TSTP Solution File: COL042-9 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL042-9 : TPTP v6.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n062.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 00:19:50 EDT 2014
% Result : Unsatisfiable 2.84s
% Output : Refutation 2.84s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL042-9 : TPTP v6.0.0. Released v2.1.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n062.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 19:33:33 CDT 2014
% % CPUTime : 2.84
% Processing problem /tmp/CiME_15191_n062.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " fixed_pt,strong_fixed_point,w1,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(w1,X),Y) = apply(apply(Y,X),X);
% strong_fixed_point = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b)));
% ";
%
% let s1 = status F "
% fixed_pt lr_lex;
% strong_fixed_point lr_lex;
% w1 lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
%
% let p1 = precedence F "
% apply > b > w1 > strong_fixed_point > fixed_pt";
%
% let s2 = status F "
% fixed_pt mul;
% strong_fixed_point mul;
% w1 mul;
% apply mul;
% b mul;
% ";
%
% let p2 = precedence F "
% apply > b = w1 = 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(w1,X),Y) = apply(apply(Y,X),X),
% strong_fixed_point =
% apply(apply(b,apply(w1,w1)),apply(apply(b,
% apply(b,w1)),
% 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;
% [w1] = 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(Y,X),X) <-> apply(apply(w1,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(w1,X),Y) <-> apply(apply(Y,X),X)
% 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(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)))
% -> 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(w1,X),w1) <-> 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(w1,X),w1)
% 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(w1,X),b),Y)
% Current number of equations to process: 3
% Current number of ordered equations: 3
% Current number of rules: 7
% New rule produced : [8] apply(Y,apply(X,X)) <-> apply(apply(w1,X),apply(b,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(w1,X),apply(b,Y)) <-> apply(Y,apply(X,X))
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [10] apply(apply(apply(w1,X),b),Y) <-> apply(X,apply(X,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(w1,X),Y),X) -> apply(apply(w1,X),apply(Y,X))
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] apply(apply(w1,X),apply(w1,Y)) <-> apply(apply(apply(X,Y),Y),X)
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [13] apply(apply(apply(X,Y),Y),X) <-> apply(apply(w1,X),apply(w1,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(w1,Z),apply(apply(b,X),Y))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [15] apply(apply(w1,Z),apply(apply(b,X),Y)) <-> 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(w1,w1),apply(w1,X)) <-> apply(apply(apply(X,X),X),w1)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [17] apply(apply(apply(X,X),X),w1) <-> apply(apply(w1,w1),apply(w1,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(w1,X),apply(w1,X)) <-> apply(apply(w1,X),apply(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(w1,X),apply(X,X)) <-> apply(apply(w1,X),apply(w1,X))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20] apply(X,apply(apply(b,X),apply(b,X))) <-> apply(apply(w1,apply(b,X)),w1)
% Current number of equations to process: 11
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [21] apply(apply(w1,apply(b,X)),w1) <-> apply(X,apply(apply(b,X),apply(b,X)))
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22] apply(apply(w1,X),apply(b,apply(w1,Y))) <-> apply(apply(apply(X,X),Y),Y)
% Current number of equations to process: 24
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [23] apply(apply(apply(X,X),Y),Y) <-> apply(apply(w1,X),apply(b,apply(w1,Y)))
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24] apply(X,apply(X,b)) <-> apply(apply(w1,b),apply(w1,X))
% Current number of equations to process: 33
% Current number of ordered equations: 2
% Current number of rules: 24
% New rule produced :
% [25] apply(apply(w1,b),apply(w1,X)) <-> apply(X,apply(X,b))
% Current number of equations to process: 33
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [26] apply(apply(apply(w1,b),w1),X) -> apply(b,apply(b,X))
