%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP190-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n040.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 00:22:36 EDT 2014

% Result   : Unsatisfiable 1.61s
% Output   : Refutation 1.61s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP190-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n040.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 07:11:13 CDT 2014
% % CPUTime  : 1.61 
% Processing problem /tmp/CiME_2898_n040.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; b,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 b = a;
% ";
% 
% let s1 = status F "
% b 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 > b";
% 
% let s2 = status F "
% b 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 = b";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " inverse(a) least_upper_bound inverse(b) = inverse(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),
% b least_upper_bound a = a } (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 = { inverse(b) least_upper_bound inverse(a) =
% inverse(b) } (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 a -> a
% 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 a -> b
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] (b greatest_lower_bound X) least_upper_bound a -> a
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] (a least_upper_bound X) greatest_lower_bound b -> b
% 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 (a least_upper_bound X) ->
% b 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,a) -> multiply(X,a)
% 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 multiply(a,X) -> multiply(a,X)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] multiply(inverse(identity),X) -> X
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [21] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Rule [21] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [23] multiply(X,identity) -> X
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [24]
% (b greatest_lower_bound X) least_upper_bound (a greatest_lower_bound X) ->
% a greatest_lower_bound X
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [25] multiply(X,b) greatest_lower_bound multiply(X,a) -> multiply(X,b)
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26] multiply(b,X) greatest_lower_bound multiply(a,X) -> multiply(b,X)
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27] identity least_upper_bound multiply(inverse(a),b) -> identity
% Current number of equations to process: 127
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% identity least_upper_bound multiply(inverse(b),a) -> multiply(inverse(b),a)
% Current number of equations to process: 138
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [29] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [30] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [31] inverse(identity) -> identity
% Rule [20] multiply(inverse(identity),X) -> X collapsed.
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [32] inverse(inverse(X)) -> X
% Rule [22] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [33] multiply(b,b) least_upper_bound multiply(a,a) -> multiply(a,a)
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [34] identity greatest_lower_bound multiply(inverse(b),a) -> identity
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [35]
% identity greatest_lower_bound multiply(inverse(a),b) ->
% multiply(inverse(a),b)
% Current number of equations to process: 204
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [36] multiply(b,b) greatest_lower_bound multiply(a,a) -> multiply(b,b)
% Current number of equations to process: 253
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [37]
% (multiply(inverse(a),b) greatest_lower_bound X) least_upper_bound identity ->
% identity
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [38] multiply(X,multiply(inverse(a),b)) least_upper_bound X -> X
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [39] multiply(inverse(a),multiply(b,X)) least_upper_bound X -> X
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [40]
% (multiply(inverse(b),a) least_upper_bound X) greatest_lower_bound identity ->
% identity
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [41] identity least_upper_bound multiply(b,inverse(a)) -> identity
% Current number of equations to process: 267
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [42] identity greatest_lower_bound multiply(a,inverse(b)) -> identity
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [43]
% identity least_upper_bound multiply(a,inverse(b)) -> multiply(a,inverse(b))
% Current number of equations to process: 276
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [44]
% identity greatest_lower_bound multiply(b,inverse(a)) ->
% multiply(b,inverse(a))
% Current number of equations to process: 275
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [45] multiply(X,multiply(Y,inverse(multiply(X,Y)))) -> identity
% Current number of equations to process: 284
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [46] multiply(b,multiply(inverse(a),X)) least_upper_bound X -> X
% Current number of equations to process: 283
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [47] multiply(a,multiply(inverse(b),X)) greatest_lower_bound X -> X
% Current number of equations to process: 282
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [48] multiply(X,multiply(inverse(b),a)) greatest_lower_bound X -> X
% Current number of equations to process: 308
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [49] multiply(inverse(b),multiply(a,X)) greatest_lower_bound X -> X
% Current number of equations to process: 307
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [50] a least_upper_bound multiply(b,multiply(inverse(a),b)) -> a
% Current number of equations to process: 364
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [51] a least_upper_bound multiply(inverse(a),multiply(b,b)) -> a
% Current number of equations to process: 388
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [52] inverse(b) least_upper_bound inverse(a) -> inverse(b)
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 402
% Current number of ordered equations: 0
% Current number of rules: 49
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 12 rules have been used:
% [2] 
% b least_upper_bound a -> a; trace = in the starting set
% [5] multiply(inverse(X),X) -> identity; trace = in the starting set
% [8] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [9] multiply(X,Y least_upper_bound Z) ->
% multiply(X,Y) least_upper_bound multiply(X,Z); trace = in the starting set
% [11] multiply(Y least_upper_bound Z,X) ->
% multiply(Y,X) least_upper_bound multiply(Z,X); trace = in the starting set
% [16] multiply(inverse(Y),multiply(Y,X)) -> X; trace = Cp of 8 and 5
% [18] multiply(X,b) least_upper_bound multiply(X,a) -> multiply(X,a); trace = Cp of 9 and 2
% [22] multiply(inverse(inverse(X)),Y) -> multiply(X,Y); trace = Self cp of 16
% [27] identity least_upper_bound multiply(inverse(a),b) -> identity; trace = Cp of 18 and 5
% [29] multiply(X,inverse(X)) -> identity; trace = Cp of 22 and 5
% [39] multiply(inverse(a),multiply(b,X)) least_upper_bound X -> X; trace = Cp of 27 and 11
% [52] inverse(b) least_upper_bound inverse(a) -> inverse(b); trace = Cp of 39 and 29
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 0.500000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------