TSTP Solution File: GRP167-5 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP167-5 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n165.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 00:22:29 EDT 2014
% Result : Unsatisfiable 16.87s
% Output : Refutation 16.87s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP167-5 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n165.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 05:52:28 CDT 2014
% % CPUTime : 16.87
% Processing problem /tmp/CiME_39628_n165.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; a,identity : constant; negative_part : 1; positive_part : 1; inverse : 1; multiply : 2;";
% let X = vars "X Y Z A B";
% 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);
% inverse(A least_upper_bound B) = inverse(A) greatest_lower_bound inverse(B);
% positive_part(X) = X least_upper_bound identity;
% negative_part(X) = X greatest_lower_bound identity;
% X least_upper_bound (Y greatest_lower_bound Z) = (X least_upper_bound Y) greatest_lower_bound (X least_upper_bound Z);
% X greatest_lower_bound (Y least_upper_bound Z) = (X greatest_lower_bound Y) least_upper_bound (X greatest_lower_bound Z);
% ";
%
% let s1 = status F "
% a lr_lex;
% negative_part lr_lex;
% positive_part lr_lex;
% inverse lr_lex;
% identity lr_lex;
% least_upper_bound mul;
% greatest_lower_bound mul;
% multiply mul;
% ";
%
% let p1 = precedence F "
% positive_part > negative_part > multiply > inverse > greatest_lower_bound > least_upper_bound > identity > a";
%
% let s2 = status F "
% a mul;
% negative_part mul;
% positive_part mul;
% least_upper_bound mul;
% greatest_lower_bound mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% positive_part > negative_part > multiply > inverse > greatest_lower_bound > least_upper_bound > identity = a";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " a = multiply(positive_part(a),negative_part(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),
% inverse(A least_upper_bound B) =
% inverse(A) greatest_lower_bound inverse(B),
% positive_part(X) = identity least_upper_bound X,
% negative_part(X) =
% identity greatest_lower_bound X,
% (Y greatest_lower_bound Z) least_upper_bound X =
% (X least_upper_bound Y) greatest_lower_bound
% (X least_upper_bound Z),
% (Y least_upper_bound Z) greatest_lower_bound X =
% (X greatest_lower_bound Y) least_upper_bound
% (X greatest_lower_bound Z) } (16 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 = { a =
% multiply(positive_part(a),negative_part(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: 15
% 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: 14
% Current number of rules: 2
% New rule produced : [3] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 3
% New rule produced : [4] identity least_upper_bound X -> positive_part(X)
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 4
% New rule produced : [5] identity greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 5
% New rule produced : [6] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 6
% New rule produced : [7] (X greatest_lower_bound Y) least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 7
% New rule produced : [8] (X least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 8
% New rule produced :
% [9]
% inverse(A least_upper_bound B) -> inverse(A) greatest_lower_bound inverse(B)
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 9
% New rule produced :
% [10] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 10
% New rule produced :
% [11]
% (X greatest_lower_bound Y) least_upper_bound (X greatest_lower_bound Z) ->
% (Y least_upper_bound Z) greatest_lower_bound X
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 11
% New rule produced :
% [12]
% (Y greatest_lower_bound Z) least_upper_bound X ->
% (X least_upper_bound Y) greatest_lower_bound (X least_upper_bound Z)
% Rule [7] (X greatest_lower_bound Y) least_upper_bound X -> X collapsed.
% Rule
% [11]
% (X greatest_lower_bound Y) least_upper_bound (X greatest_lower_bound Z) ->
% (Y least_upper_bound Z) greatest_lower_bound X collapsed.