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27] apply(apply(w1,Y),apply(apply(w1,X),b)) <-> apply(apply(X,apply(X,Y)),Y)
% Current number of equations to process: 32
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [28] apply(apply(X,apply(X,Y)),Y) <-> apply(apply(w1,Y),apply(apply(w1,X),b))
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% apply(apply(apply(w1,X),b),apply(X,Y)) ->
% apply(X,apply(apply(apply(w1,X),b),Y))
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% apply(apply(X,Y),apply(apply(w1,Y),X)) <->
% apply(apply(apply(w1,apply(X,Y)),b),Y)
% Current number of equations to process: 36
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced :
% [31]
% apply(apply(apply(w1,apply(X,Y)),b),Y) <->
% apply(apply(X,Y),apply(apply(w1,Y),X))
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32]
% apply(apply(w1,X),apply(apply(Y,X),X)) <->
% apply(apply(apply(w1,apply(w1,X)),b),Y)
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 32
% New rule produced :
% [33]
% apply(apply(apply(w1,apply(w1,X)),b),Y) <->
% apply(apply(w1,X),apply(apply(Y,X),X))
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [34]
% apply(apply(w1,X),apply(apply(X,X),X)) <->
% apply(apply(apply(w1,apply(w1,X)),b),w1)
% Current number of equations to process: 34
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [35]
% apply(apply(apply(w1,apply(w1,X)),b),w1) <->
% apply(apply(w1,X),apply(apply(X,X),X))
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [36]
% apply(apply(apply(w1,apply(X,X)),b),X) ->
% apply(apply(X,X),apply(apply(w1,X),w1))
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [37]
% apply(X,apply(apply(w1,Y),apply(Y,Y))) <->
% apply(apply(w1,apply(w1,Y)),apply(b,X))
% Current number of equations to process: 31
% Current number of ordered equations: 3
% Current number of rules: 37
% New rule produced :
% [38]
% apply(apply(Y,apply(X,X)),apply(X,X)) <->
% apply(apply(apply(w1,X),apply(b,w1)),Y)
% Current number of equations to process: 31
% Current number of ordered equations: 2
% Current number of rules: 38
% New rule produced :
% [39]
% apply(apply(w1,apply(w1,Y)),apply(b,X)) <->
% apply(X,apply(apply(w1,Y),apply(Y,Y)))
% Current number of equations to process: 31
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [40]
% apply(apply(apply(w1,X),apply(b,w1)),Y) <->
% apply(apply(Y,apply(X,X)),apply(X,X))
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [41]
% apply(X,apply(apply(w1,Y),apply(b,X))) <->
% apply(apply(apply(w1,X),b),apply(Y,Y))
% Current number of equations to process: 30
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [42]
% apply(apply(apply(w1,X),b),apply(Y,Y)) <->
% apply(X,apply(apply(w1,Y),apply(b,X)))
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [43]
% apply(apply(w1,apply(b,X)),apply(w1,Y)) <->
% apply(apply(X,apply(Y,Y)),apply(b,X))
% Current number of equations to process: 29
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced :
% [44]
% apply(apply(X,apply(Y,Y)),apply(b,X)) <->
% apply(apply(w1,apply(b,X)),apply(w1,Y))
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [45]
% apply(X,apply(apply(apply(Y,Y),Y),Y)) <->
% apply(apply(w1,apply(w1,Y)),apply(b,X))
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced :
% [46]
% apply(apply(w1,apply(w1,Y)),apply(b,X)) <->
% apply(X,apply(apply(apply(Y,Y),Y),Y))
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [47]
% apply(apply(w1,X),apply(apply(w1,Y),X)) <->
% apply(apply(apply(apply(X,Y),Y),X),X)
% Current number of equations to process: 44
% Current number of ordered equations: 1
% Current number of rules: 47
% New rule produced :
% [48]
% apply(apply(apply(apply(X,Y),Y),X),X) <->
% apply(apply(w1,X),apply(apply(w1,Y),X))
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [49]
% apply(apply(w1,X),apply(apply(b,w1),Y)) <->
% apply(apply(X,apply(Y,X)),apply(Y,X))
% Current number of equations to process: 63
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [50]
% apply(apply(X,apply(Y,X)),apply(Y,X)) <->
% apply(apply(w1,X),apply(apply(b,w1),Y))
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [51]
% apply(apply(w1,apply(apply(b,apply(b,X)),w1)),w1) ->
% apply(strong_fixed_point,X)
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [52]
% apply(apply(apply(w1,X),apply(X,X)),apply(w1,X)) ->
% apply(apply(w1,apply(w1,X)),w1)
