TSTP Solution File: COL003-15 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL003-15 : TPTP v6.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n051.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 00:19:34 EDT 2014
% Result : Unsatisfiable 11.54s
% Output : Refutation 11.54s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL003-15 : TPTP v6.0.0. Released v2.1.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n051.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 : Thu Jun 5 15:46:03 CDT 2014
% % CPUTime : 11.54
% Processing problem /tmp/CiME_8932_n051.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " fixed_pt,strong_fixed_point,w,b : constant; apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z));
% apply(apply(w,X),Y) = apply(apply(X,Y),Y);
% strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(b,b),b));
% ";
%
% let s1 = status F "
% fixed_pt lr_lex;
% strong_fixed_point lr_lex;
% w lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
%
% let p1 = precedence F "
% apply > b > w > strong_fixed_point > fixed_pt";
%
% let s2 = status F "
% fixed_pt mul;
% strong_fixed_point mul;
% w mul;
% apply mul;
% b mul;
% ";
%
% let p2 = precedence F "
% apply > b = w = strong_fixed_point = fixed_pt";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt));"
% ;
% (*
% 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 = { apply(apply(apply(b,X),Y),Z) =
% apply(X,apply(Y,Z)),
% apply(apply(w,X),Y) = apply(apply(X,Y),Y),
% strong_fixed_point =
% apply(apply(b,apply(apply(b,apply(w,w)),w)),
% apply(apply(b,b),b)) } (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [fixed_pt] = 1;
% [strong_fixed_point] = 2;
% [w] = 3;
% [b] = 4;
% [apply](x1,x2) = 1 + x1 + x2;
% Chosen ordering : KBO
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { apply(strong_fixed_point,fixed_pt) =
% apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] apply(apply(X,Y),Y) <-> apply(apply(w,X),Y)
% Current number of equations to process: 1
% Current number of ordered equations: 2
% Current number of rules: 1
% New rule produced : [2] apply(apply(w,X),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 2
% New rule produced : [3] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4]
% apply(apply(b,apply(apply(b,apply(w,w)),w)),apply(apply(w,w),b)) ->
% strong_fixed_point
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] apply(apply(w,w),X) <-> apply(apply(X,X),X)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced : [6] apply(apply(X,X),X) <-> apply(apply(w,w),X)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] apply(X,apply(X,Y)) <-> apply(apply(apply(w,b),X),Y)
% Current number of equations to process: 3
% Current number of ordered equations: 3
% Current number of rules: 7
% New rule produced : [8] apply(X,apply(Y,Y)) <-> apply(apply(w,apply(b,X)),Y)
% Current number of equations to process: 3
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced : [9] apply(apply(apply(w,b),X),Y) <-> apply(X,apply(X,Y))
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] apply(apply(w,apply(b,X)),Y) <-> apply(X,apply(Y,Y))
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] apply(apply(apply(w,X),Y),Y) -> apply(apply(w,apply(X,Y)),Y)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(w,X)),Y)
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [13] apply(apply(w,apply(w,X)),Y) <-> apply(apply(apply(X,Y),Y),Y)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] apply(apply(X,apply(Y,Z)),Z) <-> apply(apply(w,apply(apply(b,X),Y)),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [15] apply(apply(w,apply(apply(b,X),Y)),Z) <-> apply(apply(X,apply(Y,Z)),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,w)),X)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [17] apply(apply(w,apply(w,w)),X) <-> apply(apply(apply(X,X),X),X)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(X,X)),X)
% Current number of equations to process: 5
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [19] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] apply(apply(w,apply(X,Y)),Y) <-> apply(apply(w,apply(w,X)),Y)
% Rule [19] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,X)),X)
% collapsed.
% Current number of equations to process: 13
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [21] apply(apply(w,apply(w,X)),Y) <-> apply(apply(w,apply(X,Y)),Y)
% Rule [18] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(X,X)),X)
% collapsed.
