%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP178-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n075.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 2.22s
% Output   : Refutation 2.22s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP178-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n075.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 06:24:38 CDT 2014
% % CPUTime  : 2.22 
% Processing problem /tmp/CiME_39143_n075.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;
% a greatest_lower_bound b = 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) = 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 greatest_lower_bound identity = identity,
% b greatest_lower_bound identity = identity,
% c greatest_lower_bound identity = identity,
% b greatest_lower_bound a = identity }
% (15 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: 14
% 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: 13
% 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: 12
% 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: 11
% Current number of rules: 4
% New rule produced : [5] b greatest_lower_bound a -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 5
% New rule produced : [6] c greatest_lower_bound identity -> identity
% Current number of equations to process: 0
% 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: 0
% 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: 7
% 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: 6
% 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: 5
% 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: 4
% 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: 3
% 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: 2
% 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: 1
% 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: 0
% Current number of rules: 15
% New rule produced : [16] a least_upper_bound identity -> a
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] b least_upper_bound identity -> b
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] c least_upper_bound identity -> c
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19] (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: 19
% New rule produced :
% [20] (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: 20
% New rule produced :
% [21] (identity greatest_lower_bound X) least_upper_bound c -> c
% Current number of equations to process: 93
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22] (a least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 92
% 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: 0
% 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: 88
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26]
% (a greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> a greatest_lower_bound X
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% (b greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> b greatest_lower_bound X
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28]
% (c greatest_lower_bound X) least_upper_bound (identity greatest_lower_bound X)
% -> c greatest_lower_bound X
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% multiply(X,a) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity)
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% multiply(X,b) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity)
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31] 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: 31
% New rule produced :
% [32]
% multiply(X,c) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity)
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [33] multiply(a,X) greatest_lower_bound X -> X
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [34] multiply(b,X) greatest_lower_bound X -> X
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [35] multiply(c,X) greatest_lower_bound X -> X
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [36] multiply(b,X) greatest_lower_bound multiply(a,X) -> X
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [37] multiply(a,X) least_upper_bound X -> multiply(a,X)
% Current number of equations to process: 131
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [38] multiply(b,X) least_upper_bound X -> multiply(b,X)
% Current number of equations to process: 130
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [39] multiply(c,X) least_upper_bound X -> multiply(c,X)
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [40] multiply(inverse(identity),X) -> X
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [41] multiply(inverse(inverse(X)),identity) -> X
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [42] multiply(inverse(inverse(X)),Y) -> multiply(X,Y)
% Rule [41] multiply(inverse(inverse(X)),identity) -> X collapsed.
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 41
% Rule [31]
% multiply(X,b) greatest_lower_bound multiply(X,a) -> multiply(X,identity) is composed into 
% [31] multiply(X,b) greatest_lower_bound multiply(X,a) -> X
% New rule produced : [43] multiply(X,identity) -> X
% Rule
% [29]
% multiply(X,a) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity) collapsed.
% Rule
% [30]
% multiply(X,b) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity) collapsed.
% Rule
% [32]
% multiply(X,c) greatest_lower_bound multiply(X,identity) ->
% multiply(X,identity) collapsed.
