TSTP Solution File: GRP184-2 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP184-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n108.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 00:22:34 EDT 2014
% Result : Unsatisfiable 1.94s
% Output : Refutation 1.94s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP184-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n108.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 06:49:53 CDT 2014
% % CPUTime : 1.94
% Processing problem /tmp/CiME_34246_n108.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " least_upper_bound,greatest_lower_bound : AC; 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);
% inverse(identity) = identity;
% inverse(inverse(X)) = X;
% inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X));
% ";
%
% let s1 = status F "
% a lr_lex;
% inverse lr_lex;
% identity lr_lex;
% least_upper_bound mul;
% greatest_lower_bound mul;
% multiply mul;
% ";
%
% let p1 = precedence F "
% multiply > inverse > greatest_lower_bound > least_upper_bound > identity > a";
%
% let s2 = status F "
% a mul;
% least_upper_bound mul;
% greatest_lower_bound mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% 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 " multiply(a least_upper_bound identity,inverse(a greatest_lower_bound identity)) = multiply(inverse(a greatest_lower_bound identity),a least_upper_bound identity);"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
%
% let Red_Conjectures = normalize_equations Defining_rules Conjectures;
% *)
% #time on;
%
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
%
% #time off;
%
%
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
%
% F : signature = <signature>
% X : variable_set = <variable set>
%
% Axioms : (F,X) equations = { multiply(multiply(X,Y),Z) =
% multiply(X,multiply(Y,Z)),
% multiply(identity,X) = X,
% multiply(inverse(X),X) = identity,
% X least_upper_bound X = X,
% X greatest_lower_bound X = X,
% (X greatest_lower_bound Y) least_upper_bound X =
% X,
% (X least_upper_bound Y) greatest_lower_bound X =
% X,
% multiply(X,Y least_upper_bound Z) =
% multiply(X,Y) least_upper_bound multiply(X,Z),
% multiply(X,Y greatest_lower_bound Z) =
% multiply(X,Y) greatest_lower_bound multiply(X,Z),
% multiply(Y least_upper_bound Z,X) =
% multiply(Y,X) least_upper_bound multiply(Z,X),
% multiply(Y greatest_lower_bound Z,X) =
% multiply(Y,X) greatest_lower_bound multiply(Z,X),
% inverse(identity) = identity,
% inverse(inverse(X)) = X,
% inverse(multiply(X,Y)) =
% multiply(inverse(Y),inverse(X)) }
% (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 = { multiply(a least_upper_bound identity,
% inverse(a greatest_lower_bound identity)) =
% multiply(inverse(a greatest_lower_bound identity),
% a least_upper_bound identity) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] inverse(identity) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 1
% New rule produced : [2] inverse(inverse(X)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 2
% New rule produced : [3] X least_upper_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 11
% 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: 10
% 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: 9
% 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: 8
% 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: 7
% 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: 6
% Current number of rules: 8
% New rule produced :
% [9] inverse(multiply(X,Y)) -> multiply(inverse(Y),inverse(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)
% The conjecture has been reduced.
% Conjecture is now:
% multiply(a least_upper_bound identity,inverse(a greatest_lower_bound identity)) =
% multiply(inverse(a greatest_lower_bound identity),a) least_upper_bound
% multiply(inverse(a greatest_lower_bound identity),identity)
%
% 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)
% 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)
% The conjecture has been reduced.
% Conjecture is now:
% inverse(a greatest_lower_bound identity) least_upper_bound multiply(a,
% inverse(a greatest_lower_bound identity)) =
% multiply(inverse(a greatest_lower_bound identity),a) least_upper_bound
% multiply(inverse(a greatest_lower_bound identity),identity)
%
% 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)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] multiply(inverse(X),identity) -> inverse(X)
% The conjecture has been reduced.
% Conjecture is now:
% inverse(a greatest_lower_bound identity) least_upper_bound multiply(a,
% inverse(a greatest_lower_bound identity)) =
% inverse(a greatest_lower_bound identity) least_upper_bound multiply(inverse(
% a greatest_lower_bound identity),a)
%
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] multiply(X,identity) -> X
% Rule [16] multiply(inverse(X),identity) -> inverse(X) collapsed.
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [20]
% ((X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound (X greatest_lower_bound Z)
% -> (X least_upper_bound Y) greatest_lower_bound Z
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [21]
% ((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound
% (X least_upper_bound Z) -> (X greatest_lower_bound Y) least_upper_bound Z
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [22]
% inverse(multiply(X,Y) least_upper_bound multiply(X,Z)) ->
% multiply(inverse(Y least_upper_bound Z),inverse(X))
% Current number of equations to process: 218
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [23]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X))
% Current number of equations to process: 219
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [24]
% multiply(inverse(inverse(X) least_upper_bound Y),inverse(X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [25]
% inverse(identity least_upper_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X least_upper_bound Y),X)
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26]
% inverse(multiply(X,Y) least_upper_bound X) ->
% multiply(inverse(identity least_upper_bound Y),inverse(X))
% Current number of equations to process: 226
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27]
% inverse(identity least_upper_bound inverse(identity least_upper_bound
% multiply(X,Y))) -> identity
% Current number of equations to process: 242
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [28]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X)
% Rule
% [27]
% inverse(identity least_upper_bound inverse(identity least_upper_bound
% multiply(X,Y))) -> identity
% collapsed.
% Current number of equations to process: 247
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [29]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X)
% Rule
% [28]
% inverse(identity least_upper_bound inverse(X)) ->
% multiply(inverse(identity least_upper_bound X),X) collapsed.