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [53]
% apply(apply(apply(apply(w1,X),b),Y),apply(X,Y)) ->
% apply(apply(w1,apply(X,Y)),X)
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [54]
% apply(X,apply(X,apply(Y,Z))) <->
% apply(apply(apply(apply(w1,apply(b,X)),b),Y),Z)
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [55]
% apply(apply(apply(apply(w1,apply(b,X)),b),Y),Z) <->
% apply(X,apply(X,apply(Y,Z)))
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [56]
% apply(apply(w1,X),apply(b,apply(Y,apply(X,X)))) ->
% apply(apply(w1,apply(X,X)),Y)
% Current number of equations to process: 56
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [57]
% apply(apply(apply(w1,X),apply(b,Y)),apply(X,X)) ->
% apply(apply(w1,apply(X,X)),Y)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [58]
% apply(X,apply(Y,apply(Z,Z))) <->
% apply(apply(w1,Z),apply(b,apply(apply(b,X),Y)))
% Current number of equations to process: 53
% Current number of ordered equations: 5
% Current number of rules: 58
% New rule produced :
% [59]
% apply(Y,apply(apply(X,X),Z)) <->
% apply(apply(apply(w1,X),apply(b,apply(b,Y))),Z)
% Current number of equations to process: 53
% Current number of ordered equations: 4
% Current number of rules: 59
% New rule produced :
% [60]
% apply(apply(X,X),apply(Y,Z)) <->
% apply(apply(apply(apply(w1,X),apply(b,b)),Y),Z)
% Current number of equations to process: 53
% Current number of ordered equations: 3
% Current number of rules: 60
% New rule produced :
% [61]
% apply(apply(w1,Z),apply(b,apply(apply(b,X),Y))) <->
% apply(X,apply(Y,apply(Z,Z)))
% Current number of equations to process: 53
% Current number of ordered equations: 2
% Current number of rules: 61
% New rule produced :
% [62]
% apply(apply(apply(apply(w1,X),apply(b,b)),Y),Z) <->
% apply(apply(X,X),apply(Y,Z))
% Current number of equations to process: 53
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [63]
% apply(apply(apply(w1,X),apply(b,apply(b,Y))),Z) <->
% apply(Y,apply(apply(X,X),Z))
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [64]
% apply(apply(w1,X),apply(apply(w1,Y),apply(b,b))) <->
% apply(apply(Y,Y),apply(X,X))
% Current number of equations to process: 51
% Current number of ordered equations: 1
% Current number of rules: 64
% New rule produced :
% [65]
% apply(apply(Y,Y),apply(X,X)) <->
% apply(apply(w1,X),apply(apply(w1,Y),apply(b,b)))
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [66]
% apply(Y,apply(Y,apply(X,X))) <->
% apply(apply(w1,X),apply(b,apply(apply(w1,Y),b)))
% Current number of equations to process: 50
% Current number of ordered equations: 1
% Current number of rules: 66
% New rule produced :
% [67]
% apply(apply(w1,X),apply(b,apply(apply(w1,Y),b))) <->
% apply(Y,apply(Y,apply(X,X)))
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [68]
% apply(apply(apply(apply(X,X),X),X),apply(w1,X)) <->
% apply(apply(w1,apply(w1,X)),w1)
% Current number of equations to process: 48
% Current number of ordered equations: 1
% Current number of rules: 68
% New rule produced :
% [69]
% apply(apply(w1,apply(w1,X)),w1) <->
% apply(apply(apply(apply(X,X),X),X),apply(w1,X))
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [70]
% apply(X,apply(apply(Y,Z),Z)) <->
% apply(apply(w1,Z),apply(apply(b,apply(b,X)),Y))
% Current number of equations to process: 45
% Current number of ordered equations: 3
% Current number of rules: 70
% New rule produced :
% [71]
% apply(apply(Y,X),apply(X,Z)) <->
% apply(apply(apply(w1,X),apply(apply(b,b),Y)),Z)
% Current number of equations to process: 45
% Current number of ordered equations: 2
% Current number of rules: 71
% New rule produced :
% [72]
% apply(apply(w1,Z),apply(apply(b,apply(b,X)),Y)) <->
% apply(X,apply(apply(Y,Z),Z))
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [73]
% apply(apply(apply(w1,X),apply(apply(b,b),Y)),Z) <->
% apply(apply(Y,X),apply(X,Z))
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [74]
% apply(apply(w1,Y),apply(apply(b,X),X)) <->
% apply(apply(apply(apply(w1,X),b),Y),Y)
% Current number of equations to process: 67
% Current number of ordered equations: 1
% Current number of rules: 74
% New rule produced :
% [75]
% apply(apply(apply(apply(w1,X),b),Y),Y) <->
% apply(apply(w1,Y),apply(apply(b,X),X))
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [76]
% apply(apply(w1,X),apply(apply(b,apply(w1,Y)),b)) <->