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [44] multiply(X,a) greatest_lower_bound X -> X
% Current number of equations to process: 197
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [45] multiply(X,b) greatest_lower_bound X -> X
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [46] multiply(X,c) greatest_lower_bound X -> X
% Current number of equations to process: 195
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [47]
% (c greatest_lower_bound a) least_upper_bound identity ->
% c greatest_lower_bound a
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [48]
% (a least_upper_bound X) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 223
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [49] multiply(X,a) least_upper_bound X -> multiply(X,a)
% Current number of equations to process: 222
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [50]
% (b least_upper_bound X) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 221
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [51] multiply(X,b) least_upper_bound X -> multiply(X,b)
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [52]
% (c least_upper_bound X) greatest_lower_bound (identity least_upper_bound X)
% -> identity least_upper_bound X
% Current number of equations to process: 219
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced : [53] multiply(X,c) least_upper_bound X -> multiply(X,c)
% Current number of equations to process: 218
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [54]
% (c greatest_lower_bound b) least_upper_bound identity ->
% c greatest_lower_bound b
% Current number of equations to process: 235
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [55] identity greatest_lower_bound multiply(inverse(b),a) -> inverse(b)
% Current number of equations to process: 335
% Current number of ordered equations: 1
% Current number of rules: 51
% New rule produced :
% [56] identity greatest_lower_bound multiply(inverse(a),b) -> inverse(a)
% Current number of equations to process: 335
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [57] (multiply(X,a) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 333
% Current number of ordered equations: 1
% Current number of rules: 53
% New rule produced :
% [58] (multiply(X,b) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 333
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [59]
% (X greatest_lower_bound Y) least_upper_bound multiply(X,a) -> multiply(X,a)
% Current number of equations to process: 333
% Current number of ordered equations: 1
% Current number of rules: 55
% New rule produced :
% [60]
% (X greatest_lower_bound Y) least_upper_bound multiply(X,b) -> multiply(X,b)
% Current number of equations to process: 333
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [61] identity greatest_lower_bound multiply(a,a) -> identity
% Current number of equations to process: 359
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [62] identity greatest_lower_bound multiply(a,b) -> identity
% Current number of equations to process: 358
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [63] identity greatest_lower_bound multiply(a,c) -> identity
% Current number of equations to process: 355
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced : [64] b greatest_lower_bound multiply(a,a) -> identity
% Current number of equations to process: 387
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [65] identity greatest_lower_bound multiply(b,a) -> identity
% Current number of equations to process: 386
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [66] identity greatest_lower_bound multiply(b,b) -> identity
% Current number of equations to process: 385
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [67] identity greatest_lower_bound multiply(b,c) -> identity
% Current number of equations to process: 382
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced : [68] a greatest_lower_bound multiply(b,b) -> identity
% Current number of equations to process: 418
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [69] identity greatest_lower_bound multiply(c,a) -> identity
% Current number of equations to process: 417
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [70] identity greatest_lower_bound multiply(c,b) -> identity
% Current number of equations to process: 416
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [71] identity greatest_lower_bound multiply(c,c) -> identity
% Current number of equations to process: 413
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [72] a greatest_lower_bound multiply(c,b) -> c greatest_lower_bound a
% Current number of equations to process: 454
% Current number of ordered equations: 1
% Current number of rules: 68
% New rule produced :
% [73] b greatest_lower_bound multiply(c,a) -> c greatest_lower_bound b
% Current number of equations to process: 454
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [74] (multiply(a,X) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 453
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [75] multiply(a,multiply(X,a)) greatest_lower_bound X -> X
% Current number of equations to process: 451
% Current number of ordered equations: 1
% Current number of rules: 71
% New rule produced :
% [76] multiply(a,multiply(X,b)) greatest_lower_bound X -> X
% Current number of equations to process: 451
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [77] multiply(a,multiply(a,X)) greatest_lower_bound X -> X
% Current number of equations to process: 450
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [78] (multiply(b,X) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 449
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [79] multiply(b,multiply(X,a)) greatest_lower_bound X -> X
% Current number of equations to process: 447
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [80] multiply(b,multiply(X,b)) greatest_lower_bound X -> X
% Current number of equations to process: 447
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [81] multiply(b,multiply(a,X)) greatest_lower_bound X -> X
% Current number of equations to process: 445
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [82] multiply(a,multiply(b,X)) greatest_lower_bound X -> X
% Current number of equations to process: 445
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [83] multiply(b,multiply(b,X)) greatest_lower_bound X -> X
% Current number of equations to process: 444
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [84] (multiply(c,X) least_upper_bound Y) greatest_lower_bound X -> X
