TSTP Solution File: GRP175-3 by CiME---2.01
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP175-3 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n138.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 21.89s
% Output : Refutation 21.89s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP175-3 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n138.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 06:15:33 CDT 2014
% % CPUTime : 21.89
% Processing problem /tmp/CiME_6909_n138.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 least_upper_bound b = b;
% ";
%
% 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 greatest_lower_bound multiply(inverse(a),multiply(b,a)) = identity;"
% ;
% (*
% 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 least_upper_bound identity = b }
% (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 greatest_lower_bound multiply(
% inverse(a),
% multiply(b,a))
% = identity } (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] b least_upper_bound identity -> b
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 2
% New rule produced : [3] X greatest_lower_bound X -> X
% 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 greatest_lower_bound identity -> identity
% Current number of equations to process: 33
% 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 least_upper_bound X) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18] multiply(X,b) least_upper_bound multiply(X,identity) -> multiply(X,b)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] multiply(b,X) least_upper_bound X -> multiply(b,X)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] multiply(b,X) greatest_lower_bound X -> 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) least_upper_bound multiply(X,identity) -> multiply(X,b)
% 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) least_upper_bound X -> multiply(X,b)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [26]
% (b greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> b greatest_lower_bound X
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [27] multiply(X,b) greatest_lower_bound X -> X
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [28] identity least_upper_bound multiply(b,b) -> multiply(b,b)
% Current number of equations to process: 136
% 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: 135
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [30] identity greatest_lower_bound multiply(b,b) -> identity
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [31] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [32]
% (multiply(b,b) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [33] multiply(b,multiply(b,X)) greatest_lower_bound X -> X
% Current number of equations to process: 160
% 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: 160
% 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: 160
% 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: 160
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [37] identity least_upper_bound inverse(b) -> identity
% Current number of equations to process: 161
% 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: 171
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [39]
% (X greatest_lower_bound Y) least_upper_bound multiply(b,X) -> multiply(b,X)
% Current number of equations to process: 204
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [40]
% (identity greatest_lower_bound X) least_upper_bound multiply(b,b) ->
% multiply(b,b)
% Current number of equations to process: 203
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [41]
% (X greatest_lower_bound Y) least_upper_bound multiply(X,b) -> multiply(X,b)
% Current number of equations to process: 200
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [42] identity greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 206
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [43] multiply(b,multiply(X,b)) greatest_lower_bound X -> X
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [44]
% (identity least_upper_bound X) greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [45] multiply(X,multiply(b,b)) greatest_lower_bound X -> X
% Current number of equations to process: 268
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [46] identity greatest_lower_bound multiply(b,multiply(b,b)) -> identity
% Current number of equations to process: 267
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [47] b greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 306
% 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] b least_upper_bound inverse(b) -> b
% Current number of equations to process: 321
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [50]
% (inverse(b) greatest_lower_bound X) least_upper_bound identity -> identity
% Current number of equations to process: 328
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [51] multiply(X,inverse(b)) least_upper_bound X -> X
% Current number of equations to process: 330
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [52] inverse(b) least_upper_bound multiply(b,b) -> multiply(b,b)
% Current number of equations to process: 330
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [53] multiply(inverse(b),X) greatest_lower_bound X -> multiply(inverse(b),X)
% Current number of equations to process: 336
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [54] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% Current number of equations to process: 391
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [55] (multiply(inverse(b),X) greatest_lower_bound Y) least_upper_bound X -> X
% Current number of equations to process: 418
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [56] (inverse(b) greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 495
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [57] (b least_upper_bound X) greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 500
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [58] inverse(b) greatest_lower_bound multiply(b,b) -> inverse(b)
% Current number of equations to process: 499
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [59] multiply(X,inverse(b)) greatest_lower_bound X -> multiply(X,inverse(b))
% Current number of equations to process: 514
% 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: 560
% 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: 667
% 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: 666
% 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: 727
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced : [64] multiply(Y,inverse(multiply(X,Y))) -> inverse(X)
% Rule [54] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% collapsed.