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 10
% New rule produced :
% [13]
% 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: 11
% New rule produced :
% [14]
% 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: 12
% New rule produced :
% [15]
% 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: 13
% New rule produced :
% [16]
% 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: 14
% New rule produced : [17] positive_part(identity) -> identity
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [18] negative_part(identity) -> identity
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [19] positive_part(positive_part(X)) -> positive_part(X)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [20] negative_part(negative_part(X)) -> negative_part(X)
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [21] negative_part(positive_part(X)) -> identity
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [22] positive_part(X) greatest_lower_bound X -> X
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [23] positive_part(X) least_upper_bound X -> positive_part(X)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [24] negative_part(X) greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [25] negative_part(positive_part(X) least_upper_bound Y) -> identity
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [26]
% positive_part(X) least_upper_bound Y -> positive_part(X least_upper_bound Y)
% Rule [23] positive_part(X) least_upper_bound X -> positive_part(X) collapsed.
% Rule [25] negative_part(positive_part(X) least_upper_bound Y) -> identity
% collapsed.
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [27]
% negative_part(X) greatest_lower_bound Y ->
% negative_part(X greatest_lower_bound Y)
% Rule [24] negative_part(X) greatest_lower_bound X -> negative_part(X)
% collapsed.
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [28]
% negative_part(positive_part(X) greatest_lower_bound Y) -> negative_part(Y)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [29]
% inverse(positive_part(X)) ->
% inverse(identity) greatest_lower_bound inverse(X)
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [30] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [31]
% positive_part(X) greatest_lower_bound positive_part(Y) ->
% positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [32]
% negative_part(X) least_upper_bound Y ->
% (X least_upper_bound Y) greatest_lower_bound positive_part(Y)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [33]
% multiply(X,positive_part(Y)) ->
% multiply(X,identity) least_upper_bound multiply(X,Y)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [34]
% multiply(X,negative_part(Y)) ->
% multiply(X,identity) greatest_lower_bound multiply(X,Y)
% The conjecture has been reduced.
% Conjecture is now:
% a = multiply(positive_part(a),a) greatest_lower_bound multiply(positive_part(a),identity)
%
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [35] multiply(positive_part(X),Y) -> multiply(X,Y) least_upper_bound Y
% The conjecture has been reduced.
% Conjecture is now:
% a = (a least_upper_bound multiply(a,a)) greatest_lower_bound positive_part(
% multiply(a,identity))
%
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [36] multiply(negative_part(X),Y) -> multiply(X,Y) greatest_lower_bound Y
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [37] positive_part(X least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [38] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [39] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Rule [38] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 33
% Rule [34]
% multiply(X,negative_part(Y)) ->
% multiply(X,identity) greatest_lower_bound multiply(X,Y) is composed into
% [34] multiply(X,negative_part(Y)) -> multiply(X,Y) greatest_lower_bound X
% Rule [33]
% multiply(X,positive_part(Y)) ->
% multiply(X,identity) least_upper_bound multiply(X,Y) is composed into
% [33] multiply(X,positive_part(Y)) -> multiply(X,Y) least_upper_bound X
% New rule produced : [40] multiply(X,identity) -> X
% The conjecture has been reduced.
% Conjecture is now:
% a = (a least_upper_bound multiply(a,a)) greatest_lower_bound positive_part(a)
%
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [41] multiply(inverse(identity),X) -> X
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [42]
% positive_part(X greatest_lower_bound Y) greatest_lower_bound Y ->
% positive_part(X) greatest_lower_bound Y
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [43] positive_part(negative_part(X)) -> identity
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [44]
% positive_part(positive_part(X) greatest_lower_bound Y) ->
% positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [45] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [46] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 40
% Rule [29]
% inverse(positive_part(X)) ->
% inverse(identity) greatest_lower_bound inverse(X) is composed into
% [29] inverse(positive_part(X)) -> identity greatest_lower_bound inverse(X)
% New rule produced : [47] inverse(identity) -> identity
% Rule [41] multiply(inverse(identity),X) -> X collapsed.
