TSTP Solution File: COL042-8 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL042-8 : TPTP v6.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n123.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 1.26s
% Output : Refutation 1.26s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL042-8 : TPTP v6.0.0. Released v2.1.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n123.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 19:26:18 CDT 2014
% % CPUTime : 1.26
% Processing problem /tmp/CiME_30251_n123.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(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),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(apply(b,apply(w1,w1)),
% apply(apply(b,apply(b,w1)),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: 0
% Current number of ordered equations: 3
% 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(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),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(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,apply(apply(b,apply(b,b)),w1)),w1) ->
% apply(strong_fixed_point,b)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17] apply(apply(w1,w1),apply(w1,X)) <-> apply(apply(apply(X,X),X),w1)
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [18] apply(apply(apply(X,X),X),w1) <-> apply(apply(w1,w1),apply(w1,X))
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19] apply(apply(w1,X),apply(w1,X)) <-> apply(apply(w1,X),apply(X,X))
% Current number of equations to process: 4
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [20] apply(apply(w1,X),apply(X,X)) <-> apply(apply(w1,X),apply(w1,X))
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% apply(apply(w1,apply(apply(b,apply(b,X)),w1)),w1) ->
% apply(strong_fixed_point,X)
% Rule
% [16]
% apply(apply(w1,apply(apply(b,apply(b,b)),w1)),w1) ->
% apply(strong_fixed_point,b) collapsed.
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [22] apply(X,apply(apply(b,X),apply(b,X))) <-> apply(apply(w1,apply(b,X)),w1)
% Current number of equations to process: 9
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [23] apply(apply(w1,apply(b,X)),w1) <-> apply(X,apply(apply(b,X),apply(b,X)))
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [24] apply(apply(w1,X),apply(b,apply(w1,Y))) <-> apply(apply(apply(X,X),Y),Y)
% Current number of equations to process: 22
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [25] apply(apply(apply(X,X),Y),Y) <-> apply(apply(w1,X),apply(b,apply(w1,Y)))
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26] apply(X,apply(X,b)) <-> apply(apply(w1,b),apply(w1,X))
% Current number of equations to process: 31
% Current number of ordered equations: 2
% Current number of rules: 25
% New rule produced :
% [27] apply(apply(w1,b),apply(w1,X)) <-> apply(X,apply(X,b))
% Current number of equations to process: 31
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [28] apply(apply(apply(w1,b),w1),X) -> apply(b,apply(b,X))
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [29] apply(apply(w1,Y),apply(apply(w1,X),b)) <-> apply(apply(X,apply(X,Y)),Y)
% Current number of equations to process: 30
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced :
% [30] apply(apply(X,apply(X,Y)),Y) <-> apply(apply(w1,Y),apply(apply(w1,X),b))
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [31]
% apply(apply(apply(w1,X),b),apply(X,Y)) ->
% apply(X,apply(apply(apply(w1,X),b),Y))
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [32]
% apply(apply(X,Y),apply(apply(w1,Y),X)) <->
% apply(apply(apply(w1,apply(X,Y)),b),Y)
% Current number of equations to process: 34
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [33]
% apply(apply(apply(w1,apply(X,Y)),b),Y) <->
% apply(apply(X,Y),apply(apply(w1,Y),X))
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [34]
% apply(apply(w1,X),apply(apply(Y,X),X)) <->
% apply(apply(apply(w1,apply(w1,X)),b),Y)
% Current number of equations to process: 33
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [35]
% apply(apply(apply(w1,apply(w1,X)),b),Y) <->
% apply(apply(w1,X),apply(apply(Y,X),X))
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [36]
% apply(apply(w1,X),apply(apply(X,X),X)) <->
% apply(apply(apply(w1,apply(w1,X)),b),w1)
% Current number of equations to process: 32
