ->
% multiply(b,b)
% Current number of equations to process: 2294
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [108] multiply(X,multiply(inverse(b),inverse(b))) least_upper_bound X -> X
% Current number of equations to process: 2319
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [109]
% (((identity least_upper_bound X) greatest_lower_bound b) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 2359
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [110]
% (((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound Y) least_upper_bound b
% -> b
% Current number of equations to process: 2376
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [111]
% (X least_upper_bound Y) greatest_lower_bound multiply(inverse(b),X) ->
% multiply(inverse(b),X)
% Current number of equations to process: 2378
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [112]
% multiply(b,X) greatest_lower_bound multiply(inverse(b),X) ->
% multiply(inverse(b),X)
% Current number of equations to process: 2520
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [113]
% (identity least_upper_bound X) greatest_lower_bound (inverse(b) least_upper_bound X)
% -> inverse(b) least_upper_bound X
% Current number of equations to process: 2552
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [114]
% ((b greatest_lower_bound X) least_upper_bound inverse(b)) greatest_lower_bound X
% -> b greatest_lower_bound X
% Current number of equations to process: 2593
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [115]
% multiply(X,b) greatest_lower_bound multiply(X,inverse(b)) ->
% multiply(X,inverse(b))
% Current number of equations to process: 2740
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [116]
% (b least_upper_bound X) greatest_lower_bound (inverse(b) least_upper_bound X)
% -> inverse(b) least_upper_bound X
% Current number of equations to process: 2780
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [117]
% multiply(inverse(b),X) greatest_lower_bound multiply(X,b) ->
% multiply(inverse(b),X)
% Current number of equations to process: 2823
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [118]
% (X least_upper_bound Y) greatest_lower_bound multiply(X,inverse(b)) ->
% multiply(X,inverse(b))
% Current number of equations to process: 2866
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [119]
% multiply(b,X) greatest_lower_bound multiply(X,inverse(b)) ->
% multiply(X,inverse(b))
% Current number of equations to process: 2979
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [120]
% (identity least_upper_bound X) greatest_lower_bound multiply(inverse(b),
% inverse(b)) ->
% multiply(inverse(b),inverse(b))
% Current number of equations to process: 3020
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [121]
% (b least_upper_bound X) greatest_lower_bound multiply(inverse(b),inverse(b))
% -> multiply(inverse(b),inverse(b))
% Current number of equations to process: 3045
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [122]
% multiply(b,b) greatest_lower_bound multiply(inverse(b),inverse(b)) ->
% multiply(inverse(b),inverse(b))
% Current number of equations to process: 3064
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [123]
% (b greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X greatest_lower_bound Y)
% -> b greatest_lower_bound X
% Current number of equations to process: 3084
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [124]
% ((b greatest_lower_bound X) least_upper_bound Y) greatest_lower_bound identity greatest_lower_bound X
% -> identity greatest_lower_bound X
% Current number of equations to process: 3372
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [125]
% ((identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound b least_upper_bound X
% -> b least_upper_bound X
% Current number of equations to process: 3613
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [126]
% (b least_upper_bound X least_upper_bound Y) greatest_lower_bound (identity least_upper_bound Y)
% -> identity least_upper_bound Y
% Current number of equations to process: 3821
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [127]
% multiply(X,multiply(b,Y)) greatest_lower_bound multiply(X,Y) -> multiply(X,Y)
% Current number of equations to process: 4070
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [128]
% identity greatest_lower_bound multiply(inverse(X),multiply(b,X)) -> identity
% Current number of equations to process: 4085
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [129]
% identity greatest_lower_bound multiply(X,multiply(b,inverse(X))) -> identity
% Current number of equations to process: 4102
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [130]
% inverse(b) greatest_lower_bound multiply(inverse(X),multiply(b,X)) ->
% inverse(b)
% Current number of equations to process: 4279