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [48] inverse(inverse(X)) -> X
% Rule [39] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [49] negative_part(inverse(negative_part(X))) -> identity
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [50] positive_part(inverse(X) greatest_lower_bound X) -> identity
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [51] inverse(negative_part(inverse(X))) -> positive_part(X)
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [52]
% negative_part(inverse(negative_part(Y)) greatest_lower_bound X) ->
% negative_part(X)
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [53]
% negative_part(inverse(X) greatest_lower_bound X) ->
% inverse(X) greatest_lower_bound X
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [54] negative_part(inverse(inverse(X) greatest_lower_bound X)) -> identity
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [55] positive_part(inverse(X)) greatest_lower_bound X -> negative_part(X)
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [56]
% positive_part(X) greatest_lower_bound inverse(X) -> negative_part(inverse(X))
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [57] inverse(negative_part(X)) -> positive_part(inverse(X))
% Rule [49] negative_part(inverse(negative_part(X))) -> identity collapsed.
% Rule [51] inverse(negative_part(inverse(X))) -> positive_part(X) collapsed.
% Rule
% [52]
% negative_part(inverse(negative_part(Y)) greatest_lower_bound X) ->
% negative_part(X) collapsed.
% Current number of equations to process: 101
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [58]
% inverse(inverse(X) greatest_lower_bound inverse(Y)) -> X least_upper_bound Y
% Current number of equations to process: 101
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [59]
% positive_part(inverse(X) greatest_lower_bound X greatest_lower_bound Y) ->
% identity
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [60]
% inverse(inverse(X) greatest_lower_bound Y) -> inverse(Y) least_upper_bound X
% Rule
% [54] negative_part(inverse(inverse(X) greatest_lower_bound X)) -> identity
% collapsed.
% Rule
% [58]
% inverse(inverse(X) greatest_lower_bound inverse(Y)) -> X least_upper_bound Y
% collapsed.
% Current number of equations to process: 192
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [61] negative_part(inverse(X) least_upper_bound X) -> identity
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [62]
% positive_part(inverse(positive_part(Y) greatest_lower_bound X)) ->
% positive_part(inverse(X))
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [63]
% positive_part(inverse(X) greatest_lower_bound Y) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 197
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [64]
% negative_part(inverse(X greatest_lower_bound Y) least_upper_bound X) ->
% identity
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [65]
% inverse(X greatest_lower_bound Y) -> inverse(X) least_upper_bound inverse(Y)
% Rule
% [60]
% inverse(inverse(X) greatest_lower_bound Y) -> inverse(Y) least_upper_bound X
% collapsed.
% Rule
% [62]
% positive_part(inverse(positive_part(Y) greatest_lower_bound X)) ->
% positive_part(inverse(X)) collapsed.
% Rule
% [64]
% negative_part(inverse(X greatest_lower_bound Y) least_upper_bound X) ->
% identity collapsed.
% Current number of equations to process: 227
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [66]
% negative_part((inverse(Y) least_upper_bound Y) greatest_lower_bound X) ->
% negative_part(X)
% Current number of equations to process: 238
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [67] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% Current number of equations to process: 236
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [68]
% positive_part(X greatest_lower_bound Y) greatest_lower_bound inverse(X) ->
% negative_part(inverse(X))
% Current number of equations to process: 234
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [69]
% positive_part(inverse(X) least_upper_bound X) ->
% inverse(X) least_upper_bound X
% Current number of equations to process: 232
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [70]
% negative_part(inverse(X) least_upper_bound inverse(Y) least_upper_bound X) ->
% identity
% Current number of equations to process: 231
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [71]
% negative_part(inverse(X) least_upper_bound X least_upper_bound Y) -> identity
% Rule
% [70]
% negative_part(inverse(X) least_upper_bound inverse(Y) least_upper_bound X) ->
% identity collapsed.
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [72]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(X) ->
% positive_part(X)
% Current number of equations to process: 268
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced : [73] multiply(Y,inverse(multiply(X,Y))) -> inverse(X)
% Rule [67] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% collapsed.
% Current number of equations to process: 276
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced : [74] multiply(inverse(multiply(X,Y)),X) -> inverse(Y)
% Current number of equations to process: 348
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [75] inverse(multiply(Y,X)) -> multiply(inverse(X),inverse(Y))
% Rule [73] multiply(Y,inverse(multiply(X,Y))) -> inverse(X) collapsed.