% apply(apply(X,apply(Y,Y)),X)
% Current number of equations to process: 66
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [77]
% apply(apply(X,apply(Y,Y)),X) <->
% apply(apply(w1,X),apply(apply(b,apply(w1,Y)),b))
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [78]
% apply(apply(w1,X),apply(b,apply(w1,X))) -> apply(apply(w1,X),apply(w1,X))
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [79]
% apply(apply(b,apply(b,b)),apply(w1,b)) -> apply(apply(w1,apply(w1,b)),w1)
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [80] apply(apply(w1,apply(w1,b)),apply(b,X)) -> apply(X,apply(b,apply(b,b)))
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [81] apply(apply(w1,w1),apply(w1,b)) -> apply(b,apply(b,w1))
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [82]
% apply(apply(w1,X),apply(apply(w1,b),w1)) <-> apply(apply(b,apply(b,X)),X)
% Current number of equations to process: 161
% Current number of ordered equations: 1
% Current number of rules: 82
% New rule produced :
% [83]
% apply(apply(b,apply(b,X)),X) <-> apply(apply(w1,X),apply(apply(w1,b),w1))
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [84]
% apply(apply(w1,b),apply(w1,apply(X,b))) <->
% apply(apply(X,b),apply(apply(w1,b),X))
% Current number of equations to process: 171
% Current number of ordered equations: 1
% Current number of rules: 84
% New rule produced :
% [85]
% apply(apply(X,b),apply(apply(w1,b),X)) <->
% apply(apply(w1,b),apply(w1,apply(X,b)))
% Current number of equations to process: 171
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [86]
% apply(apply(w1,X),apply(apply(b,X),X)) <->
% apply(apply(w1,b),apply(w1,apply(w1,X)))
% Current number of equations to process: 170
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [87]
% apply(apply(w1,b),apply(w1,apply(w1,X))) <->
% apply(apply(w1,X),apply(apply(b,X),X))
% Current number of equations to process: 170
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [88]
% apply(apply(b,b),apply(apply(w1,b),w1)) ->
% apply(apply(w1,w1),apply(w1,apply(w1,b)))
% Current number of equations to process: 169
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [89]
% apply(apply(w1,apply(w1,X)),apply(w1,b)) <->
% apply(apply(X,apply(X,b)),apply(w1,X))
% Current number of equations to process: 168
% Current number of ordered equations: 1
% Current number of rules: 89
% New rule produced :
% [90]
% apply(apply(X,apply(X,b)),apply(w1,X)) <->
% apply(apply(w1,apply(w1,X)),apply(w1,b))
% Rule
% [79]
% apply(apply(b,apply(b,b)),apply(w1,b)) -> apply(apply(w1,apply(w1,b)),w1)
% collapsed.
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [91] apply(apply(w1,b),apply(w1,apply(w1,b))) -> apply(apply(b,apply(b,b)),b)
% Current number of equations to process: 167
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [92]
% apply(apply(apply(w1,b),apply(w1,X)),apply(X,b)) ->
% apply(apply(w1,apply(X,b)),X)
% Current number of equations to process: 166
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [93]
% apply(X,apply(X,apply(b,Y))) <->
% apply(apply(apply(w1,b),apply(w1,apply(b,X))),Y)
% Current number of equations to process: 165
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [94]
% apply(apply(apply(w1,b),apply(w1,apply(b,X))),Y) <->
% apply(X,apply(X,apply(b,Y)))
% Current number of equations to process: 165
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [95]
% apply(apply(w1,X),apply(apply(b,apply(w1,b)),w1)) <->
% apply(apply(X,apply(X,b)),X)
% Current number of equations to process: 163
% Current number of ordered equations: 1
% Current number of rules: 94
% New rule produced :
% [96]
% apply(apply(X,apply(X,b)),X) <->
% apply(apply(w1,X),apply(apply(b,apply(w1,b)),w1))
% Current number of equations to process: 163
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [97]
% apply(b,apply(b,apply(X,X))) <->
% apply(apply(w1,X),apply(b,apply(apply(w1,b),w1)))
% Current number of equations to process: 162
% Current number of ordered equations: 1
% Current number of rules: 96
% New rule produced :
% [98]
% apply(apply(w1,X),apply(b,apply(apply(w1,b),w1))) <->
% apply(b,apply(b,apply(X,X)))
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [99]
% apply(apply(w1,b),apply(w1,apply(w1,X))) <-> apply(apply(X,apply(X,X)),X)
% Rule
% [91] apply(apply(w1,b),apply(w1,apply(w1,b))) -> apply(apply(b,apply(b,b)),b)
% collapsed.