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [22] apply(X,apply(X,X)) <-> apply(apply(w,apply(w,b)),X)
% Current number of equations to process: 28
% Current number of ordered equations: 2
% Current number of rules: 20
% New rule produced : [23] apply(apply(apply(w,w),b),X) -> apply(b,apply(b,X))
% Current number of equations to process: 28
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced : [24] apply(apply(w,apply(w,b)),X) <-> apply(X,apply(X,X))
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [25] apply(X,apply(apply(b,X),apply(b,X))) <-> apply(apply(w,w),apply(b,X))
% Current number of equations to process: 38
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [26] apply(apply(w,w),apply(b,X)) <-> apply(X,apply(apply(b,X),apply(b,X)))
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [27] apply(apply(apply(w,apply(b,w)),X),Y) <-> apply(apply(apply(X,X),Y),Y)
% Current number of equations to process: 37
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [28] apply(apply(apply(X,X),Y),Y) <-> apply(apply(apply(w,apply(b,w)),X),Y)
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [29] apply(apply(X,apply(X,Y)),Y) <-> apply(apply(w,apply(apply(w,b),X)),Y)
% Current number of equations to process: 36
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [30] apply(apply(w,apply(apply(w,b),X)),Y) <-> apply(apply(X,apply(X,Y)),Y)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [31] apply(apply(X,apply(Y,Y)),Y) <-> apply(apply(w,apply(w,apply(b,X))),Y)
% Current number of equations to process: 34
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [32] apply(apply(w,apply(w,apply(b,X))),Y) <-> apply(apply(X,apply(Y,Y)),Y)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [33] apply(apply(w,apply(w,w)),X) <-> apply(apply(w,apply(X,X)),X)
% Current number of equations to process: 56
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [34] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,w)),X)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [35] apply(apply(X,apply(X,X)),X) <-> apply(apply(w,apply(w,apply(w,b))),X)
% Current number of equations to process: 55
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [36] apply(apply(w,apply(w,apply(w,b))),X) <-> apply(apply(X,apply(X,X)),X)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [37] apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(apply(b,w),X)),Y)
% Current number of equations to process: 69
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [38] apply(apply(w,apply(apply(b,w),X)),Y) <-> apply(apply(apply(X,Y),Y),Y)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [39]
% apply(apply(apply(w,b),X),apply(X,Y)) ->
% apply(X,apply(apply(apply(w,b),X),Y))
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [40]
% apply(apply(X,Y),apply(apply(w,X),Y)) <->
% apply(apply(apply(w,b),apply(X,Y)),Y)
% Current number of equations to process: 67
% Current number of ordered equations: 1
% Current number of rules: 38
% New rule produced :
% [41]
% apply(apply(apply(w,b),apply(X,Y)),Y) <->
% apply(apply(X,Y),apply(apply(w,X),Y))
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [42]
% apply(apply(w,X),apply(apply(X,Y),Y)) <->
% apply(apply(apply(w,b),apply(w,X)),Y)
% Current number of equations to process: 66
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced :
% [43]
% apply(apply(apply(w,b),apply(w,X)),Y) <->
% apply(apply(w,X),apply(apply(X,Y),Y))
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [44]
% apply(apply(apply(w,b),apply(X,X)),X) ->
% apply(apply(X,X),apply(apply(w,w),X))
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [45]
% apply(apply(X,apply(Y,Y)),apply(Y,Y)) <->
% apply(apply(w,apply(b,apply(w,X))),Y)
% Current number of equations to process: 64
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced :
% [46]
% apply(apply(w,apply(b,apply(w,X))),Y) <->
% apply(apply(X,apply(Y,Y)),apply(Y,Y))
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [47]
% apply(X,apply(apply(w,apply(b,X)),Y)) <->
% apply(apply(apply(w,b),X),apply(Y,Y))
% Current number of equations to process: 63
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced :
% [48]
% apply(apply(apply(w,b),X),apply(Y,Y)) <->
% apply(X,apply(apply(w,apply(b,X)),Y))
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [49]
% apply(apply(w,apply(apply(w,X),Y)),Y) ->
% apply(apply(w,apply(w,apply(X,Y))),Y)
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [50]
% apply(apply(apply(apply(X,Y),Y),Y),Y) <->
% apply(apply(w,apply(w,apply(w,X))),Y)
% Current number of equations to process: 61
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [51]
% apply(apply(w,apply(w,apply(w,X))),Y) <->
% apply(apply(apply(apply(X,Y),Y),Y),Y)
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [52]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Current number of equations to process: 60
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [53]
% apply(apply(w,apply(w,apply(w,w))),X) <->
% apply(apply(apply(apply(X,X),X),X),X)
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [54]
% apply(apply(w,apply(apply(X,Y),Y)),Y) <->
% apply(apply(w,apply(w,apply(w,X))),Y)
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [55]
% apply(apply(w,apply(w,apply(w,X))),Y) <->
% apply(apply(w,apply(apply(X,Y),Y)),Y)
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [56] apply(X,apply(X,X)) <-> apply(apply(w,apply(apply(b,w),b)),X)
% Current number of equations to process: 72
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [57] apply(apply(w,apply(apply(b,w),b)),X) <-> apply(X,apply(X,X))
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [58] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(apply(w,b),w)),X)
% Current number of equations to process: 73
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [59] apply(apply(w,apply(apply(w,b),w)),X) <-> apply(apply(apply(X,X),X),X)
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [60]
% apply(apply(apply(apply(w,b),X),Y),Y) <->
% apply(apply(w,apply(apply(b,X),X)),Y)
% Current number of equations to process: 72
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [61]
% apply(apply(w,apply(apply(b,X),X)),Y) <->
% apply(apply(apply(apply(w,b),X),Y),Y)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [62] apply(apply(w,apply(apply(b,w),X)),X) -> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 60
% Rule [56] apply(X,apply(X,X)) <-> apply(apply(w,apply(apply(b,w),b)),X) is composed into
% [56] apply(X,apply(X,X)) <-> apply(apply(w,apply(w,b)),X)
% Rule [37]
% apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(apply(b,w),X)),Y) is composed into
% [37] apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(w,X)),Y)
% New rule produced :
% [63] apply(apply(w,apply(apply(b,w),X)),Y) -> apply(apply(w,apply(w,X)),Y)
% Rule
% [38] apply(apply(w,apply(apply(b,w),X)),Y) <-> apply(apply(apply(X,Y),Y),Y)
% collapsed.