% Rule [74] multiply(inverse(multiply(X,Y)),X) -> inverse(Y) collapsed.
% Current number of equations to process: 352
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [76]
% positive_part(Y) greatest_lower_bound inverse(X) greatest_lower_bound X ->
% inverse(X) greatest_lower_bound X
% Current number of equations to process: 363
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [77]
% (multiply(X,inverse(Y)) least_upper_bound multiply(X,Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 382
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [78] positive_part(multiply(X,X)) greatest_lower_bound X -> X
% Current number of equations to process: 422
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [79] positive_part(multiply(X,X) greatest_lower_bound X) -> positive_part(X)
% Current number of equations to process: 455
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [80]
% (multiply(inverse(Y),X) least_upper_bound multiply(Y,X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 466
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [81]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(inverse(X))
% -> positive_part(inverse(X))
% Current number of equations to process: 505
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [82]
% positive_part((X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> positive_part(Z) greatest_lower_bound X
% Current number of equations to process: 525
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [83]
% negative_part(inverse(X) greatest_lower_bound X greatest_lower_bound Y) ->
% inverse(X) greatest_lower_bound X greatest_lower_bound Y
% Current number of equations to process: 525
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [84]
% positive_part((inverse(Y) least_upper_bound X) greatest_lower_bound (X least_upper_bound Y))
% -> positive_part(X)
% Current number of equations to process: 534
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [85]
% positive_part(inverse(Y) least_upper_bound X) greatest_lower_bound Y ->
% positive_part(X) greatest_lower_bound Y
% Current number of equations to process: 561
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [86]
% positive_part(X least_upper_bound Y) greatest_lower_bound inverse(Y) ->
% positive_part(X) greatest_lower_bound inverse(Y)
% Current number of equations to process: 560
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [87]
% positive_part((inverse(Y) least_upper_bound X) greatest_lower_bound Y) ->
% positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 594
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [88]
% positive_part((X least_upper_bound Y) greatest_lower_bound inverse(X)) ->
% positive_part(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 629
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [89]
% negative_part((inverse(X) least_upper_bound inverse(Y) least_upper_bound X) greatest_lower_bound Z)
% -> negative_part(Z)
% Current number of equations to process: 658
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [90]
% (inverse(Y) least_upper_bound X least_upper_bound Y) greatest_lower_bound
% positive_part(X) -> positive_part(X)
% Current number of equations to process: 670
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [91]
% negative_part((inverse(Y) least_upper_bound Y least_upper_bound Z) greatest_lower_bound X)
% -> negative_part(X)
% Rule
% [89]
% negative_part((inverse(X) least_upper_bound inverse(Y) least_upper_bound X) greatest_lower_bound Z)
% -> negative_part(Z) collapsed.