% Current number of equations to process: 176
% Current number of ordered equations: 1
% Current number of rules: 97
% New rule produced :
% [100]
% apply(apply(X,apply(X,X)),X) <-> apply(apply(w1,b),apply(w1,apply(w1,X)))
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [101]
% apply(X,apply(X,apply(Y,Y))) <->
% apply(apply(w1,Y),apply(apply(w1,apply(b,X)),b))
% Current number of equations to process: 174
% Current number of ordered equations: 3
% Current number of rules: 99
% New rule produced :
% [102]
% apply(apply(b,X),apply(X,Y)) <->
% apply(apply(apply(w1,X),apply(apply(w1,b),w1)),Y)
% Current number of equations to process: 174
% Current number of ordered equations: 2
% Current number of rules: 100
% New rule produced :
% [103]
% apply(apply(w1,Y),apply(apply(w1,apply(b,X)),b)) <->
% apply(X,apply(X,apply(Y,Y)))
% Current number of equations to process: 174
% Current number of ordered equations: 1
% Current number of rules: 101
% New rule produced :
% [104]
% apply(apply(apply(w1,X),apply(apply(w1,b),w1)),Y) <->
% apply(apply(b,X),apply(X,Y))
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [105]
% apply(apply(apply(w1,apply(w1,Y)),b),X) <->
% apply(apply(apply(apply(X,Y),Y),Y),Y)
% Current number of equations to process: 315
% Current number of ordered equations: 1
% Current number of rules: 103
% New rule produced :
% [106]
% apply(apply(apply(apply(X,Y),Y),Y),Y) <->
% apply(apply(apply(w1,apply(w1,Y)),b),X)
% Current number of equations to process: 315
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [107]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(apply(w1,apply(w1,X)),b),w1)
% Current number of equations to process: 352
% Current number of ordered equations: 1
% Current number of rules: 105
% New rule produced :
% [108]
% apply(apply(apply(w1,apply(w1,X)),b),w1) <->
% apply(apply(apply(apply(X,X),X),X),X)
% Current number of equations to process: 352
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [109]
% apply(apply(w1,b),apply(w1,apply(b,b))) ->
% apply(apply(w1,w1),apply(w1,apply(w1,b)))
% Current number of equations to process: 370
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [110]
% apply(apply(w1,apply(b,b)),apply(w1,b)) -> apply(apply(w1,apply(b,b)),b)
% Current number of equations to process: 463
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [111]
% apply(w1,apply(apply(X,X),apply(X,X))) <->
% apply(apply(w1,apply(b,w1)),apply(w1,X))
% Current number of equations to process: 489
% Current number of ordered equations: 1
% Current number of rules: 109
% New rule produced :
% [112]
% apply(apply(w1,apply(b,w1)),apply(w1,X)) <->
% apply(w1,apply(apply(X,X),apply(X,X)))
% Current number of equations to process: 489
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [113]
% apply(apply(w1,apply(b,apply(w1,b))),apply(w1,w1)) ->
% apply(apply(b,b),apply(b,b))
% Current number of equations to process: 649
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [114]
% apply(X,apply(Y,apply(X,apply(Y,Z)))) <->
% apply(apply(apply(w1,apply(apply(b,X),Y)),b),Z)
% Current number of equations to process: 648
% Current number of ordered equations: 1
% Current number of rules: 112
% New rule produced :
% [115]
% apply(apply(apply(w1,apply(apply(b,X),Y)),b),Z) <->
% apply(X,apply(Y,apply(X,apply(Y,Z))))
% Current number of equations to process: 648
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [116]
% apply(X,apply(apply(w1,Y),apply(b,apply(Y,Y)))) ->
% apply(apply(w1,apply(Y,Y)),apply(b,X))
% Current number of equations to process: 647
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [117]
% apply(apply(w1,X),apply(apply(w1,X),w1)) <->
% apply(apply(apply(apply(X,X),X),X),X)
% Current number of equations to process: 726
% Current number of ordered equations: 1
% Current number of rules: 115
% New rule produced :
% [118]
% apply(apply(apply(apply(X,X),X),X),X) <->
% apply(apply(w1,X),apply(apply(w1,X),w1))
% Current number of equations to process: 726
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [119]
% apply(apply(w1,X),apply(Y,apply(X,X))) <->
% apply(apply(apply(w1,apply(w1,X)),b),apply(b,Y))
% Current number of equations to process: 754
% Current number of ordered equations: 1
% Current number of rules: 117
% New rule produced :
% [120]
% apply(apply(apply(w1,apply(w1,X)),b),apply(b,Y)) <->
% apply(apply(w1,X),apply(Y,apply(X,X)))
% Current number of equations to process: 754
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [121]
% apply(Y,apply(apply(X,X),apply(X,X))) <->