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [131]
% inverse(b) greatest_lower_bound multiply(X,multiply(b,inverse(X))) ->
% inverse(b)
% Current number of equations to process: 4322
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [132]
% (multiply(b,X) least_upper_bound Y) greatest_lower_bound (X least_upper_bound Y)
% -> X least_upper_bound Y
% Current number of equations to process: 4377
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [133]
% multiply(X,multiply(Y,b)) greatest_lower_bound multiply(X,Y) -> multiply(X,Y)
% Current number of equations to process: 4604
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [134]
% (multiply(X,b) least_upper_bound Y) greatest_lower_bound (X least_upper_bound Y)
% -> X least_upper_bound Y
% Current number of equations to process: 4673
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [135]
% (identity least_upper_bound X) greatest_lower_bound (multiply(b,b) least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 4885
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [136]
% inverse(b) least_upper_bound multiply(b,multiply(b,b)) ->
% multiply(b,multiply(b,b))
% Current number of equations to process: 4936
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [137]
% identity least_upper_bound multiply(inverse(b),multiply(inverse(b),inverse(b)))
% -> identity
% Current number of equations to process: 4965
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [138]
% b least_upper_bound multiply(inverse(b),multiply(inverse(b),inverse(b))) -> b
% Current number of equations to process: 2278
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [139]
% (((X greatest_lower_bound Y) least_upper_bound identity) greatest_lower_bound b) least_upper_bound X
% -> identity least_upper_bound X
% Current number of equations to process: 2308
% Current number of ordered equations: 1
% Current number of rules: 123
% New rule produced :
% [140]
% (((X least_upper_bound Y) greatest_lower_bound b) least_upper_bound identity) greatest_lower_bound X
% -> b greatest_lower_bound X
% Current number of equations to process: 2817
% Current number of ordered equations: 1
% Current number of rules: 124
% New rule produced :
% [141]
% ((b greatest_lower_bound multiply(b,X)) least_upper_bound identity) greatest_lower_bound X
% -> b greatest_lower_bound X
% Current number of equations to process: 3278
% Current number of ordered equations: 1
% Current number of rules: 125
% New rule produced :
% [142]
% ((b greatest_lower_bound multiply(X,b)) least_upper_bound identity) greatest_lower_bound X
% -> b greatest_lower_bound X
% Current number of equations to process: 3347
% Current number of ordered equations: 1
% Current number of rules: 126
% New rule produced :
% [143]
% ((identity least_upper_bound X) greatest_lower_bound b) least_upper_bound
% inverse(b) -> (identity least_upper_bound X) greatest_lower_bound b
% Current number of equations to process: 3387
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [144]
% (((b greatest_lower_bound X) least_upper_bound inverse(b)) greatest_lower_bound Y) least_upper_bound b
% -> b
% Current number of equations to process: 3420
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [145]
% (b least_upper_bound multiply(b,X)) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 3460
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [146]
% (b least_upper_bound multiply(X,b)) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 3513
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [147]
% multiply(inverse(X),multiply(b,multiply(X,Y))) greatest_lower_bound Y -> Y
% Current number of equations to process: 3556
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [148]
% multiply(X,multiply(b,multiply(inverse(X),Y))) greatest_lower_bound Y -> Y
% Current number of equations to process: 3706
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [149]
% (multiply(inverse(X),multiply(b,X)) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 3856
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [150]
% multiply(X,multiply(inverse(Y),multiply(b,Y))) greatest_lower_bound X -> X
% Current number of equations to process: 3911
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [151]
% identity greatest_lower_bound multiply(b,multiply(inverse(X),multiply(b,X)))
% -> identity
% Current number of equations to process: 4022
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [152]
% identity greatest_lower_bound multiply(inverse(X),multiply(b,multiply(b,X)))
% -> identity
% Current number of equations to process: 4070
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [153]
% (multiply(X,multiply(b,inverse(X))) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 4137
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [154]
% multiply(X,multiply(Y,multiply(b,inverse(Y)))) greatest_lower_bound X -> X