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [37]
% apply(apply(apply(w1,apply(w1,X)),b),w1) <->
% apply(apply(w1,X),apply(apply(X,X),X))
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [38]
% apply(apply(apply(w1,apply(X,X)),b),X) ->
% apply(apply(X,X),apply(apply(w1,X),w1))
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [39]
% apply(X,apply(apply(w1,Y),apply(Y,Y))) <->
% apply(apply(w1,apply(w1,Y)),apply(b,X))
% Current number of equations to process: 29
% Current number of ordered equations: 3
% Current number of rules: 38
% New rule produced :
% [40]
% apply(apply(Y,apply(X,X)),apply(X,X)) <->
% apply(apply(apply(w1,X),apply(b,w1)),Y)
% Current number of equations to process: 29
% Current number of ordered equations: 2
% Current number of rules: 39
% New rule produced :
% [41]
% apply(apply(w1,apply(w1,Y)),apply(b,X)) <->
% apply(X,apply(apply(w1,Y),apply(Y,Y)))
% Current number of equations to process: 29
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced :
% [42]
% apply(apply(apply(w1,X),apply(b,w1)),Y) <->
% apply(apply(Y,apply(X,X)),apply(X,X))
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [43]
% apply(X,apply(apply(w1,Y),apply(b,X))) <->
% apply(apply(apply(w1,X),b),apply(Y,Y))
% Current number of equations to process: 28
% Current number of ordered equations: 1
% Current number of rules: 42
% New rule produced :
% [44]
% apply(apply(apply(w1,X),b),apply(Y,Y)) <->
% apply(X,apply(apply(w1,Y),apply(b,X)))
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [45]
% apply(apply(w1,apply(b,X)),apply(w1,Y)) <->
% apply(apply(X,apply(Y,Y)),apply(b,X))
% Current number of equations to process: 27
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced :
% [46]
% apply(apply(X,apply(Y,Y)),apply(b,X)) <->
% apply(apply(w1,apply(b,X)),apply(w1,Y))
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [47]
% apply(X,apply(apply(apply(Y,Y),Y),Y)) <->
% apply(apply(w1,apply(w1,Y)),apply(b,X))
% Current number of equations to process: 43
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced :
% [48]
% apply(apply(w1,apply(w1,Y)),apply(b,X)) <->
% apply(X,apply(apply(apply(Y,Y),Y),Y))
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [49]
% apply(apply(w1,X),apply(apply(w1,Y),X)) <->
% apply(apply(apply(apply(X,Y),Y),X),X)
% Current number of equations to process: 42
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [50]
% apply(apply(apply(apply(X,Y),Y),X),X) <->
% apply(apply(w1,X),apply(apply(w1,Y),X))
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [51]
% apply(apply(w1,X),apply(apply(b,w1),Y)) <->
% apply(apply(X,apply(Y,X)),apply(Y,X))
% Current number of equations to process: 61
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [52]
% apply(apply(X,apply(Y,X)),apply(Y,X)) <->
% apply(apply(w1,X),apply(apply(b,w1),Y))
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [53]
% apply(apply(apply(w1,X),apply(X,X)),apply(w1,X)) ->
% apply(apply(w1,apply(w1,X)),w1)
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [54]
% apply(apply(apply(apply(w1,X),b),Y),apply(X,Y)) ->
% apply(apply(w1,apply(X,Y)),X)
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [55]
% apply(X,apply(X,apply(Y,Z))) <->
% apply(apply(apply(apply(w1,apply(b,X)),b),Y),Z)
% Current number of equations to process: 57
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [56]
% apply(apply(apply(apply(w1,apply(b,X)),b),Y),Z) <->
% apply(X,apply(X,apply(Y,Z)))
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [57]
% apply(apply(w1,X),apply(b,apply(Y,apply(X,X)))) ->
% apply(apply(w1,apply(X,X)),Y)
% Current number of equations to process: 55
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [58]
% apply(apply(apply(w1,X),apply(b,Y)),apply(X,X)) ->
% apply(apply(w1,apply(X,X)),Y)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [59]
% apply(X,apply(Y,apply(Z,Z))) <->
% apply(apply(w1,Z),apply(b,apply(apply(b,X),Y)))
% Current number of equations to process: 52
% Current number of ordered equations: 5
% Current number of rules: 58
% New rule produced :
% [60]
% apply(Y,apply(apply(X,X),Z)) <->
% apply(apply(apply(w1,X),apply(b,apply(b,Y))),Z)
% Current number of equations to process: 52
% Current number of ordered equations: 4
% Current number of rules: 59
% New rule produced :
% [61]