% Rule [57] apply(apply(w,apply(apply(b,w),b)),X) <-> apply(X,apply(X,X))
% collapsed.
% Rule
% [62] apply(apply(w,apply(apply(b,w),X)),X) -> apply(apply(w,apply(w,X)),X)
% collapsed.
% Current number of equations to process: 108
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced : [64] apply(apply(w,apply(w,w)),b) -> apply(b,apply(b,b))
% Current number of equations to process: 135
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [65] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(apply(w,b),w)),X)
% Current number of equations to process: 156
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [66] apply(apply(w,apply(apply(w,b),w)),X) <-> apply(apply(w,apply(X,X)),X)
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [67] apply(apply(b,apply(b,X)),X) <-> apply(apply(w,apply(apply(w,w),b)),X)
% Current number of equations to process: 155
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [68] apply(apply(w,apply(apply(w,w),b)),X) <-> apply(apply(b,apply(b,X)),X)
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [69] apply(apply(w,apply(w,X)),X) <-> apply(apply(apply(w,w),apply(b,w)),X)
% Current number of equations to process: 154
% Current number of ordered equations: 1
% Current number of rules: 64
% New rule produced :
% [70] apply(apply(apply(w,w),apply(b,w)),X) <-> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [71]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X)
% Current number of equations to process: 153
% Current number of ordered equations: 1
% Current number of rules: 66
% New rule produced :
% [72]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,X))),X)
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [73]
% apply(apply(w,apply(w,apply(w,w))),X) <->
% apply(apply(w,apply(apply(X,X),X)),X)
% Current number of equations to process: 152
% Current number of ordered equations: 1
% Current number of rules: 68
% New rule produced :
% [74]
% apply(apply(w,apply(apply(X,X),X)),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [75]
% apply(apply(w,apply(w,apply(X,Y))),Y) <->
% apply(apply(w,apply(w,apply(w,X))),Y)
% Rule
% [72]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,X))),X) collapsed.
% Current number of equations to process: 150
% Current number of ordered equations: 1
% Current number of rules: 69
% New rule produced :
% [76]
% apply(apply(w,apply(w,apply(w,X))),Y) <->
% apply(apply(w,apply(w,apply(X,Y))),Y)
% Rule
% [71]
% apply(apply(w,apply(w,apply(w,X))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X) collapsed.
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [77]
% apply(apply(w,apply(w,apply(w,w))),X) <->
% apply(apply(w,apply(w,apply(X,X))),X)
% Current number of equations to process: 149
% Current number of ordered equations: 1
% Current number of rules: 70
% New rule produced :
% [78]
% apply(apply(w,apply(w,apply(X,X))),X) <->
% apply(apply(w,apply(w,apply(w,w))),X)
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [79] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,apply(b,w))),X)
% Current number of equations to process: 170
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [80] apply(apply(w,apply(w,apply(b,w))),X) <-> apply(apply(apply(X,X),X),X)
% Current number of equations to process: 170
% Current number of ordered equations: 0
% Current number of rules: 73
% Rule [65]
% apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(apply(w,b),w)),X) is composed into
% [65] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,w)),X)
% Rule [58]
% apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(apply(w,b),w)),X) is composed into
% [58] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,w)),X)
% New rule produced :
% [81] apply(apply(w,apply(apply(w,b),w)),X) -> apply(apply(w,apply(w,w)),X)
% Rule
% [59] apply(apply(w,apply(apply(w,b),w)),X) <-> apply(apply(apply(X,X),X),X)
% collapsed.
% Rule
% [66] apply(apply(w,apply(apply(w,b),w)),X) <-> apply(apply(w,apply(X,X)),X)
% collapsed.