% Current number of equations to process: 704
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [92]
% positive_part(inverse(X) least_upper_bound X least_upper_bound Y) ->
% inverse(X) least_upper_bound X least_upper_bound Y
% Current number of equations to process: 709
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [93]
% (inverse(X) least_upper_bound X least_upper_bound Y) greatest_lower_bound
% positive_part(X) -> positive_part(X)
% Current number of equations to process: 723
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [94]
% positive_part(multiply(X,X) greatest_lower_bound Y) greatest_lower_bound X ->
% positive_part(Y) greatest_lower_bound X
% Current number of equations to process: 744
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [95]
% positive_part(multiply(X,X) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 749
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [96]
% positive_part((multiply(X,X) least_upper_bound Y) greatest_lower_bound X) ->
% positive_part(X)
% Current number of equations to process: 806
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [97]
% positive_part(multiply(X,X) greatest_lower_bound X greatest_lower_bound Y) ->
% positive_part(X greatest_lower_bound Y)
% Current number of equations to process: 826
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [98]
% positive_part(multiply(X,inverse(Y)) greatest_lower_bound multiply(Y,
% inverse(X))) ->
% identity
% Current number of equations to process: 826
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [99]
% positive_part((X least_upper_bound Y) greatest_lower_bound inverse(X) greatest_lower_bound
% inverse(Y)) -> identity
% Current number of equations to process: 842
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [100]
% positive_part(multiply(inverse(X),inverse(Y)) greatest_lower_bound multiply(Y,X))
% -> identity
% Current number of equations to process: 855
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [101]
% positive_part(multiply(X,X)) greatest_lower_bound inverse(X) ->
% negative_part(inverse(X))
% Current number of equations to process: 882
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [102]
% positive_part(multiply(inverse(X),inverse(X))) greatest_lower_bound X ->
% negative_part(X)
% Current number of equations to process: 881
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [103]
% positive_part(inverse(X) greatest_lower_bound multiply(X,X)) -> identity
% Current number of equations to process: 910
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [104]
% positive_part(multiply(inverse(X),inverse(X)) greatest_lower_bound X) ->
% identity
% Current number of equations to process: 942
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [105]
% positive_part(inverse(X) greatest_lower_bound multiply(X,X) greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 943
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [106]
% negative_part(multiply(inverse(X),inverse(X)) least_upper_bound X) ->
% identity
% Current number of equations to process: 954
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [107] negative_part(inverse(X) least_upper_bound multiply(X,X)) -> identity
% Current number of equations to process: 959
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [108]
% positive_part(inverse(X)) greatest_lower_bound multiply(X,X) ->
% negative_part(multiply(X,X))
% Current number of equations to process: 965
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [109]
% negative_part(inverse(X) greatest_lower_bound multiply(X,X)) ->
% inverse(X) greatest_lower_bound multiply(X,X)
% Current number of equations to process: 1028
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [110]
% negative_part((inverse(Y) least_upper_bound multiply(Y,Y)) greatest_lower_bound X)
% -> negative_part(X)
% Current number of equations to process: 1034
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [111]
% negative_part(inverse(X) least_upper_bound multiply(X,X) least_upper_bound Y)
% -> identity
% Current number of equations to process: 1038
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [112]
% positive_part((inverse(X) least_upper_bound inverse(Y)) greatest_lower_bound X greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 1053
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [113]
% positive_part(multiply(inverse(X),Y) greatest_lower_bound multiply(inverse(Y),X))
% -> identity
% Current number of equations to process: 1068
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [114]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(Y) ->
% positive_part((inverse(X) least_upper_bound X) greatest_lower_bound Y)
% Rule
% [72]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(X) ->
% positive_part(X) collapsed.
% Rule
% [81]
% (inverse(X) least_upper_bound X) greatest_lower_bound positive_part(inverse(X))
% -> positive_part(inverse(X)) collapsed.
% Current number of equations to process: 1082
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [115]
% negative_part(multiply(inverse(X),inverse(Y)) least_upper_bound multiply(Y,X))
% -> identity
% Current number of equations to process: 1141
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [116]
% (multiply(X,multiply(inverse(Y),X)) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 1155
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [117]
% negative_part(inverse(X) least_upper_bound multiply(inverse(X),inverse(X)))
% -> negative_part(inverse(X))
% Current number of equations to process: 1200
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [118] negative_part(multiply(X,X) least_upper_bound X) -> negative_part(X)
% Rule
% [117]
% negative_part(inverse(X) least_upper_bound multiply(inverse(X),inverse(X)))
% -> negative_part(inverse(X)) collapsed.
