%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL008-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n053.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 00:19:39 EDT 2014
% Result : Unsatisfiable 1.22s
% Output : Refutation 1.22s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL008-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n053.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 17:02:43 CDT 2014
% % CPUTime : 1.22
% Processing problem /tmp/CiME_34259_n053.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " combinator,m,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(m,X) = apply(X,X);
% ";
%
% let s1 = status F "
% combinator lr_lex;
% m lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
%
% let p1 = precedence F "
% apply > b > m > combinator";
%
% let s2 = status F "
% combinator mul;
% m mul;
% apply mul;
% b mul;
% ";
%
% let p2 = precedence F "
% apply > b = m = combinator";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " Y = apply(combinator,Y);"
% ;
% (*
% 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(m,X) = apply(X,X) } (2 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [combinator] = 1;
% [m] = 2;
% [b] = 3;
% [apply](x1,x2) = 1 + x1 + x2;
% Chosen ordering : RPO
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { Y = apply(combinator,Y) } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] (eq)(Y,apply(combinator,Y)) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 1
% New rule produced : [2] (eq)(X,X) -> (true)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 2
% New rule produced : [3] apply(X,X) <-> apply(m,X)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 3
% New rule produced : [4] apply(m,X) <-> apply(X,X)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 4
% New rule produced : [5] apply(X,apply(Y,Z)) <-> apply(apply(apply(b,X),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 5
% New rule produced : [6] 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: 6
% New rule produced : [7] (eq)(combinator,apply(m,combinator)) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8] (eq)(apply(X,Y),apply(apply(apply(b,combinator),X),Y)) -> (false)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9] (eq)(apply(m,X),apply(apply(apply(b,combinator),X),X)) -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11]
% (eq)(apply(apply(b,combinator),X),apply(apply(m,apply(b,combinator)),X)) ->
% (false)
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(m,apply(apply(b,combinator),X)))
% -> (false)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% (eq)(apply(m,apply(b,combinator)),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Z))
% -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (false)
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (false)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% (eq)(apply(apply(apply(b,m),X),Y),apply(apply(apply(b,combinator),apply(X,Y)),
% apply(X,Y))) -> (false)
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(b,m),b),combinator),X))
% -> (false)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),apply(m,apply(apply(b,combinator),combinator)))
% -> (false)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(m,apply(apply(b,combinator),b)))
% -> (false)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Z))
% -> (false)
% Current number of equations to process: 22
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [23]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),Z))
% -> (false)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(apply(b,combinator),m),
% apply(X,Y))) -> (false)
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(apply(m,
% apply(b,combinator)),
% apply(X,Y))) ->
% (false)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(apply(apply(b,m),
% apply(b,combinator)),X))
% -> (false)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (false)
% Current number of equations to process: 25
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [28]
% (eq)(apply(apply(apply(m,b),X),Y),apply(apply(apply(b,combinator),b),
% apply(X,Y))) -> (false)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (false)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% (eq)(apply(apply(m,apply(b,X)),Y),apply(apply(apply(b,combinator),X),
% apply(apply(b,X),Y))) -> (false)
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(combinator,apply(X,apply(Y,Z)))) ->
% (false)
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32]
% (eq)(apply(apply(apply(b,m),b),combinator),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(b,m),b),combinator),
% apply(b,combinator))) -> (false)
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [34]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),b),combinator))
% -> (false)
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [35]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Y))
% -> (false)
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [36]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),m)),Y))
% -> (false)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [37]
% (eq)(apply(apply(apply(b,b),X),Y),apply(apply(apply(b,combinator),apply(
% apply(m,b),X)),Y))
% -> (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [38]
% (eq)(apply(apply(b,combinator),apply(X,Y)),apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),X),Y))
% -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [39]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),b),combinator),X),
% apply(m,apply(apply(b,combinator),X))) -> (false)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [40]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (false)
% Current number of equations to process: 31
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced :
% [41]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),V_3),apply(apply(apply(b,combinator),
% apply(X,Y)),
% apply(Z,V_3))) ->
% (false)
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [42]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),V_3),apply(apply(apply(b,combinator),X),
% apply(Y,apply(Z,V_3))))
% -> (false)
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [43]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(apply(b,combinator),
% apply(apply(b,m),X)),Y))
% -> (false)
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [44]
% (eq)(apply(X,apply(Y,Z)),apply(combinator,apply(apply(apply(b,X),Y),Z))) ->
% (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [45]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(m,apply(X,Y)))) ->
% (false)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [46]
% (eq)(apply(apply(apply(b,m),X),X),apply(apply(apply(b,combinator),apply(m,X)),
% apply(X,X))) -> (false)
% Current number of equations to process: 42
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced :
% [47]
% (eq)(apply(apply(apply(b,m),X),X),apply(apply(apply(b,combinator),apply(X,X)),
% apply(m,X))) -> (false)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [48]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),apply(m,X)),
% apply(X,X))) -> (false)
% Current number of equations to process: 40
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [49]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),apply(X,X)),