% Current number of equations to process: 230
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [82] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(w,apply(b,w))),X)
% Current number of equations to process: 278
% Current number of ordered equations: 1
% Current number of rules: 73
% New rule produced :
% [83] apply(apply(w,apply(w,apply(b,w))),X) <-> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 278
% Current number of ordered equations: 0
% Current number of rules: 74
% Rule [82]
% apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(w,apply(b,w))),X) is composed into
% [82] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(w,w)),X)
% Rule [79]
% apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,apply(b,w))),X) is composed into
% [79] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,w)),X)
% New rule produced :
% [84] apply(apply(w,apply(w,apply(b,w))),X) -> apply(apply(w,apply(w,w)),X)
% Rule
% [80] apply(apply(w,apply(w,apply(b,w))),X) <-> apply(apply(apply(X,X),X),X)
% collapsed.
% Rule
% [83] apply(apply(w,apply(w,apply(b,w))),X) <-> apply(apply(w,apply(w,X)),X)
% collapsed.
% Current number of equations to process: 308
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [85]
% apply(apply(w,w),apply(w,apply(b,apply(b,X)))) -> apply(strong_fixed_point,X)
% Current number of equations to process: 649
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [86]
% apply(apply(apply(apply(w,b),X),Y),apply(X,Y)) ->
% apply(apply(w,X),apply(X,Y))
% Current number of equations to process: 719
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [87]
% apply(X,apply(X,apply(Y,Z))) <->
% apply(apply(apply(apply(w,b),apply(b,X)),Y),Z)
% Current number of equations to process: 717
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [88]
% apply(apply(apply(apply(w,b),apply(b,X)),Y),Z) <->
% apply(X,apply(X,apply(Y,Z)))
% Current number of equations to process: 717
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [89]
% apply(apply(apply(w,apply(b,X)),Y),apply(Y,Y)) ->
% apply(apply(w,X),apply(Y,Y))
% Current number of equations to process: 818
% Current number of ordered equations: 1
% Current number of rules: 78
% New rule produced :
% [90]
% apply(apply(w,apply(b,apply(X,apply(Y,Y)))),Y) ->
% apply(apply(w,X),apply(Y,Y))
% Current number of equations to process: 818
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [91]
% apply(X,apply(Y,apply(Z,Z))) <->
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Z)
% Current number of equations to process: 920
% Current number of ordered equations: 5
% Current number of rules: 80
% New rule produced :
% [92]
% apply(X,apply(apply(Y,Y),Z)) <->
% apply(apply(apply(w,apply(b,apply(b,X))),Y),Z)
% Current number of equations to process: 920
% Current number of ordered equations: 4
% Current number of rules: 81
% New rule produced :
% [93]
% apply(apply(X,X),apply(Y,Z)) <->
% apply(apply(apply(apply(w,apply(b,b)),X),Y),Z)
% Current number of equations to process: 920
% Current number of ordered equations: 3
% Current number of rules: 82
% New rule produced :
% [94]
% apply(apply(apply(apply(w,apply(b,b)),X),Y),Z) <->
% apply(apply(X,X),apply(Y,Z))
% Current number of equations to process: 920
% Current number of ordered equations: 2
% Current number of rules: 83
% New rule produced :
% [95]
% apply(apply(apply(w,apply(b,apply(b,X))),Y),Z) <->
% apply(X,apply(apply(Y,Y),Z))
% Current number of equations to process: 920
% Current number of ordered equations: 1
% Current number of rules: 84
% New rule produced :
% [96]
% apply(apply(w,apply(b,apply(apply(b,X),Y))),Z) <->
% apply(X,apply(Y,apply(Z,Z)))
% Current number of equations to process: 920
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [97]
% apply(X,apply(X,apply(Y,Y))) <->
% apply(apply(w,apply(b,apply(apply(w,b),X))),Y)
% Current number of equations to process: 919
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [98]
% apply(apply(w,apply(b,apply(apply(w,b),X))),Y) <->
% apply(X,apply(X,apply(Y,Y)))
% Current number of equations to process: 919
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [99]
% apply(apply(X,X),apply(Y,Y)) <->
% apply(apply(w,apply(apply(w,apply(b,b)),X)),Y)
% Current number of equations to process: 918
% Current number of ordered equations: 1
% Current number of rules: 88
% New rule produced :
% [100]
% apply(apply(w,apply(apply(w,apply(b,b)),X)),Y) <->
% apply(apply(X,X),apply(Y,Y))
% Current number of equations to process: 918
% Current number of ordered equations: 0
% Current number of rules: 89
% Rule [69]
% apply(apply(w,apply(w,X)),X) <-> apply(apply(apply(w,w),apply(b,w)),X) is composed into
% [69] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(w,w)),X)
% New rule produced :
% [101] apply(apply(apply(w,w),apply(b,w)),X) -> apply(apply(w,apply(w,w)),X)
% Rule
% [70] apply(apply(apply(w,w),apply(b,w)),X) <-> apply(apply(w,apply(w,X)),X)
% collapsed.