% Current number of equations to process: 1200
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [119]
% negative_part((multiply(X,X) least_upper_bound X) greatest_lower_bound Y) ->
% negative_part(X greatest_lower_bound Y)
% Current number of equations to process: 1207
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [120]
% negative_part(multiply(X,X) greatest_lower_bound X) ->
% negative_part(multiply(X,X))
% Current number of equations to process: 1210
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [121]
% (inverse(X) least_upper_bound multiply(Y,Y) least_upper_bound X) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 1224
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [122]
% positive_part((inverse(X) least_upper_bound Y) greatest_lower_bound inverse(Y) greatest_lower_bound X)
% -> identity
% Current number of equations to process: 1255
% Current number of ordered equations: 1
% Current number of rules: 98
% New rule produced :
% [123]
% positive_part(multiply(X,X) greatest_lower_bound Y) greatest_lower_bound
% inverse(X) -> negative_part(inverse(X))
% Current number of equations to process: 1275
% Current number of ordered equations: 1
% Current number of rules: 99
% New rule produced :
% [124]
% positive_part(multiply(inverse(X),inverse(X)) greatest_lower_bound X greatest_lower_bound Y)
% -> identity
% Current number of equations to process: 1302
% Current number of ordered equations: 1
% Current number of rules: 100
% New rule produced :
% [125]
% negative_part(multiply(inverse(X),inverse(X)) least_upper_bound X least_upper_bound Y)
% -> identity
% Current number of equations to process: 1319
% Current number of ordered equations: 1
% Current number of rules: 101
% New rule produced :
% [126]
% negative_part(multiply(X,inverse(Y)) least_upper_bound multiply(Y,inverse(X)))
% -> identity
% Current number of equations to process: 1326
% Current number of ordered equations: 1
% Current number of rules: 102
% New rule produced :
% [127]
% negative_part(multiply(inverse(X),Y) least_upper_bound multiply(inverse(Y),X))
% -> identity
% Current number of equations to process: 1326
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [128]
% (inverse(X) least_upper_bound multiply(Y,multiply(X,Y))) greatest_lower_bound Y
% -> Y
% Current number of equations to process: 1347
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [129]
% positive_part(multiply(X,multiply(X,X)) greatest_lower_bound X) ->
% positive_part(X)
% Current number of equations to process: 1395
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [130] positive_part(multiply(X,multiply(X,X))) greatest_lower_bound X -> X
% Current number of equations to process: 1409
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [131]
% (inverse(X) least_upper_bound X) greatest_lower_bound inverse(Y) greatest_lower_bound Y
% -> inverse(Y) greatest_lower_bound Y
% Current number of equations to process: 1425
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [132]
% (multiply(inverse(X),inverse(X)) least_upper_bound X) greatest_lower_bound
% positive_part(X) -> positive_part(X)
% Current number of equations to process: 1448
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [133]
% positive_part(multiply(inverse(X),inverse(X)) greatest_lower_bound Y) greatest_lower_bound X
% -> negative_part(X)
% Current number of equations to process: 1480
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [134]
% positive_part(X) greatest_lower_bound multiply(inverse(X),inverse(X)) ->
% negative_part(multiply(inverse(X),inverse(X)))
% Current number of equations to process: 1505
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [135]
% positive_part(inverse(X) greatest_lower_bound Y) greatest_lower_bound
% multiply(X,X) -> negative_part(multiply(X,X))
% Current number of equations to process: 1540
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [136]
% negative_part((multiply(inverse(Y),inverse(Y)) least_upper_bound Y) greatest_lower_bound X)
% -> negative_part(X)
% Current number of equations to process: 1567