% Current number of equations to process: 443
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [85] multiply(c,multiply(X,a)) greatest_lower_bound X -> X
% Current number of equations to process: 441
% Current number of ordered equations: 1
% Current number of rules: 81
% New rule produced :
% [86] multiply(c,multiply(X,b)) greatest_lower_bound X -> X
% Current number of equations to process: 441
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [87] multiply(c,multiply(a,X)) greatest_lower_bound X -> X
% Current number of equations to process: 439
% Current number of ordered equations: 1
% Current number of rules: 83
% New rule produced :
% [88] multiply(a,multiply(c,X)) greatest_lower_bound X -> X
% Current number of equations to process: 439
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [89] multiply(c,multiply(b,X)) greatest_lower_bound X -> X
% Current number of equations to process: 437
% Current number of ordered equations: 1
% Current number of rules: 85
% New rule produced :
% [90] multiply(b,multiply(c,X)) greatest_lower_bound X -> X
% Current number of equations to process: 437
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [91] multiply(c,multiply(c,X)) greatest_lower_bound X -> X
% Current number of equations to process: 436
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [92] identity least_upper_bound multiply(a,a) -> multiply(a,a)
% Current number of equations to process: 469
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [93] identity least_upper_bound multiply(a,b) -> multiply(a,b)
% Current number of equations to process: 468
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [94] identity least_upper_bound multiply(a,c) -> multiply(a,c)
% Current number of equations to process: 467
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [95]
% (multiply(a,a) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 476
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [96]
% (multiply(a,b) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 475
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [97]
% (multiply(a,c) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 474
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [98] identity least_upper_bound multiply(b,a) -> multiply(b,a)
% Current number of equations to process: 496
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [99] identity least_upper_bound multiply(b,b) -> multiply(b,b)
% Current number of equations to process: 495
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [100] identity least_upper_bound multiply(b,c) -> multiply(b,c)
% Current number of equations to process: 494
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [101]
% (multiply(b,a) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 507
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [102]
% (multiply(b,b) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 506
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [103]
% (multiply(b,c) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 505
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [104] identity least_upper_bound multiply(c,a) -> multiply(c,a)
% Current number of equations to process: 527
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [105] identity least_upper_bound multiply(c,b) -> multiply(c,b)
% Current number of equations to process: 526
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [106] identity least_upper_bound multiply(c,c) -> multiply(c,c)
% Current number of equations to process: 525
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced : [107] inverse(identity) -> identity
% Rule [40] multiply(inverse(identity),X) -> X collapsed.
% Current number of equations to process: 536
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced : [108] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 535
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [109]
% (multiply(c,a) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 534
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [110]
% (multiply(c,b) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 533
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [111]
% (multiply(c,c) least_upper_bound X) greatest_lower_bound identity -> identity
% Current number of equations to process: 532
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced : [112] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 532
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced : [113] inverse(inverse(X)) -> X
% Rule [42] multiply(inverse(inverse(X)),Y) -> multiply(X,Y) collapsed.
% Current number of equations to process: 533
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [114] identity greatest_lower_bound inverse(a) -> inverse(a)
% Current number of equations to process: 533
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [115] identity greatest_lower_bound inverse(b) -> inverse(b)
% Current number of equations to process: 549
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [116] identity greatest_lower_bound inverse(c) -> inverse(c)
% Current number of equations to process: 565
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [117] a greatest_lower_bound multiply(b,c) -> c greatest_lower_bound a
% The conjecture has been reduced. 
% Conjecture is now:
% Trivial
% 
% Current number of equations to process: 592
% Current number of ordered equations: 1
% Current number of rules: 111
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% 
% The following 7 rules have been used:
% [5] 
% b greatest_lower_bound a -> identity; trace = in the starting set
% [6] c greatest_lower_bound identity -> identity; trace = in the starting set
% [13] multiply(X,Y greatest_lower_bound Z) ->
% multiply(X,Y) greatest_lower_bound multiply(X,Z); trace = in the starting set
% [15] multiply(Y greatest_lower_bound Z,X) ->
% multiply(Y,X) greatest_lower_bound multiply(Z,X); trace = in the starting set
% [36] multiply(b,X) greatest_lower_bound multiply(a,X) -> X; trace = Cp of 15 and 5
% [46] multiply(X,c) greatest_lower_bound X -> X; trace = Cp of 13 and 6
% [117] a greatest_lower_bound multiply(b,c) -> c greatest_lower_bound a; trace = Cp of 46 and 36
% % SZS output end Refutation
% All conjectures have been proven
% 
% Execution time: 1.100000 sec
% res : bool = true
% time is now off
% 
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
% 
% EOF
%------------------------------------------------------------------------------