% Current number of equations to process: 976
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [102] apply(apply(w,apply(w,apply(w,w))),b) -> apply(apply(b,apply(b,b)),b)
% Current number of equations to process: 989
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [103]
% apply(X,apply(apply(Y,Z),Z)) <->
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z)
% Current number of equations to process: 1153
% Current number of ordered equations: 3
% Current number of rules: 91
% New rule produced :
% [104]
% apply(apply(X,Y),apply(Y,Z)) <->
% apply(apply(apply(w,apply(apply(b,b),X)),Y),Z)
% Current number of equations to process: 1153
% Current number of ordered equations: 2
% Current number of rules: 92
% New rule produced :
% [105]
% apply(apply(apply(w,apply(apply(b,b),X)),Y),Z) <->
% apply(apply(X,Y),apply(Y,Z))
% Current number of equations to process: 1153
% Current number of ordered equations: 1
% Current number of rules: 93
% New rule produced :
% [106]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z) <->
% apply(X,apply(apply(Y,Z),Z))
% Current number of equations to process: 1153
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [107]
% apply(apply(apply(w,apply(w,b)),X),apply(X,X)) ->
% apply(apply(w,X),apply(X,X))
% Current number of equations to process: 1244
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [108]
% apply(b,apply(b,apply(X,X))) <->
% apply(apply(w,apply(b,apply(apply(w,w),b))),X)
% Current number of equations to process: 1242
% Current number of ordered equations: 1
% Current number of rules: 96
% New rule produced :
% [109]
% apply(apply(w,apply(b,apply(apply(w,w),b))),X) <->
% apply(b,apply(b,apply(X,X)))
% Current number of equations to process: 1242
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [110]
% apply(apply(b,X),apply(X,X)) <->
% apply(apply(w,apply(w,apply(apply(w,w),b))),X)
% Current number of equations to process: 1241
% Current number of ordered equations: 1
% Current number of rules: 98
% New rule produced :
% [111]
% apply(apply(w,apply(w,apply(apply(w,w),b))),X) <->
% apply(apply(b,X),apply(X,X))
% Current number of equations to process: 1241
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [112]
% apply(X,apply(X,apply(Y,Y))) <->
% apply(apply(w,apply(apply(w,b),apply(b,X))),Y)
% Current number of equations to process: 1238
% Current number of ordered equations: 3
% Current number of rules: 100
% New rule produced :
% [113]
% apply(apply(b,X),apply(X,Y)) <->
% apply(apply(apply(w,apply(apply(w,w),b)),X),Y)
% Current number of equations to process: 1238
% Current number of ordered equations: 2
% Current number of rules: 101
% New rule produced :
% [114]
% apply(apply(apply(w,apply(apply(w,w),b)),X),Y) <->
% apply(apply(b,X),apply(X,Y))
% Current number of equations to process: 1238
% Current number of ordered equations: 1
% Current number of rules: 102
% New rule produced :
% [115]
% apply(apply(w,apply(apply(w,b),apply(b,X))),Y) <->
% apply(X,apply(X,apply(Y,Y)))
% Current number of equations to process: 1238
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [116]
% apply(X,apply(apply(Y,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y)
% Current number of equations to process: 1236
% Current number of ordered equations: 3
% Current number of rules: 104
% New rule produced :
% [117]
% apply(apply(X,X),apply(X,Y)) <->
% apply(apply(apply(w,apply(w,apply(b,b))),X),Y)
% Current number of equations to process: 1236
% Current number of ordered equations: 2
% Current number of rules: 105
% New rule produced :
% [118]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) <->
% apply(X,apply(apply(Y,Y),Y))
% Current number of equations to process: 1236
% Current number of ordered equations: 1
% Current number of rules: 106
% New rule produced :
% [119]
% apply(apply(apply(w,apply(w,apply(b,b))),X),Y) <->
% apply(apply(X,X),apply(X,Y))
% Current number of equations to process: 1236
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [120]
% apply(apply(w,apply(w,apply(w,apply(w,w)))),b) ->
% apply(apply(b,b),apply(b,b))
% Current number of equations to process: 1227
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [121]
% apply(apply(w,apply(apply(w,w),apply(b,b))),b) ->
% apply(apply(w,w),apply(b,b))
% Current number of equations to process: 1650