% Current number of equations to process: 768
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [65] identity least_upper_bound inverse(multiply(b,b)) -> identity
% Current number of equations to process: 920
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [66]
% (inverse(multiply(b,b)) greatest_lower_bound X) least_upper_bound identity ->
% identity
% Current number of equations to process: 923
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced : [67] b least_upper_bound inverse(multiply(b,b)) -> b
% Current number of equations to process: 934
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [68] b greatest_lower_bound inverse(multiply(b,b)) -> inverse(multiply(b,b))
% Current number of equations to process: 935
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [69] inverse(b) least_upper_bound inverse(multiply(b,b)) -> inverse(b)
% Current number of equations to process: 942
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [70] (inverse(multiply(b,b)) greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 1009
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced : [71] multiply(inverse(multiply(X,Y)),X) -> inverse(Y)
% Current number of equations to process: 1033
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [72] 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 [64] multiply(Y,inverse(multiply(X,Y))) -> inverse(X) collapsed.
% Rule [65] identity least_upper_bound inverse(multiply(b,b)) -> identity
% collapsed.
% Rule
% [66]
% (inverse(multiply(b,b)) greatest_lower_bound X) least_upper_bound identity ->
% identity collapsed.
% Rule [67] b least_upper_bound inverse(multiply(b,b)) -> b collapsed.
% Rule
% [68] b greatest_lower_bound inverse(multiply(b,b)) -> inverse(multiply(b,b))
% collapsed.
% Rule [69] inverse(b) least_upper_bound inverse(multiply(b,b)) -> inverse(b)
% collapsed.
% Rule
% [70] (inverse(multiply(b,b)) greatest_lower_bound X) least_upper_bound b -> b
% collapsed.
% Rule [71] multiply(inverse(multiply(X,Y)),X) -> inverse(Y) collapsed.
% Current number of equations to process: 1049
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [73]
% (multiply(b,b) least_upper_bound X) greatest_lower_bound inverse(b) ->
% inverse(b)
% Current number of equations to process: 1051
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [74] inverse(b) greatest_lower_bound multiply(b,multiply(b,b)) -> inverse(b)
% Current number of equations to process: 1060
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [75]
% ((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: 1087
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [76]
% ((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound X
% -> b greatest_lower_bound X
% Current number of equations to process: 1102
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [77]
% multiply(b,multiply(b,X)) least_upper_bound X -> multiply(b,multiply(b,X))
% Current number of equations to process: 1196
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [78]
% multiply(b,multiply(X,b)) least_upper_bound X -> multiply(b,multiply(X,b))
% Current number of equations to process: 1267
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [79]
% ((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: 1312
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [80]
% ((identity least_upper_bound X) greatest_lower_bound b) least_upper_bound X
% -> identity least_upper_bound X
% Current number of equations to process: 1327
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [81]
% multiply(X,multiply(b,b)) least_upper_bound X -> multiply(X,multiply(b,b))
% Current number of equations to process: 1420
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [82]
% identity least_upper_bound multiply(b,multiply(b,b)) ->
% multiply(b,multiply(b,b))
% Current number of equations to process: 1468
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [83]
% (multiply(b,multiply(b,X)) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1492
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [84]
% (multiply(b,multiply(X,b)) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1545
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [85]
% (multiply(b,multiply(b,b)) least_upper_bound X) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 1586
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [86] multiply(b,multiply(b,multiply(b,X))) greatest_lower_bound X -> X
% Current number of equations to process: 1605
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [87] multiply(b,multiply(b,multiply(X,b))) greatest_lower_bound X -> X
% Current number of equations to process: 1666
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [88]
% identity greatest_lower_bound multiply(b,multiply(b,multiply(b,b))) ->
% identity
% Current number of equations to process: 1714
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [89]
% (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: 1738
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [90]
% (inverse(b) greatest_lower_bound X) least_upper_bound multiply(b,b) ->
% multiply(b,b)
% Current number of equations to process: 1777
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [91] multiply(b,multiply(X,multiply(b,b))) greatest_lower_bound X -> X
% Current number of equations to process: 1793
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [92]
% identity greatest_lower_bound multiply(inverse(b),inverse(b)) ->
% multiply(inverse(b),inverse(b))
% Current number of equations to process: 1839
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [93]
% (multiply(X,multiply(b,b)) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 1878
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [94] 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 :
% [95]
% (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: 1957
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [96] multiply(inverse(b),multiply(inverse(b),X)) least_upper_bound X -> X
% Current number of equations to process: 1999
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [97] multiply(b,X) least_upper_bound multiply(inverse(b),X) -> multiply(b,X)