% apply(apply(apply(w1,X),apply(b,w1)),apply(b,Y))
% Current number of equations to process: 753
% Current number of ordered equations: 1
% Current number of rules: 119
% New rule produced :
% [122]
% apply(apply(apply(w1,X),apply(b,w1)),apply(b,Y)) <->
% apply(Y,apply(apply(X,X),apply(X,X)))
% Current number of equations to process: 753
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [123]
% apply(apply(X,X),apply(apply(X,X),Y)) <->
% apply(apply(apply(apply(w1,X),apply(b,w1)),b),Y)
% Current number of equations to process: 879
% Current number of ordered equations: 1
% Current number of rules: 121
% New rule produced :
% [124]
% apply(apply(apply(apply(w1,X),apply(b,w1)),b),Y) <->
% apply(apply(X,X),apply(apply(X,X),Y))
% Current number of equations to process: 879
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [125]
% apply(apply(w1,Y),apply(apply(X,X),Y)) <->
% apply(apply(apply(w1,X),apply(b,apply(w1,Y))),Y)
% Current number of equations to process: 878
% Current number of ordered equations: 1
% Current number of rules: 123
% New rule produced :
% [126]
% apply(apply(apply(w1,X),apply(b,apply(w1,Y))),Y) <->
% apply(apply(w1,Y),apply(apply(X,X),Y))
% Current number of equations to process: 878
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [127]
% apply(apply(apply(apply(X,Y),Y),X),apply(w1,Y)) <->
% apply(apply(w1,apply(w1,Y)),apply(w1,X))
% Current number of equations to process: 877
% Current number of ordered equations: 1
% Current number of rules: 125
% New rule produced :
% [128]
% apply(apply(w1,apply(w1,Y)),apply(w1,X)) <->
% apply(apply(apply(apply(X,Y),Y),X),apply(w1,Y))
% Current number of equations to process: 877
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [129]
% apply(apply(apply(w1,X),apply(w1,X)),apply(X,X)) ->
% apply(apply(w1,apply(X,X)),apply(w1,X))
% Current number of equations to process: 876
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [130]
% apply(apply(w1,Y),apply(apply(b,X),apply(Z,Y))) ->
% apply(apply(X,apply(apply(w1,Y),Z)),Y)
% Current number of equations to process: 873
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [131]
% apply(apply(w1,Y),apply(apply(b,X),apply(w1,Z))) <->
% apply(apply(X,apply(apply(Y,Z),Z)),Y)
% Current number of equations to process: 871
% Current number of ordered equations: 3
% Current number of rules: 129
% New rule produced :
% [132]
% apply(apply(w1,Y),apply(apply(b,apply(w1,Z)),X)) <->
% apply(apply(apply(apply(X,Y),Z),Z),Y)
% Current number of equations to process: 871
% Current number of ordered equations: 2
% Current number of rules: 130
% New rule produced :
% [133]
% apply(apply(X,apply(apply(Y,Z),Z)),Y) <->
% apply(apply(w1,Y),apply(apply(b,X),apply(w1,Z)))
% Current number of equations to process: 871
% Current number of ordered equations: 1
% Current number of rules: 131
% New rule produced :
% [134]
% apply(apply(apply(apply(X,Y),Z),Z),Y) <->
% apply(apply(w1,Y),apply(apply(b,apply(w1,Z)),X))
% Current number of equations to process: 871
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [135]
% apply(apply(w1,X),apply(apply(Y,X),X)) <->
% apply(apply(w1,X),apply(apply(b,apply(w1,X)),Y))
% Current number of equations to process: 869
% Current number of ordered equations: 1
% Current number of rules: 133
% New rule produced :
% [136]
% apply(apply(w1,X),apply(apply(b,apply(w1,X)),Y)) <->
% apply(apply(w1,X),apply(apply(Y,X),X))
% Current number of equations to process: 869
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [137]
% apply(apply(w1,Y),apply(apply(b,apply(w1,X)),w1)) <->
% apply(apply(apply(apply(X,Y),Y),X),Y)
% Current number of equations to process: 868
% Current number of ordered equations: 1
% Current number of rules: 135
% New rule produced :
% [138]
% apply(apply(apply(apply(X,Y),Y),X),Y) <->
% apply(apply(w1,Y),apply(apply(b,apply(w1,X)),w1))
% Current number of equations to process: 868
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [139]
% apply(apply(w1,apply(b,X)),apply(b,apply(w1,Y))) <->
% apply(apply(X,apply(apply(b,X),Y)),Y)
% Current number of equations to process: 867
% Current number of ordered equations: 1
% Current number of rules: 137
% New rule produced :
% [140]
% apply(apply(X,apply(apply(b,X),Y)),Y) <->
% apply(apply(w1,apply(b,X)),apply(b,apply(w1,Y)))
% Current number of equations to process: 867
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [141]
% apply(apply(apply(apply(X,X),X),w1),apply(w1,X)) <->
% apply(apply(w1,apply(w1,X)),apply(w1,w1))
% Current number of equations to process: 866
