TSTP Solution File: GRP177-2 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP177-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n128.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 00:22:32 EDT 2014
% Result : Unsatisfiable 1.36s
% Output : Refutation 1.36s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP177-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n128.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 06:21:58 CDT 2014
% % CPUTime : 1.36
% Processing problem /tmp/CiME_21998_n128.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; c,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);
% identity greatest_lower_bound a = identity;
% identity greatest_lower_bound b = identity;
% identity greatest_lower_bound c = identity;
% ";
%
% let s1 = status F "
% c lr_lex;
% 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 > c";
%
% let s2 = status F "
% c mul;
% 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 = c";
%
% 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 multiply(b,c)) greatest_lower_bound multiply(a greatest_lower_bound b,a greatest_lower_bound c) = a greatest_lower_bound multiply(b,c);"
% ;
% (*
% 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),
% a greatest_lower_bound identity = identity,
% b greatest_lower_bound identity = identity,
% c greatest_lower_bound identity = identity }
% (14 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 greatest_lower_bound multiply(b greatest_lower_bound a,
% c greatest_lower_bound a) greatest_lower_bound
% multiply(b,c) =
% a greatest_lower_bound multiply(b,c) }
% (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: 13
% 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: 12
% Current number of rules: 2
% New rule produced : [3] a greatest_lower_bound identity -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 3
% New rule produced : [4] b greatest_lower_bound identity -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 4
% New rule produced : [5] c greatest_lower_bound identity -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 5
% New rule produced : [6] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 6
% New rule produced : [7] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 7
% New rule produced : [8] (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: 8
% New rule produced : [9] (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: 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: 4
% Current number of rules: 10
% New rule produced :
% [11]
% 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 :
% [12]
% multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z)
% The conjecture has been reduced.
% Conjecture is now:
% a greatest_lower_bound multiply(b greatest_lower_bound a,c) greatest_lower_bound
% multiply(b greatest_lower_bound a,a) greatest_lower_bound multiply(b,c) =
% a greatest_lower_bound multiply(b,c)
%
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 12
% New rule produced :
% [13]
% 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 :
% [14]
% multiply(Y greatest_lower_bound Z,X) ->
% multiply(Y,X) greatest_lower_bound multiply(Z,X)
% The conjecture has been reduced.
% Conjecture is now:
% a greatest_lower_bound multiply(b,c) greatest_lower_bound multiply(b,a) greatest_lower_bound
% multiply(a,c) greatest_lower_bound multiply(a,a) = a greatest_lower_bound
% multiply(b,c)
%
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] a least_upper_bound identity -> a
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] b least_upper_bound identity -> b
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] c least_upper_bound identity -> c
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18] (identity greatest_lower_bound X) least_upper_bound a -> a
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19] (identity greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] (identity greatest_lower_bound X) least_upper_bound c -> c
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21] (a least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22] (b least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23] (c least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% (a greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> a greatest_lower_bound X
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 25
% 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: 66
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% (c greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> c greatest_lower_bound X
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28]
% multiply(X,a) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity)
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% multiply(X,b) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity)
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% multiply(X,c) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [31] multiply(a,X) greatest_lower_bound X -> X
% The conjecture has been reduced.
% Conjecture is now:
% a greatest_lower_bound multiply(b,c) greatest_lower_bound multiply(b,a) greatest_lower_bound
% multiply(a,c) = a greatest_lower_bound multiply(b,c)
%
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [32] multiply(b,X) greatest_lower_bound X -> X
% The conjecture has been reduced.
% Conjecture is now:
% a greatest_lower_bound multiply(b,c) greatest_lower_bound multiply(a,c) =
% a greatest_lower_bound multiply(b,c)
%
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [33] multiply(c,X) greatest_lower_bound X -> X
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [34] multiply(a,X) least_upper_bound X -> multiply(a,X)
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [35] multiply(b,X) least_upper_bound X -> multiply(b,X)
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [36] multiply(c,X) least_upper_bound X -> multiply(c,X)
% Current number of equations to process: 116
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [37] multiply(inverse(identity),X) -> X
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [38] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 38
% 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: 183
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [40] multiply(X,identity) -> X
% Rule
% [28]
% multiply(X,a) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity) collapsed.
% Rule
% [29]
% multiply(X,b) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity) collapsed.
% Rule
% [30]
% multiply(X,c) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity) collapsed.
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [41] multiply(X,a) greatest_lower_bound X -> X
% Current number of equations to process: 184
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [42] multiply(X,b) greatest_lower_bound X -> X
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [43] multiply(X,c) greatest_lower_bound X -> X
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 182
% Current number of ordered equations: 0
% Current number of rules: 39
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 8 rules have been used:
% [3]
% a greatest_lower_bound identity -> identity; trace = in the starting set
% [4] b greatest_lower_bound identity -> identity; trace = in the starting set
% [5] c greatest_lower_bound identity -> identity; trace = in the starting set
% [12] multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z); trace = in the starting set
% [14] multiply(Y greatest_lower_bound Z,X) ->
% multiply(Y,X) greatest_lower_bound multiply(Z,X); trace = in the starting set
% [31] multiply(a,X) greatest_lower_bound X -> X; trace = Cp of 14 and 3
% [32] multiply(b,X) greatest_lower_bound X -> X; trace = Cp of 14 and 4
% [43] multiply(X,c) greatest_lower_bound X -> X; trace = Cp of 12 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.260000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------