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [122]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Y) ->
% apply(X,apply(apply(w,Y),Y))
% Current number of equations to process: 1836
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [123]
% apply(X,apply(X,apply(strong_fixed_point,X))) -> apply(strong_fixed_point,X)
% Current number of equations to process: 2185
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [124]
% apply(apply(X,X),apply(X,X)) <->
% apply(apply(w,apply(w,apply(w,apply(b,b)))),X)
% Current number of equations to process: 2704
% Current number of ordered equations: 1
% Current number of rules: 112
% New rule produced :
% [125]
% apply(apply(w,apply(w,apply(w,apply(b,b)))),X) <->
% apply(apply(X,X),apply(X,X))
% Current number of equations to process: 2704
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [126]
% apply(apply(X,X),apply(X,X)) <->
% apply(apply(w,apply(w,apply(apply(b,b),X))),X)
% Current number of equations to process: 2703
% Current number of ordered equations: 1
% Current number of rules: 114
% New rule produced :
% [127]
% apply(apply(w,apply(w,apply(apply(b,b),X))),X) <->
% apply(apply(X,X),apply(X,X))
% Current number of equations to process: 2703
% Current number of ordered equations: 0
% Current number of rules: 115
% Rule [103]
% apply(X,apply(apply(Y,Z),Z)) <->
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z) is composed into
% [103] apply(X,apply(apply(Y,Z),Z)) <-> apply(X,apply(apply(w,Y),Z))
% New rule produced :
% [128]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z) ->
% apply(X,apply(apply(w,Y),Z))
% Rule
% [106]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Z) <->
% apply(X,apply(apply(Y,Z),Z)) collapsed.
% Rule
% [122]
% apply(apply(w,apply(apply(b,apply(b,X)),Y)),Y) ->
% apply(X,apply(apply(w,Y),Y)) collapsed.
% Current number of equations to process: 2702
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [129]
% apply(apply(X,Y),apply(Y,Y)) <->
% apply(apply(w,apply(w,apply(apply(b,b),X))),Y)
% Rule
% [126]
% apply(apply(X,X),apply(X,X)) <->
% apply(apply(w,apply(w,apply(apply(b,b),X))),X) collapsed.
% Current number of equations to process: 3082
% Current number of ordered equations: 1
% Current number of rules: 114
% New rule produced :
% [130]
% apply(apply(w,apply(w,apply(apply(b,b),X))),Y) <->
% apply(apply(X,Y),apply(Y,Y))
% Rule
% [127]
% apply(apply(w,apply(w,apply(apply(b,b),X))),X) <->
% apply(apply(X,X),apply(X,X)) collapsed.
% Current number of equations to process: 3082
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [131]
% apply(X,apply(apply(w,X),X)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),X)
% Current number of equations to process: 3366
% Current number of ordered equations: 1
% Current number of rules: 115
% New rule produced :
% [132]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),X) <->
% apply(X,apply(apply(w,X),X))
% Current number of equations to process: 3366
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [133]
% apply(X,apply(apply(w,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y)
% Rule
% [131]
% apply(X,apply(apply(w,X),X)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),X) collapsed.
% Current number of equations to process: 3863
% Current number of ordered equations: 1
% Current number of rules: 116
% New rule produced :
% [134]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) <->
% apply(X,apply(apply(w,Y),Y))
% Rule
% [132]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),X) <->
% apply(X,apply(apply(w,X),X)) collapsed.
% Current number of equations to process: 3863
% Current number of ordered equations: 0
% Current number of rules: 116
% Rule [133]
% apply(X,apply(apply(w,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) is composed into
% [133] apply(X,apply(apply(w,Y),Y)) <-> apply(X,apply(apply(w,w),Y))
% Rule [116]
% apply(X,apply(apply(Y,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) is composed into
% [116] apply(X,apply(apply(Y,Y),Y)) <-> apply(X,apply(apply(w,w),Y))
% New rule produced :
% [135]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) ->
% apply(X,apply(apply(w,w),Y))
% Rule
% [118]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) <->
% apply(X,apply(apply(Y,Y),Y)) collapsed.
% Rule
% [134]
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) <->
% apply(X,apply(apply(w,Y),Y)) collapsed.