% apply(apply(X,X),apply(Y,Z)) <->
% apply(apply(apply(apply(w1,X),apply(b,b)),Y),Z)
% Current number of equations to process: 52
% Current number of ordered equations: 3
% Current number of rules: 60
% New rule produced :
% [62]
% apply(apply(w1,Z),apply(b,apply(apply(b,X),Y))) <->
% apply(X,apply(Y,apply(Z,Z)))
% Current number of equations to process: 52
% Current number of ordered equations: 2
% Current number of rules: 61
% New rule produced :
% [63]
% apply(apply(apply(apply(w1,X),apply(b,b)),Y),Z) <->
% apply(apply(X,X),apply(Y,Z))
% Current number of equations to process: 52
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [64]
% apply(apply(apply(w1,X),apply(b,apply(b,Y))),Z) <->
% apply(Y,apply(apply(X,X),Z))
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [65]
% apply(apply(w1,X),apply(apply(w1,Y),apply(b,b))) <->
% apply(apply(Y,Y),apply(X,X))
% Current number of equations to process: 50
% Current number of ordered equations: 1
% Current number of rules: 64
% New rule produced :
% [66]
% apply(apply(Y,Y),apply(X,X)) <->
% apply(apply(w1,X),apply(apply(w1,Y),apply(b,b)))
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [67]
% apply(Y,apply(Y,apply(X,X))) <->
% apply(apply(w1,X),apply(b,apply(apply(w1,Y),b)))
% Current number of equations to process: 49
% Current number of ordered equations: 1
% Current number of rules: 66
% New rule produced :
% [68]
% apply(apply(w1,X),apply(b,apply(apply(w1,Y),b))) <->
% apply(Y,apply(Y,apply(X,X)))
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [69]
% apply(apply(apply(apply(X,X),X),X),apply(w1,X)) <->
% apply(apply(w1,apply(w1,X)),w1)
% Current number of equations to process: 47
% Current number of ordered equations: 1
% Current number of rules: 68
% New rule produced :
% [70]
% apply(apply(w1,apply(w1,X)),w1) <->
% apply(apply(apply(apply(X,X),X),X),apply(w1,X))
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [71]
% apply(X,apply(apply(Y,Z),Z)) <->
% apply(apply(w1,Z),apply(apply(b,apply(b,X)),Y))
% Current number of equations to process: 44
% Current number of ordered equations: 3
% Current number of rules: 70
% New rule produced :
% [72]
% apply(apply(Y,X),apply(X,Z)) <->
% apply(apply(apply(w1,X),apply(apply(b,b),Y)),Z)
% Current number of equations to process: 44
% Current number of ordered equations: 2
% Current number of rules: 71
% New rule produced :
% [73]
% apply(apply(w1,Z),apply(apply(b,apply(b,X)),Y)) <->
% apply(X,apply(apply(Y,Z),Z))
% Current number of equations to process: 44
% Current number of ordered equations: 1
% Current number of rules: 72
% New rule produced :
% [74]
% apply(apply(apply(w1,X),apply(apply(b,b),Y)),Z) <->
% apply(apply(Y,X),apply(X,Z))
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [75]
% apply(apply(w1,Y),apply(apply(b,X),X)) <->
% apply(apply(apply(apply(w1,X),b),Y),Y)
% Current number of equations to process: 65
% Current number of ordered equations: 1
% Current number of rules: 74
% New rule produced :
% [76]
% apply(apply(apply(apply(w1,X),b),Y),Y) <->
% apply(apply(w1,Y),apply(apply(b,X),X))
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [77]
% apply(apply(w1,X),apply(apply(b,apply(w1,Y)),b)) <->
% apply(apply(X,apply(Y,Y)),X)
% Current number of equations to process: 64
% Current number of ordered equations: 1
% Current number of rules: 76
% New rule produced :
% [78]
% apply(apply(X,apply(Y,Y)),X) <->
% apply(apply(w1,X),apply(apply(b,apply(w1,Y)),b))
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [79]
% apply(apply(w1,X),apply(b,apply(w1,X))) -> apply(apply(w1,X),apply(w1,X))
% Current number of equations to process: 93
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [80] 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: 93
% Current number of ordered equations: 0
% Current number of rules: 79
% 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(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)
% -> 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
% [21] apply(apply(w1,apply(apply(b,apply(b,X)),w1)),w1) ->
% apply(strong_fixed_point,X); trace = Cp of 4 and 3
% [80] apply(X,apply(strong_fixed_point,X)) -> apply(strong_fixed_point,X); trace = Cp of 21 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.150000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------