% Current number of equations to process: 2049
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [98] 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 :
% [99] multiply(X,b) least_upper_bound multiply(X,inverse(b)) -> multiply(X,b)
% Current number of equations to process: 2114
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [100] multiply(b,X) least_upper_bound multiply(X,inverse(b)) -> multiply(b,X)
% Current number of equations to process: 2146
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [101] multiply(inverse(b),multiply(X,inverse(b))) least_upper_bound X -> X
% Current number of equations to process: 2180
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [102]
% b greatest_lower_bound multiply(inverse(b),inverse(b)) ->
% multiply(inverse(b),inverse(b))
% Current number of equations to process: 2223
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [103]
% (multiply(inverse(b),inverse(b)) greatest_lower_bound X) least_upper_bound identity
% -> identity
% Current number of equations to process: 2266
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [104]
% (multiply(inverse(b),inverse(b)) greatest_lower_bound X) least_upper_bound b
% -> b
% Current number of equations to process: 2292
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [105]
% multiply(b,b) least_upper_bound multiply(inverse(b),inverse(b)) ->
% multiply(b,b)
% Current number of equations to process: 2297
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [106] multiply(X,multiply(inverse(b),inverse(b))) least_upper_bound X -> X
% Current number of equations to process: 2320
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [107]
% (((b greatest_lower_bound X) least_upper_bound identity) greatest_lower_bound Y) least_upper_bound b
% -> b
% Current number of equations to process: 2360
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [108]
% (((identity least_upper_bound X) greatest_lower_bound b) least_upper_bound Y) greatest_lower_bound identity
% -> identity
% Current number of equations to process: 2373
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [109]
% (X least_upper_bound Y) greatest_lower_bound multiply(inverse(b),X) ->
% multiply(inverse(b),X)
% Current number of equations to process: 2381
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [110]
% multiply(b,X) greatest_lower_bound multiply(inverse(b),X) ->
% multiply(inverse(b),X)
% Current number of equations to process: 2508
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [111]
% (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: 2542
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [112]
% ((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: 2579
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [113]
% multiply(X,b) greatest_lower_bound multiply(X,inverse(b)) ->
% multiply(X,inverse(b))
% Current number of equations to process: 2728
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [114]
% (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: 2768
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [115]
% (X least_upper_bound Y) greatest_lower_bound multiply(X,inverse(b)) ->
% multiply(X,inverse(b))
% Current number of equations to process: 2813
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [116]
% multiply(inverse(b),X) greatest_lower_bound multiply(X,b) ->
% multiply(inverse(b),X)
% Current number of equations to process: 2902
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [117]
% multiply(b,X) greatest_lower_bound multiply(X,inverse(b)) ->
% multiply(X,inverse(b))
% Current number of equations to process: 2945
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [118]
% (identity least_upper_bound X) greatest_lower_bound multiply(inverse(b),
% inverse(b)) ->
% multiply(inverse(b),inverse(b))
% Current number of equations to process: 2986
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [119]
% (b least_upper_bound X) greatest_lower_bound multiply(inverse(b),inverse(b))
% -> multiply(inverse(b),inverse(b))
% Current number of equations to process: 3010
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [120]
% multiply(b,b) greatest_lower_bound multiply(inverse(b),inverse(b)) ->
% multiply(inverse(b),inverse(b))
% Current number of equations to process: 3028
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [121]
% ((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: 3047
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [122]
% (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: 3255
% Current number of ordered equations: 0
% Current number of rules: 108
% 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: 3502
% Current number of ordered equations: 0
% Current number of rules: 109
% 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: 3796
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [125]
% (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: 4031
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [126]
% multiply(X,multiply(b,Y)) greatest_lower_bound multiply(X,Y) -> multiply(X,Y)
% Current number of equations to process: 4249
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [127]
% identity greatest_lower_bound multiply(inverse(X),multiply(b,X)) -> identity
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 4268
% Current number of ordered equations: 0
% Current number of rules: 113
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 9 rules have been used:
% [2]
% b least_upper_bound identity -> b; trace = in the starting set
% [5] multiply(inverse(X),X) -> identity; trace = in the starting set
% [7] (X least_upper_bound Y) greatest_lower_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
% [13] b greatest_lower_bound identity -> identity; trace = Cp of 7 and 2
% [20] multiply(b,X) greatest_lower_bound X -> X; trace = Cp of 13 and 12
% [126] multiply(X,multiply(b,Y)) greatest_lower_bound multiply(X,Y) ->
% multiply(X,Y); trace = Cp of 20 and 10
% [127] identity greatest_lower_bound multiply(inverse(X),multiply(b,X)) ->
% identity; trace = Cp of 126 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 20.730000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------