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [137]
% negative_part(multiply(X,X) greatest_lower_bound X greatest_lower_bound Y) ->
% negative_part(multiply(X,X) greatest_lower_bound Y)
% Current number of equations to process: 1572
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [138]
% negative_part((X least_upper_bound Y) greatest_lower_bound multiply(X,X)) ->
% negative_part(multiply(X,X))
% Current number of equations to process: 1579
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [139]
% inverse(X) greatest_lower_bound multiply(X,X) greatest_lower_bound X ->
% inverse(X) greatest_lower_bound multiply(X,X)
% Current number of equations to process: 1603
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [140]
% positive_part((inverse(X) least_upper_bound inverse(Z)) greatest_lower_bound
% (inverse(Y) least_upper_bound inverse(Z)) greatest_lower_bound X greatest_lower_bound Z)
% -> identity
% Current number of equations to process: 1638
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [141]
% positive_part(multiply(X,inverse(Y)) least_upper_bound multiply(X,Y)) greatest_lower_bound X
% -> X
% Current number of equations to process: 1681
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [142]
% (X least_upper_bound Y) greatest_lower_bound positive_part(multiply(Y,Y) least_upper_bound X)
% -> X least_upper_bound Y
% Current number of equations to process: 1724
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [143]
% positive_part(multiply(inverse(Y),X) least_upper_bound multiply(Y,X)) greatest_lower_bound X
% -> X
% Current number of equations to process: 1796
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [144]
% (inverse(X) least_upper_bound X least_upper_bound Y) greatest_lower_bound
% positive_part(inverse(X)) -> positive_part(inverse(X))
% Current number of equations to process: 1841
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [145]
% negative_part(multiply(inverse(X),inverse(X)) greatest_lower_bound X) ->
% multiply(inverse(X),inverse(X)) greatest_lower_bound X
% Current number of equations to process: 1859
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [146]
% positive_part(inverse(X) least_upper_bound multiply(X,X)) ->
% inverse(X) least_upper_bound multiply(X,X)
% Current number of equations to process: 1860
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [147]
% (inverse(X) least_upper_bound multiply(X,X)) greatest_lower_bound X -> X
% Current number of equations to process: 1883
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [148]
% (inverse(X) least_upper_bound multiply(X,X) least_upper_bound Y) greatest_lower_bound X
% -> X
% Current number of equations to process: 1916
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [149]
% (multiply(inverse(X),inverse(X)) least_upper_bound X) greatest_lower_bound
% inverse(X) -> inverse(X)
% Current number of equations to process: 1941
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [150]
% (inverse(X) least_upper_bound X) greatest_lower_bound (multiply(X,X) least_upper_bound X)
% -> X
% Current number of equations to process: 1965
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [151]
% (multiply(X,X) least_upper_bound X) greatest_lower_bound positive_part(X) ->
% X
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 1993
% Current number of ordered equations: 0
% Current number of rules: 127
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 43 rules have been used:
% [4]
% identity least_upper_bound X -> positive_part(X); trace = in the starting set
% [5] identity greatest_lower_bound X -> negative_part(X); trace = in the starting set
% [6] multiply(inverse(X),X) -> identity; trace = in the starting set
% [8] (X least_upper_bound Y) greatest_lower_bound X -> X; trace = in the starting set
% [9] inverse(A least_upper_bound B) ->
% inverse(A) greatest_lower_bound inverse(B); trace = in the starting set
% [10] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [12] (Y greatest_lower_bound Z) least_upper_bound X ->
% (X least_upper_bound Y) greatest_lower_bound (X least_upper_bound Z); trace = in the starting set
