TSTP Solution File: GRP193-1 by CiME---2.01
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP193-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n038.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 00:22:37 EDT 2014
% Result : Unsatisfiable 1.32s
% Output : Refutation 1.32s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP193-1 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n038.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 07:18:28 CDT 2014
% % CPUTime : 1.32
% Processing problem /tmp/CiME_46721_n038.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 least_upper_bound a = a;
% identity least_upper_bound b = b;
% identity least_upper_bound c = c;
% a greatest_lower_bound b = identity;
% (a greatest_lower_bound multiply(b,c)) least_upper_bound multiply(a greatest_lower_bound b,a greatest_lower_bound c) = multiply(a greatest_lower_bound b,a greatest_lower_bound c);
% ";
%
% 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) = a greatest_lower_bound 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 least_upper_bound identity = a,
% b least_upper_bound identity = b,
% c least_upper_bound identity = c,
% b greatest_lower_bound a = identity,
% (a greatest_lower_bound multiply(b,c)) least_upper_bound
% multiply(b greatest_lower_bound a,c greatest_lower_bound a)
% =
% multiply(b greatest_lower_bound a,c greatest_lower_bound a) }
% (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 greatest_lower_bound multiply(b,c) =
% c 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: 15
% Current number of rules: 1
% New rule produced : [2] a least_upper_bound identity -> a
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 2
% New rule produced : [3] b least_upper_bound identity -> b
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 3
% New rule produced : [4] c least_upper_bound identity -> c
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 4
% New rule produced : [5] X greatest_lower_bound X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 5
% New rule produced : [6] b greatest_lower_bound a -> identity
% Current number of equations to process: 1
% Current number of ordered equations: 9
% Current number of rules: 6
% New rule produced : [7] multiply(identity,X) -> X
% Current number of equations to process: 1
% Current number of ordered equations: 8
% Current number of rules: 7
% New rule produced : [8] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 8
% New rule produced : [9] (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: 9
% New rule produced : [10] (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: 10
% New rule produced :
% [11] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 11
% New rule produced :
% [12]
% 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: 4
% Current number of rules: 12
% New rule produced :
% [13]
% 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: 3
% Current number of rules: 13
% New rule produced :
% [14]
% 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: 2
% Current number of rules: 14
% New rule produced :
% [15]
% 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: 1
% Current number of rules: 15
% New rule produced :
% [16]
% (c greatest_lower_bound a) least_upper_bound (a greatest_lower_bound
% multiply(b,c)) ->
% c greatest_lower_bound a
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] a greatest_lower_bound identity -> identity
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced : [18] b greatest_lower_bound identity -> identity
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] c greatest_lower_bound identity -> identity
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] (identity greatest_lower_bound X) least_upper_bound a -> a
% Current number of equations to process: 97
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21] (identity greatest_lower_bound X) least_upper_bound b -> b
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22] (identity greatest_lower_bound X) least_upper_bound c -> c
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23] (b least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 91
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [24] (c least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 90
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [25] (a least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% (a greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> a greatest_lower_bound X
% Current number of equations to process: 79
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [28]
% (b greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> b greatest_lower_bound X
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% (a least_upper_bound X) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% (b least_upper_bound X) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31]
% (c least_upper_bound X) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32] multiply(X,a) least_upper_bound multiply(X,identity) -> multiply(X,a)
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33] multiply(X,b) least_upper_bound multiply(X,identity) -> multiply(X,b)
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [34] multiply(X,c) least_upper_bound multiply(X,identity) -> multiply(X,c)
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [35] multiply(X,b) greatest_lower_bound multiply(X,a) -> multiply(X,identity)
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [36] multiply(a,X) least_upper_bound X -> multiply(a,X)
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [37] multiply(b,X) least_upper_bound X -> multiply(b,X)
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [38] multiply(c,X) least_upper_bound X -> multiply(c,X)
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [39] multiply(b,X) greatest_lower_bound multiply(a,X) -> X
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [40]
% ((identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound a least_upper_bound X
% -> a least_upper_bound X
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [41]
% ((identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound b least_upper_bound X
