TSTP Solution File: GRP138-1 by CiME---2.01
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP138-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n060.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 00:22:25 EDT 2014
% Result : Unsatisfiable 1.50s
% Output : Refutation 1.50s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP138-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n060.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 04:55:48 CDT 2014
% % CPUTime : 1.50
% Processing problem /tmp/CiME_44876_n060.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; b,c,a,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);
% a least_upper_bound c = a;
% b least_upper_bound c = b;
% ";
%
% let s1 = status F "
% b lr_lex;
% c lr_lex;
% a 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 > a > c > b";
%
% let s2 = status F "
% b mul;
% c mul;
% a 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 = a = c = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " (a greatest_lower_bound b) least_upper_bound c = a greatest_lower_bound b;"
% ;
% (*
% 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),
% c least_upper_bound a = a,
% b least_upper_bound c = b } (13 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 = { (b greatest_lower_bound a) least_upper_bound c
% = b greatest_lower_bound 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: 12
% Current number of rules: 1
% New rule produced : [2] c least_upper_bound a -> a
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 2
% New rule produced : [3] b least_upper_bound c -> b
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 3
% New rule produced : [4] X greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 4
% New rule produced : [5] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% 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: 7
% 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: 6
% 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: 5
% Current number of rules: 8
% New rule produced :
% [9] 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: 9
% New rule produced :
% [10]
% 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: 10
% New rule produced :
% [11]
% 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: 11
% New rule produced :
% [12]
% 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: 12
% New rule produced :
% [13]
% 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: 13
% New rule produced : [14] c greatest_lower_bound a -> c
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] b greatest_lower_bound c -> c
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] (c greatest_lower_bound X) least_upper_bound a -> a
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] (c greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] (a least_upper_bound X) greatest_lower_bound c -> c
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] (b least_upper_bound X) greatest_lower_bound c -> c
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% (c least_upper_bound X) greatest_lower_bound (a least_upper_bound X) ->
% c least_upper_bound X
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22]
% (b least_upper_bound X) greatest_lower_bound (c least_upper_bound X) ->
% c least_upper_bound X
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23] multiply(X,c) least_upper_bound multiply(X,a) -> multiply(X,a)
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24] multiply(X,b) least_upper_bound multiply(X,c) -> multiply(X,b)
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25] multiply(c,X) least_upper_bound multiply(a,X) -> multiply(a,X)
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26] multiply(b,X) least_upper_bound multiply(c,X) -> multiply(b,X)
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [27] multiply(inverse(identity),X) -> X
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [28] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [29] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Rule [28] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [30] multiply(X,identity) -> X
% Current number of equations to process: 140
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [31]
% (c greatest_lower_bound X) least_upper_bound (a greatest_lower_bound X) ->
% a greatest_lower_bound X
% Current number of equations to process: 165
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [32] multiply(X,c) greatest_lower_bound multiply(X,a) -> multiply(X,c)
% Current number of equations to process: 164
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [33] multiply(c,X) greatest_lower_bound multiply(a,X) -> multiply(c,X)
% Current number of equations to process: 163
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [34]
% (b greatest_lower_bound X) least_upper_bound (c greatest_lower_bound X) ->
% b greatest_lower_bound X
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [35] multiply(X,b) greatest_lower_bound multiply(X,c) -> multiply(X,c)
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [36] multiply(b,X) greatest_lower_bound multiply(c,X) -> multiply(c,X)
% Current number of equations to process: 160
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [37] identity least_upper_bound multiply(inverse(a),c) -> identity
% Current number of equations to process: 199
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [38]
% identity least_upper_bound multiply(inverse(c),a) -> multiply(inverse(c),a)
% Current number of equations to process: 210
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [39] identity least_upper_bound multiply(inverse(b),c) -> identity
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [40]
% identity least_upper_bound multiply(inverse(c),b) -> multiply(inverse(c),b)
% Current number of equations to process: 231
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [41] multiply(c,c) least_upper_bound multiply(a,a) -> multiply(a,a)
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [42] multiply(c,c) least_upper_bound multiply(a,b) -> multiply(a,b)
% Current number of equations to process: 265
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [43] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 274
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [44] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 274
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [45] inverse(identity) -> identity
% Rule [27] multiply(inverse(identity),X) -> X collapsed.
% Current number of equations to process: 274
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [46] inverse(inverse(X)) -> X
% Rule [29] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 274
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [47] multiply(b,a) least_upper_bound multiply(c,c) -> multiply(b,a)
% Current number of equations to process: 297
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [48] multiply(b,b) least_upper_bound multiply(c,c) -> multiply(b,b)
% Current number of equations to process: 296
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [49]
% (b greatest_lower_bound a) least_upper_bound c -> b greatest_lower_bound a
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 305
% Current number of ordered equations: 0
% Current number of rules: 46
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 8 rules have been used:
% [2]
% c least_upper_bound a -> a; trace = in the starting set
% [3] b least_upper_bound c -> b; trace = in the starting set
% [7] (X greatest_lower_bound Y) least_upper_bound X -> X; trace = in the starting set
% [8] (X least_upper_bound Y) greatest_lower_bound X -> X; trace = in the starting set
% [14] c greatest_lower_bound a -> c; trace = Cp of 8 and 2
% [15] b greatest_lower_bound c -> c; trace = Cp of 8 and 3
% [31] (c greatest_lower_bound X) least_upper_bound (a greatest_lower_bound X)
% -> a greatest_lower_bound X; trace = Cp of 14 and 7
% [49] (b greatest_lower_bound a) least_upper_bound c ->
% b greatest_lower_bound a; trace = Cp of 31 and 15
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.390000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------