% Current number of equations to process: 4188
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [155]
% identity greatest_lower_bound multiply(b,multiply(X,multiply(b,inverse(X))))
% -> identity
% Current number of equations to process: 4293
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [156]
% identity greatest_lower_bound multiply(X,multiply(b,multiply(b,inverse(X))))
% -> identity
% Current number of equations to process: 4337
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [157]
% (((identity greatest_lower_bound X) least_upper_bound inverse(b)) greatest_lower_bound Y) least_upper_bound b
% -> b
% Current number of equations to process: 4395
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [158]
% identity greatest_lower_bound multiply(inverse(X),multiply(b,multiply(X,b)))
% -> identity
% Current number of equations to process: 4432
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [159]
% identity greatest_lower_bound multiply(X,multiply(b,multiply(inverse(X),b)))
% -> identity
% Current number of equations to process: 4482
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [160]
% (multiply(b,multiply(b,b)) least_upper_bound X) greatest_lower_bound
% inverse(b) -> inverse(b)
% Current number of equations to process: 4519
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [161]
% inverse(b) greatest_lower_bound multiply(b,multiply(b,multiply(b,b))) ->
% inverse(b)
% Current number of equations to process: 4549
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [162]
% multiply(X,multiply(inverse(b),inverse(b))) greatest_lower_bound X ->
% multiply(X,multiply(inverse(b),inverse(b)))
% Current number of equations to process: 4582
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [163]
% multiply(inverse(b),multiply(inverse(b),X)) greatest_lower_bound X ->
% multiply(inverse(b),multiply(inverse(b),X))
% Current number of equations to process: 4720
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [164]
% (((identity least_upper_bound X) greatest_lower_bound b) least_upper_bound Y) greatest_lower_bound
% inverse(b) -> inverse(b)
% Current number of equations to process: 4891
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [165]
% ((identity greatest_lower_bound X) least_upper_bound inverse(b)) greatest_lower_bound identity
% -> (identity greatest_lower_bound X) least_upper_bound inverse(b)
% Current number of equations to process: 4914
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [166]
% ((identity greatest_lower_bound X) least_upper_bound inverse(b)) greatest_lower_bound X
% -> identity greatest_lower_bound X
% Current number of equations to process: 4931
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [167]
% (((identity greatest_lower_bound X) least_upper_bound inverse(b)) greatest_lower_bound Y) least_upper_bound identity
% -> identity
% Current number of equations to process: 4954
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [168]
% ((b greatest_lower_bound X) least_upper_bound inverse(b)) greatest_lower_bound b
% -> (b greatest_lower_bound X) least_upper_bound inverse(b)
% Current number of equations to process: 3479
% Current number of ordered equations: 0
% Current number of rules: 152
% New rule produced :
% [169]
% ((identity greatest_lower_bound X) least_upper_bound inverse(b)) greatest_lower_bound b
% -> (identity greatest_lower_bound X) least_upper_bound inverse(b)
% Current number of equations to process: 3542
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [170]
% identity least_upper_bound multiply(inverse(X),multiply(b,X)) ->
% multiply(inverse(X),multiply(b,X))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 3590
% Current number of ordered equations: 0
% Current number of rules: 154
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 9 rules have been used:
% [3]
% b greatest_lower_bound identity -> identity; trace = in the starting set
% [5] multiply(inverse(X),X) -> identity; trace = in the starting set
% [6] (X greatest_lower_bound Y) least_upper_bound X -> X; trace = in the starting set
% [10] multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z); trace = in the starting set
% [12] multiply(Y greatest_lower_bound Z,X) ->
% multiply(Y,X) greatest_lower_bound multiply(Z,X); trace = in the starting set
% [19] multiply(b,X) greatest_lower_bound X -> X; trace = Cp of 12 and 3
% [127] multiply(X,multiply(b,Y)) greatest_lower_bound multiply(X,Y) ->
% multiply(X,Y); trace = Cp of 19 and 10
% [128] identity greatest_lower_bound multiply(inverse(X),multiply(b,X)) ->
% identity; trace = Cp of 127 and 5
% [170] identity least_upper_bound multiply(inverse(X),multiply(b,X)) ->
% multiply(inverse(X),multiply(b,X)); trace = Cp of 128 and 6
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 53.750000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------