% Current number of ordered equations: 1
% Current number of rules: 139
% New rule produced :
% [142]
% apply(apply(w1,apply(w1,X)),apply(w1,w1)) <->
% apply(apply(apply(apply(X,X),X),w1),apply(w1,X))
% Current number of equations to process: 866
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [143]
% apply(apply(w1,X),apply(apply(b,apply(w1,w1)),w1)) <->
% apply(apply(apply(apply(X,X),X),w1),X)
% Current number of equations to process: 865
% Current number of ordered equations: 1
% Current number of rules: 141
% New rule produced :
% [144]
% apply(apply(apply(apply(X,X),X),w1),X) <->
% apply(apply(w1,X),apply(apply(b,apply(w1,w1)),w1))
% Current number of equations to process: 865
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [145]
% apply(apply(w1,X),apply(apply(X,X),X)) <->
% apply(apply(w1,X),apply(apply(b,apply(w1,X)),w1))
% Current number of equations to process: 864
% Current number of ordered equations: 1
% Current number of rules: 143
% New rule produced :
% [146]
% apply(apply(w1,X),apply(apply(b,apply(w1,X)),w1)) <->
% apply(apply(w1,X),apply(apply(X,X),X))
% Current number of equations to process: 864
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [147]
% apply(apply(w1,X),apply(apply(b,apply(w1,X)),X)) ->
% apply(apply(w1,X),apply(apply(w1,X),X))
% Current number of equations to process: 862
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [148]
% apply(apply(w1,X),apply(apply(w1,X),apply(X,X))) <->
% apply(apply(w1,apply(b,apply(w1,X))),w1)
% Current number of equations to process: 861
% Current number of ordered equations: 1
% Current number of rules: 146
% New rule produced :
% [149]
% apply(apply(w1,apply(b,apply(w1,X))),w1) <->
% apply(apply(w1,X),apply(apply(w1,X),apply(X,X)))
% Current number of equations to process: 861
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [150]
% apply(apply(apply(apply(w1,apply(b,b)),w1),X),Y) ->
% apply(b,apply(apply(b,b),apply(X,Y)))
% Current number of equations to process: 860
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [151]
% apply(b,apply(apply(b,b),apply(X,X))) <->
% apply(apply(w1,X),apply(apply(w1,apply(b,b)),w1))
% Current number of equations to process: 859
% Current number of ordered equations: 1
% Current number of rules: 149
% New rule produced :
% [152]
% apply(apply(w1,X),apply(apply(w1,apply(b,b)),w1)) <->
% apply(b,apply(apply(b,b),apply(X,X)))
% Current number of equations to process: 859
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [153]
% apply(apply(X,apply(apply(b,X),apply(b,X))),w1) ->
% apply(apply(w1,w1),apply(w1,apply(b,X)))
% Current number of equations to process: 857
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [154]
% apply(X,apply(Y,apply(X,apply(Y,b)))) <->
% apply(apply(w1,b),apply(w1,apply(apply(b,X),Y)))
% Current number of equations to process: 850
% Current number of ordered equations: 1
% Current number of rules: 152
% New rule produced :
% [155]
% apply(apply(w1,b),apply(w1,apply(apply(b,X),Y))) <->
% apply(X,apply(Y,apply(X,apply(Y,b))))
% Current number of equations to process: 850
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [156]
% apply(apply(w1,apply(w1,b)),apply(w1,apply(w1,b))) ->
% apply(apply(b,b),apply(b,apply(b,b)))
% Current number of equations to process: 849
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [157]
% apply(apply(w1,b),apply(apply(w1,X),apply(b,w1))) <->
% apply(apply(X,X),apply(apply(X,X),b))
% Current number of equations to process: 848
% Current number of ordered equations: 1
% Current number of rules: 155
% New rule produced :
% [158]
% apply(apply(X,X),apply(apply(X,X),b)) <->
% apply(apply(w1,b),apply(apply(w1,X),apply(b,w1)))
% Current number of equations to process: 848
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [159]
% apply(apply(apply(w1,apply(apply(w1,b),w1)),b),X) ->
% apply(b,apply(b,apply(b,apply(b,X))))
% Current number of equations to process: 846
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [160]
% apply(apply(w1,Y),apply(apply(apply(w1,X),b),Y)) <->
% apply(apply(apply(X,apply(X,Y)),Y),Y)
% Current number of equations to process: 845
% Current number of ordered equations: 1
% Current number of rules: 158
% New rule produced :
% [161]
% apply(apply(apply(X,apply(X,Y)),Y),Y) <->
% apply(apply(w1,Y),apply(apply(apply(w1,X),b),Y))
% Current number of equations to process: 845
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced :
% [162]
% apply(apply(w1,b),apply(apply(w1,apply(w1,X)),b)) <->