% [14] multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z); trace = in the starting set
% [15] multiply(Y least_upper_bound Z,X) ->
% multiply(Y,X) least_upper_bound multiply(Z,X); trace = in the starting set
% [22] positive_part(X) greatest_lower_bound X -> X; trace = Cp of 8 and 4
% [26] positive_part(X) least_upper_bound Y ->
% positive_part(X least_upper_bound Y); trace = Self cp of 4
% [29] inverse(positive_part(X)) -> identity greatest_lower_bound inverse(X); trace = Cp of 9 and 4
% [30] multiply(inverse(Y),multiply(Y,X)) -> X; trace = Cp of 10 and 6
% [31] positive_part(X) greatest_lower_bound positive_part(Y) ->
% positive_part(X greatest_lower_bound Y); trace = Cp of 12 and 4
% [34] multiply(X,negative_part(Y)) -> multiply(X,Y) greatest_lower_bound X; trace = Cp of 14 and 5
% [35] multiply(positive_part(X),Y) -> multiply(X,Y) least_upper_bound Y; trace = Cp of 15 and 4
% [37] positive_part(X least_upper_bound Y) greatest_lower_bound X -> X; trace = Cp of 22 and 8
% [39] multiply(inverse(inverse(X)),Y) -> multiply(X,Y); trace = Self cp of 30
% [40] multiply(X,identity) -> X; trace = Cp of 30 and 6
% [42] positive_part(X greatest_lower_bound Y) greatest_lower_bound Y ->
% positive_part(X) greatest_lower_bound Y; trace = Cp of 31 and 22
% [45] multiply(X,inverse(X)) -> identity; trace = Cp of 39 and 6
% [48] inverse(inverse(X)) -> X; trace = Cp of 40 and 39
% [50] positive_part(inverse(X) greatest_lower_bound X) -> identity; trace = Cp of 45 and 29
% [51] inverse(negative_part(inverse(X))) -> positive_part(X); trace = Cp of 48 and 29
% [54] negative_part(inverse(inverse(X) greatest_lower_bound X)) -> identity; trace = Cp of 50 and 29
% [57] inverse(negative_part(X)) -> positive_part(inverse(X)); trace = Cp of 51 and 48
% [58] inverse(inverse(X) greatest_lower_bound inverse(Y)) ->
% X least_upper_bound Y; trace = Cp of 48 and 9
% [60] inverse(inverse(X) greatest_lower_bound Y) ->
% inverse(Y) least_upper_bound X; trace = Cp of 58 and 48
% [65] inverse(X greatest_lower_bound Y) ->
% inverse(X) least_upper_bound inverse(Y); trace = Cp of 60 and 48
% [77] (multiply(X,inverse(Y)) least_upper_bound multiply(X,Y)) greatest_lower_bound X
% -> X; trace = Cp of 54 and 34
% [78] positive_part(multiply(X,X)) greatest_lower_bound X -> X; trace = Cp of 77 and 45
% [82] positive_part((X least_upper_bound Y) greatest_lower_bound Z) greatest_lower_bound X
% -> positive_part(Z) greatest_lower_bound X; trace = Cp of 37 and 31
% [84] positive_part((inverse(Y) least_upper_bound X) greatest_lower_bound
% (X least_upper_bound Y)) -> positive_part(X); trace = Cp of 50 and 26
% [85] positive_part(inverse(Y) least_upper_bound X) greatest_lower_bound Y ->
% positive_part(X) greatest_lower_bound Y; trace = Cp of 84 and 82
% [94] positive_part(multiply(X,X) greatest_lower_bound Y) greatest_lower_bound X
% -> positive_part(Y) greatest_lower_bound X; trace = Cp of 78 and 31
% [100] positive_part(multiply(inverse(X),inverse(Y)) greatest_lower_bound
% multiply(Y,X)) -> identity; trace = Cp of 60 and 6
% [102] positive_part(multiply(inverse(X),inverse(X))) greatest_lower_bound X
% -> negative_part(X); trace = Cp of 100 and 94
% [145] negative_part(multiply(inverse(X),inverse(X)) greatest_lower_bound X)
% -> multiply(inverse(X),inverse(X)) greatest_lower_bound X; trace = Cp of 102 and 22
% [146] positive_part(inverse(X) least_upper_bound multiply(X,X)) ->
% inverse(X) least_upper_bound multiply(X,X); trace = Cp of 145 and 57
% [147] (inverse(X) least_upper_bound multiply(X,X)) greatest_lower_bound X ->
% X; trace = Cp of 146 and 85
% [149] (multiply(inverse(X),inverse(X)) least_upper_bound X) greatest_lower_bound
% inverse(X) -> inverse(X); trace = Cp of 147 and 48
% [150] (inverse(X) least_upper_bound X) greatest_lower_bound (multiply(X,X) least_upper_bound X)
% -> X; trace = Cp of 149 and 65
% [151] (multiply(X,X) least_upper_bound X) greatest_lower_bound positive_part(X)
% -> X; trace = Cp of 150 and 42
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 15.710000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------