% Current number of equations to process: 256
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [30]
% multiply(inverse(identity least_upper_bound multiply(X,Y)),X) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [31]
% inverse(multiply(X,Y) greatest_lower_bound multiply(X,Z)) ->
% multiply(inverse(Y greatest_lower_bound Z),inverse(X))
% Current number of equations to process: 285
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [32]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 286
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [33]
% multiply(inverse(inverse(X) greatest_lower_bound Y),inverse(X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 286
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [34]
% inverse(identity greatest_lower_bound multiply(inverse(X),Y)) ->
% multiply(inverse(X greatest_lower_bound Y),X)
% Current number of equations to process: 287
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [35]
% inverse(multiply(X,Y) greatest_lower_bound X) ->
% multiply(inverse(identity greatest_lower_bound Y),inverse(X))
% Current number of equations to process: 294
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [36]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X)
% Current number of equations to process: 337
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [37]
% inverse(inverse(X) greatest_lower_bound Y) <->
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X)
% Rule
% [36]
% inverse(identity greatest_lower_bound inverse(X)) ->
% multiply(inverse(identity greatest_lower_bound X),X) collapsed.
% Current number of equations to process: 356
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [38]
% multiply(inverse(identity greatest_lower_bound multiply(X,Y)),X) <->
% inverse(inverse(X) greatest_lower_bound Y)
% Current number of equations to process: 356
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [39]
% inverse(multiply(X,Y) least_upper_bound multiply(Z,Y)) ->
% multiply(inverse(Y),inverse(X least_upper_bound Z))
% Current number of equations to process: 405
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [40]
% inverse(identity least_upper_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X least_upper_bound Y))
% Current number of equations to process: 406
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [41]
% inverse(multiply(X,Y) least_upper_bound Y) ->
% multiply(inverse(Y),inverse(identity least_upper_bound X))
% Current number of equations to process: 409
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [42]
% inverse(identity least_upper_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 415
% Current number of ordered equations: 1
% Current number of rules: 38
% New rule produced :
% [43]
% multiply(inverse(Y),inverse(inverse(Y) least_upper_bound X)) <->
% inverse(identity least_upper_bound multiply(X,Y))
% Current number of equations to process: 415
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [44]
% multiply(inverse(identity least_upper_bound X),X) ->
% multiply(X,inverse(identity least_upper_bound X))
% Current number of equations to process: 432
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [45]
% multiply(X,inverse(inverse(Y) least_upper_bound X)) <->
% multiply(inverse(inverse(X) least_upper_bound Y),Y)
% Current number of equations to process: 444
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [46]
% multiply(inverse(inverse(X) least_upper_bound Y),Y) <->
% multiply(X,inverse(inverse(Y) least_upper_bound X))
% Current number of equations to process: 444
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [47]
% multiply(inverse(identity least_upper_bound X),inverse(X)) ->
% multiply(inverse(X),inverse(identity least_upper_bound X))
% Current number of equations to process: 460
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [48]
% inverse(inverse(X) least_upper_bound inverse(Y)) ->
% multiply(X,multiply(inverse(X least_upper_bound Y),Y))
% Current number of equations to process: 477
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [49]
% inverse(inverse(X) least_upper_bound Y) <->
% multiply(X,inverse(identity least_upper_bound multiply(Y,X)))
% Current number of equations to process: 497
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced :
% [50]
% multiply(X,inverse(identity least_upper_bound multiply(Y,X))) <->
% inverse(inverse(X) least_upper_bound Y)
% Current number of equations to process: 497
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [51]
% inverse(multiply(X,Y) greatest_lower_bound multiply(Z,Y)) ->
% multiply(inverse(Y),inverse(X greatest_lower_bound Z))
% Current number of equations to process: 735
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [52]
% inverse(identity greatest_lower_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X greatest_lower_bound Y))
% Current number of equations to process: 736
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [53]
% inverse(multiply(X,Y) greatest_lower_bound Y) ->
% multiply(inverse(Y),inverse(identity greatest_lower_bound X))
% Current number of equations to process: 739
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [54]
% inverse(identity greatest_lower_bound multiply(X,Y)) <->
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X))
% Current number of equations to process: 745
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [55]
% multiply(inverse(Y),inverse(inverse(Y) greatest_lower_bound X)) <->
% inverse(identity greatest_lower_bound multiply(X,Y))
% Current number of equations to process: 745
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [56]
% multiply(inverse(identity greatest_lower_bound X),X) ->
% multiply(X,inverse(identity greatest_lower_bound X))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 776
% Current number of ordered equations: 0
% Current number of rules: 52
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 12 rules have been used:
% [2]
% inverse(inverse(X)) -> X; trace = in the starting set
% [5] multiply(identity,X) -> X; trace = in the starting set
% [6] multiply(inverse(X),X) -> identity; trace = in the starting set
% [9] inverse(multiply(X,Y)) -> multiply(inverse(Y),inverse(X)); trace = in the starting set
% [11] multiply(X,Y least_upper_bound Z) ->
% multiply(X,Y) least_upper_bound multiply(X,Z); trace = in the starting set
% [13] multiply(Y least_upper_bound Z,X) ->
% multiply(Y,X) least_upper_bound multiply(Z,X); 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
% [15] multiply(X,inverse(X)) -> identity; trace = Cp of 6 and 2
% [16] multiply(inverse(X),identity) -> inverse(X); trace = Cp of 9 and 5
% [51] inverse(multiply(X,Y) greatest_lower_bound multiply(Z,Y)) ->
% multiply(inverse(Y),inverse(X greatest_lower_bound Z)); trace = Cp of 14 and 9
% [52] inverse(identity greatest_lower_bound multiply(X,inverse(Y))) ->
% multiply(Y,inverse(X greatest_lower_bound Y)); trace = Cp of 51 and 15
% [56] multiply(inverse(identity greatest_lower_bound X),X) ->
% multiply(X,inverse(identity greatest_lower_bound X)); trace = Cp of 52 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.820000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------