% Current number of equations to process: 4025
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [136]
% apply(apply(w,apply(apply(strong_fixed_point,w),X)),X) ->
% apply(apply(strong_fixed_point,w),X)
% Current number of equations to process: 4297
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [137]
% apply(apply(apply(w,b),X),apply(strong_fixed_point,X)) ->
% apply(strong_fixed_point,X)
% Current number of equations to process: 4319
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [138]
% apply(apply(apply(apply(strong_fixed_point,w),X),X),X) ->
% apply(apply(strong_fixed_point,w),X)
% Current number of equations to process: 4395
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [139]
% apply(apply(w,apply(w,apply(w,strong_fixed_point))),w) ->
% apply(apply(strong_fixed_point,w),w)
% Current number of equations to process: 4394
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [140]
% apply(apply(w,w),apply(w,apply(strong_fixed_point,b))) ->
% apply(strong_fixed_point,apply(strong_fixed_point,b))
% Current number of equations to process: 4393
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [141]
% apply(apply(w,apply(w,w)),apply(strong_fixed_point,w)) ->
% apply(apply(strong_fixed_point,w),apply(strong_fixed_point,w))
% Current number of equations to process: 4392
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [142]
% apply(apply(b,apply(strong_fixed_point,b)),apply(X,Y)) ->
% apply(apply(apply(strong_fixed_point,b),X),Y)
% Current number of equations to process: 4391
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [143]
% apply(apply(apply(apply(w,b),apply(b,X)),strong_fixed_point),X) ->
% apply(strong_fixed_point,X)
% Current number of equations to process: 4388
% Current number of ordered equations: 0
% Current number of rules: 123
% New rule produced :
% [144]
% apply(apply(w,X),apply(X,apply(strong_fixed_point,X))) <->
% apply(apply(strong_fixed_point,X),apply(X,apply(strong_fixed_point,X)))
% Current number of equations to process: 4389
% Current number of ordered equations: 1
% Current number of rules: 124
% New rule produced :
% [145]
% apply(apply(strong_fixed_point,X),apply(X,apply(strong_fixed_point,X))) <->
% apply(apply(w,X),apply(X,apply(strong_fixed_point,X)))
% Current number of equations to process: 4389
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [146]
% apply(apply(w,apply(apply(strong_fixed_point,b),X)),Y) <->
% apply(apply(strong_fixed_point,b),apply(apply(X,Y),Y))
% Current number of equations to process: 4387
% Current number of ordered equations: 1
% Current number of rules: 126
% New rule produced :
% [147]
% apply(apply(strong_fixed_point,b),apply(apply(X,Y),Y)) <->
% apply(apply(w,apply(apply(strong_fixed_point,b),X)),Y)
% Current number of equations to process: 4387
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [148]
% apply(apply(w,apply(w,apply(strong_fixed_point,b))),X) <->
% apply(apply(strong_fixed_point,b),apply(apply(X,X),X))
% Current number of equations to process: 4386
% Current number of ordered equations: 1
% Current number of rules: 128
% New rule produced :
% [149]
% apply(apply(strong_fixed_point,b),apply(apply(X,X),X)) <->
% apply(apply(w,apply(w,apply(strong_fixed_point,b))),X)
% Current number of equations to process: 4386
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [150]
% apply(apply(apply(w,apply(strong_fixed_point,b)),X),Y) <->
% apply(apply(strong_fixed_point,b),apply(apply(X,X),Y))
% Current number of equations to process: 4385
% Current number of ordered equations: 1
% Current number of rules: 130
% New rule produced :
% [151]
% apply(apply(strong_fixed_point,b),apply(apply(X,X),Y)) <->
% apply(apply(apply(w,apply(strong_fixed_point,b)),X),Y)
% Current number of equations to process: 4385
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [152]
% apply(X,apply(X,apply(apply(strong_fixed_point,apply(b,X)),Y))) ->
% apply(apply(strong_fixed_point,apply(b,X)),Y)
% Current number of equations to process: 4387
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [153]
% apply(apply(w,apply(w,apply(apply(strong_fixed_point,w),X))),X) ->
% apply(apply(apply(strong_fixed_point,w),X),X)
% Current number of equations to process: 4386
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [154]
% apply(apply(w,apply(apply(b,X),X)),apply(strong_fixed_point,X)) ->
% apply(apply(strong_fixed_point,X),apply(strong_fixed_point,X))
% Current number of equations to process: 4385
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [155]
% apply(apply(w,apply(apply(w,b),X)),apply(strong_fixed_point,X)) ->
% apply(apply(strong_fixed_point,X),apply(strong_fixed_point,X))
% Current number of equations to process: 4383
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [156]
% apply(apply(w,apply(apply(apply(strong_fixed_point,w),X),X)),X) ->
% apply(apply(w,apply(strong_fixed_point,w)),X)
% Current number of equations to process: 4381
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [157]
% apply(apply(w,apply(w,apply(w,w))),apply(strong_fixed_point,w)) ->
% apply(apply(w,w),apply(strong_fixed_point,w))
% Current number of equations to process: 4380
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [158]
% apply(apply(w,w),apply(w,apply(b,apply(strong_fixed_point,b)))) ->
% apply(strong_fixed_point,apply(b,apply(strong_fixed_point,b)))
% Current number of equations to process: 4378
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [159]
% apply(apply(strong_fixed_point,apply(strong_fixed_point,strong_fixed_point)),
% apply(apply(w,strong_fixed_point),apply(strong_fixed_point,strong_fixed_point)))
% -> apply(strong_fixed_point,strong_fixed_point)
% Current number of equations to process: 4377
% Current number of ordered equations: 0
% Current number of rules: 139
% Rule [147]
% apply(apply(strong_fixed_point,b),apply(apply(X,Y),Y)) <->
% apply(apply(w,apply(apply(strong_fixed_point,b),X)),Y) is composed into
% [147]
% apply(apply(strong_fixed_point,b),apply(apply(X,Y),Y)) <->
% apply(apply(strong_fixed_point,b),apply(apply(w,X),Y))
% New rule produced :
% [160]
% apply(apply(w,apply(apply(strong_fixed_point,b),X)),Y) ->
% apply(apply(strong_fixed_point,b),apply(apply(w,X),Y))
% Rule
% [146]
% apply(apply(w,apply(apply(strong_fixed_point,b),X)),Y) <->
% apply(apply(strong_fixed_point,b),apply(apply(X,Y),Y)) collapsed.