% -> b least_upper_bound X
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [42]
% ((identity least_upper_bound X) greatest_lower_bound Y) least_upper_bound c least_upper_bound X
% -> c least_upper_bound X
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [43]
% (a greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X greatest_lower_bound Y)
% -> a greatest_lower_bound X
% Current number of equations to process: 86
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced :
% [44]
% (b greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X greatest_lower_bound Y)
% -> b greatest_lower_bound X
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [45]
% (a least_upper_bound X least_upper_bound Y) greatest_lower_bound (identity least_upper_bound Y)
% -> identity least_upper_bound Y
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [46]
% (b least_upper_bound X least_upper_bound Y) greatest_lower_bound (identity least_upper_bound Y)
% -> identity least_upper_bound Y
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [47]
% (c least_upper_bound X least_upper_bound Y) greatest_lower_bound (identity least_upper_bound Y)
% -> identity least_upper_bound Y
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [48]
% ((b greatest_lower_bound X) least_upper_bound Y) greatest_lower_bound identity greatest_lower_bound X
% -> identity greatest_lower_bound X
% Current number of equations to process: 81
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [49]
% ((a greatest_lower_bound X) least_upper_bound Y) greatest_lower_bound identity greatest_lower_bound X
% -> identity greatest_lower_bound X
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [50]
% ((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: 74
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [51]
% ((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: 74
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [52]
% (((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound V_3) least_upper_bound X least_upper_bound Z
% -> X least_upper_bound Z
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [53]
% (((X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound V_3) greatest_lower_bound X greatest_lower_bound Z
% -> X greatest_lower_bound Z
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [54]
% ((X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound (X greatest_lower_bound Z greatest_lower_bound V_3)
% -> (X least_upper_bound Y) greatest_lower_bound Z
% Current number of equations to process: 55
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [55]
% ((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound
% (X least_upper_bound Z least_upper_bound V_3) ->
% (X greatest_lower_bound Y) least_upper_bound Z
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [56]
% multiply(inverse(X least_upper_bound Y),X) least_upper_bound multiply(
% inverse(
% X least_upper_bound Y),Y)
% -> identity
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [57]
% multiply(inverse(X greatest_lower_bound Y),X) greatest_lower_bound multiply(
% inverse(
% X greatest_lower_bound Y),Y)
% -> identity
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [58]
% ((((X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound Y) greatest_lower_bound V_3) least_upper_bound X least_upper_bound Y
% -> X least_upper_bound Y
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [59]
% ((((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound Y) least_upper_bound V_3) greatest_lower_bound X greatest_lower_bound Y
% -> X greatest_lower_bound Y
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [60]
% (((X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound Y) greatest_lower_bound
% (X least_upper_bound Y) ->
% ((X least_upper_bound Y) greatest_lower_bound Z) least_upper_bound Y
% Current number of equations to process: 46
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [61]
% (((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound Y) least_upper_bound
% (X greatest_lower_bound Y) ->
% ((X greatest_lower_bound Y) least_upper_bound Z) greatest_lower_bound Y
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [62] (a greatest_lower_bound multiply(b,c)) least_upper_bound c -> c
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [63]
% c greatest_lower_bound a greatest_lower_bound multiply(b,c) ->
% a greatest_lower_bound multiply(b,c)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [64]
% (c greatest_lower_bound a) least_upper_bound (a greatest_lower_bound
% multiply(b,c) greatest_lower_bound X)
% -> c greatest_lower_bound a
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced : [65] multiply(a,X) greatest_lower_bound X -> X
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [66]
% multiply(X,a) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced : [67] multiply(b,X) greatest_lower_bound X -> X
% Rule
% [63]
% c greatest_lower_bound a greatest_lower_bound multiply(b,c) ->
% a greatest_lower_bound multiply(b,c) collapsed.
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [68] a greatest_lower_bound multiply(b,c) -> c greatest_lower_bound a
% Rule
% [16]
% (c greatest_lower_bound a) least_upper_bound (a greatest_lower_bound
% multiply(b,c)) ->
% c greatest_lower_bound a collapsed.
% Rule [62] (a greatest_lower_bound multiply(b,c)) least_upper_bound c -> c
% collapsed.
% Rule
% [64]
% (c greatest_lower_bound a) least_upper_bound (a greatest_lower_bound
% multiply(b,c) greatest_lower_bound X)
% -> c greatest_lower_bound a collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 64
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 3 rules have been used:
% [10]
% (X least_upper_bound Y) greatest_lower_bound X -> X; trace = in the starting set
% [16] (c greatest_lower_bound a) least_upper_bound (a greatest_lower_bound
% multiply(b,c)) ->
% c greatest_lower_bound a; trace = in the starting set
% [68] a greatest_lower_bound multiply(b,c) -> c greatest_lower_bound a; trace = Cp of 16 and 10
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.210000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------