% apply(apply(apply(X,apply(X,X)),X),b)
% Current number of equations to process: 844
% Current number of ordered equations: 1
% Current number of rules: 160
% New rule produced :
% [163]
% apply(apply(apply(X,apply(X,X)),X),b) <->
% apply(apply(w1,b),apply(apply(w1,apply(w1,X)),b))
% Current number of equations to process: 844
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [164]
% apply(X,apply(apply(w1,X),apply(b,X))) <->
% apply(apply(w1,X),apply(b,apply(apply(w1,X),b)))
% Current number of equations to process: 843
% Current number of ordered equations: 1
% Current number of rules: 162
% New rule produced :
% [165]
% apply(apply(w1,X),apply(b,apply(apply(w1,X),b))) <->
% apply(X,apply(apply(w1,X),apply(b,X)))
% Current number of equations to process: 843
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [166]
% apply(apply(X,X),apply(apply(w1,X),X)) <->
% apply(apply(apply(apply(w1,X),apply(b,w1)),b),X)
% Current number of equations to process: 841
% Current number of ordered equations: 1
% Current number of rules: 164
% New rule produced :
% [167]
% apply(apply(apply(apply(w1,X),apply(b,w1)),b),X) <->
% apply(apply(X,X),apply(apply(w1,X),X))
% Current number of equations to process: 841
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [168]
% apply(apply(X,X),apply(apply(w1,X),w1)) <->
% apply(apply(apply(apply(w1,X),apply(b,w1)),b),X)
% Current number of equations to process: 839
% Current number of ordered equations: 1
% Current number of rules: 166
% New rule produced :
% [169]
% apply(apply(apply(apply(w1,X),apply(b,w1)),b),X) <->
% apply(apply(X,X),apply(apply(w1,X),w1))
% Current number of equations to process: 839
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [170]
% apply(apply(w1,Y),apply(w1,apply(X,X))) <->
% apply(apply(apply(apply(w1,X),apply(b,w1)),Y),Y)
% Current number of equations to process: 836
% Current number of ordered equations: 1
% Current number of rules: 168
% New rule produced :
% [171]
% apply(apply(apply(apply(w1,X),apply(b,w1)),Y),Y) <->
% apply(apply(w1,Y),apply(w1,apply(X,X)))
% Current number of equations to process: 836
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [172]
% apply(Y,apply(apply(w1,X),apply(b,Y))) <->
% apply(apply(w1,X),apply(b,apply(apply(w1,Y),b)))
% Rule
% [164]
% apply(X,apply(apply(w1,X),apply(b,X))) <->
% apply(apply(w1,X),apply(b,apply(apply(w1,X),b))) collapsed.
% Current number of equations to process: 835
% Current number of ordered equations: 1
% Current number of rules: 169
% New rule produced :
% [173]
% apply(apply(w1,X),apply(b,apply(apply(w1,Y),b))) <->
% apply(Y,apply(apply(w1,X),apply(b,Y)))
% Rule
% [165]
% apply(apply(w1,X),apply(b,apply(apply(w1,X),b))) <->
% apply(X,apply(apply(w1,X),apply(b,X))) collapsed.
% Current number of equations to process: 835
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [174]
% apply(apply(X,X),apply(apply(b,b),Y)) <->
% apply(apply(apply(w1,apply(b,b)),apply(w1,X)),Y)
% Current number of equations to process: 834
% Current number of ordered equations: 1
% Current number of rules: 170
% New rule produced :
% [175]
% apply(apply(apply(w1,apply(b,b)),apply(w1,X)),Y) <->
% apply(apply(X,X),apply(apply(b,b),Y))
% Current number of equations to process: 834
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [176]
% apply(apply(w1,w1),apply(w1,apply(apply(b,apply(b,X)),w1))) ->
% apply(apply(strong_fixed_point,X),w1)
% Current number of equations to process: 833
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [177] apply(X,apply(strong_fixed_point,X)) -> apply(strong_fixed_point,X)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 833
% Current number of ordered equations: 0
% Current number of rules: 173
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [1]
% apply(apply(Y,X),X) <-> apply(apply(w1,X),Y); trace = in the starting set
% [2] apply(apply(w1,X),Y) <-> apply(apply(Y,X),X); trace = in the starting set
% [3] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z)); trace = in the starting set
% [4] apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)))
% -> strong_fixed_point; trace = in the starting set
% [5] apply(apply(w1,X),w1) <-> apply(apply(X,X),X); trace = Cp of 2 and 1
% [51] apply(apply(w1,apply(apply(b,apply(b,X)),w1)),w1) ->
% apply(strong_fixed_point,X); trace = Cp of 4 and 3
% [177] apply(X,apply(strong_fixed_point,X)) -> apply(strong_fixed_point,X); trace = Cp of 51 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 1.710000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------