% Current number of equations to process: 4594
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [161]
% apply(apply(w,apply(apply(w,w),X)),Y) <->
% apply(apply(apply(apply(w,X),X),Y),Y)
% Current number of equations to process: 4954
% Current number of ordered equations: 1
% Current number of rules: 140
% New rule produced :
% [162]
% apply(apply(apply(apply(w,X),X),Y),Y) <->
% apply(apply(w,apply(apply(w,w),X)),Y)
% Current number of equations to process: 4954
% Current number of ordered equations: 0
% Current number of rules: 141
% Rule [156]
% apply(apply(w,apply(apply(apply(strong_fixed_point,w),X),X)),X) ->
% apply(apply(w,apply(strong_fixed_point,w)),X) is composed into [156]
% apply(
% apply(w,
% apply(
% apply(
% apply(strong_fixed_point,w),X),X)),X)
% ->
% apply(
% apply(strong_fixed_point,w),X)
% New rule produced :
% [163] apply(X,apply(strong_fixed_point,X)) -> apply(strong_fixed_point,X)
% Rule
% [123]
% apply(X,apply(X,apply(strong_fixed_point,X))) -> apply(strong_fixed_point,X)
% collapsed.
% Rule
% [142]
% apply(apply(b,apply(strong_fixed_point,b)),apply(X,Y)) ->
% apply(apply(apply(strong_fixed_point,b),X),Y) collapsed.
% Rule
% [144]
% apply(apply(w,X),apply(X,apply(strong_fixed_point,X))) <->
% apply(apply(strong_fixed_point,X),apply(X,apply(strong_fixed_point,X)))
% collapsed.
% Rule
% [145]
% apply(apply(strong_fixed_point,X),apply(X,apply(strong_fixed_point,X))) <->
% apply(apply(w,X),apply(X,apply(strong_fixed_point,X))) collapsed.
% Rule
% [158]
% apply(apply(w,w),apply(w,apply(b,apply(strong_fixed_point,b)))) ->
% apply(strong_fixed_point,apply(b,apply(strong_fixed_point,b))) collapsed.
% Rule
% [159]
% apply(apply(strong_fixed_point,apply(strong_fixed_point,strong_fixed_point)),
% apply(apply(w,strong_fixed_point),apply(strong_fixed_point,strong_fixed_point)))
% -> apply(strong_fixed_point,strong_fixed_point) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 2046
% Current number of ordered equations: 0
% Current number of rules: 136
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 9 rules have been used:
% [1]
% apply(apply(X,Y),Y) <-> apply(apply(w,X),Y); trace = in the starting set
% [2] apply(apply(w,X),Y) <-> apply(apply(X,Y),Y); trace = in the starting set
% [3] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z)); trace = in the starting set
% [6] apply(apply(X,X),X) <-> apply(apply(w,w),X); trace = Cp of 2 and 1
% [10] apply(apply(w,apply(b,X)),Y) <-> apply(X,apply(Y,Y)); trace = Cp of 3 and 1
% [31] apply(apply(X,apply(Y,Y)),Y) <-> apply(apply(w,apply(w,apply(b,X))),Y); trace = Cp of 10 and 1
% [116] apply(X,apply(apply(Y,Y),Y)) <->
% apply(apply(w,apply(w,apply(b,apply(b,X)))),Y); trace = Cp of 31 and 3
% [135] apply(apply(w,apply(w,apply(b,apply(b,X)))),Y) ->
% apply(X,apply(apply(w,w),Y)); trace = Cp of 116 and 6
% [163] apply(X,apply(strong_fixed_point,X)) -> apply(strong_fixed_point,X); trace = Cp of 135 and 1
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 10.410000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------