% apply(m,X))) -> (false)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [50]
% (eq)(apply(m,apply(X,Y)),apply(combinator,apply(apply(apply(apply(apply(b,b),X),Y),X),Y)))
% -> (false)
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [51]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(apply(apply(b,m),X),Y)))
% -> (false)
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [52]
% (eq)(apply(apply(apply(b,m),X),Y),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (false)
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [53]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),apply(apply(apply(b,m),
% apply(b,combinator)),combinator))
% -> (false)
% Current number of equations to process: 49
% Current number of ordered equations: 1
% Current number of rules: 53
% New rule produced :
% [54]
% (eq)(apply(apply(apply(apply(b,m),b),combinator),combinator),apply(m,
% apply(apply(b,combinator),combinator)))
% -> (false)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [55]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(apply(apply(b,m),
% apply(b,combinator)),b))
% -> (false)
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [56]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),Y),Z))
% -> (false)
% Current number of equations to process: 57
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [57]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Y))
% -> (false)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [58]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),m),Y))
% -> (false)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [59]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(apply(
% apply(
% apply(b,m),b),combinator),
% apply(X,Y))) ->
% (false)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [60]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),m),b),b),combinator),b),
% apply(m,apply(apply(b,combinator),b))) -> (false)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [61]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(X,Y))) -> (false)
% Current number of equations to process: 52
% Current number of ordered equations: 1
% Current number of rules: 61
% New rule produced :
% [62]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),
% apply(X,Y)),X),Y)) -> (false)
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [63]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),apply(b,combinator)),
% apply(apply(apply(b,m),m),apply(b,combinator))) -> (false)
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [64]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,V_3)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,Y),Z),V_3)))
% -> (false)
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [65]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(b,combinator),apply(apply(
% apply(
% apply(b,b),X),Y),X)),Y))
% -> (false)
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [66]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Z)) -> (false)
% Current number of equations to process: 46
% Current number of ordered equations: 1
% Current number of rules: 66
% New rule produced :
% [67]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),V_3)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,V_3))) -> (false)
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [68]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),Z))
% -> (false)
% Current number of equations to process: 56
% Current number of ordered equations: 1
% Current number of rules: 68
% New rule produced :
% [69]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),Y))
% -> (false)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [70]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),Y))
% -> (false)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [71]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),apply(apply(apply(b,combinator),m),
% apply(m,X))) -> (false)
% Current number of equations to process: 65
% Current number of ordered equations: 1
% Current number of rules: 71
% New rule produced :
% [72]
% (eq)(apply(apply(apply(apply(apply(m,b),X),Y),X),Y),apply(apply(apply(b,combinator),m),
% apply(X,Y))) -> (false)
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [73]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),apply(apply(apply(b,combinator),m),
% apply(X,X))) -> (false)
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [74]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),apply(apply(m,
% apply(b,combinator)),
% apply(m,X))) ->
% (false)
% Current number of equations to process: 75
% Current number of ordered equations: 1
% Current number of rules: 74
% New rule produced :
% [75]
% (eq)(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),apply(apply(m,
% apply(b,combinator)),
% apply(X,Y))) ->
% (false)
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [76]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),apply(apply(m,
% apply(b,combinator)),
% apply(X,X))) ->
% (false)
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 76
% Rule [76]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),apply(
% apply(m,
% apply(b,combinator)),
% apply(X,X)))
% -> (false) is composed into [76]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),
% apply(apply(m,apply(b,combinator)),apply(X,X)))
% -> (true)
% Rule [75]
% (eq)(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),apply(
% apply(m,
% apply(b,combinator)),
% apply(X,Y)))
% -> (false) is composed into [75]
% (eq)(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),
% apply(apply(m,apply(b,combinator)),apply(X,Y)))
% -> (true)
% Rule [74]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),apply(
% apply(m,
% apply(b,combinator)),
% apply(m,X)))
% -> (false) is composed into [74]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),
% apply(apply(m,apply(b,combinator)),apply(m,X)))
% -> (true)
% Rule [73]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),apply(apply(
% apply(b,combinator),m),
% apply(X,X))) ->
% (false) is composed into [73]
% (eq)(apply(apply(apply(apply(apply(b,b),m),X),m),X),
% apply(apply(apply(b,combinator),m),apply(X,X)))
% -> (true)
% Rule [72]
% (eq)(apply(apply(apply(apply(apply(m,b),X),Y),X),Y),apply(apply(
% apply(b,combinator),m),
% apply(X,Y))) ->
% (false) is composed into [72]
% (eq)(apply(apply(apply(apply(apply(m,b),X),Y),X),Y),
% apply(apply(apply(b,combinator),m),apply(X,Y)))
% -> (true)
% Rule [71]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),apply(apply(
% apply(b,combinator),m),
% apply(m,X))) ->
% (false) is composed into [71]
% (eq)(apply(apply(apply(apply(apply(b,b),X),X),X),X),
% apply(apply(apply(b,combinator),m),apply(m,X)))
% -> (true)
% Rule [70]
% (eq)(apply(apply(X,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),m),X),Y))
% -> (false) is composed into [70]
% (eq)(apply(apply(X,X),Y),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),m),X),Y))
% -> (true)
% Rule [69]
% (eq)(apply(apply(m,X),Y),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),X),Y))
% -> (false) is composed into [69]
% (eq)(apply(apply(m,X),Y),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),X),X),Y))
% -> (true)
% Rule [68]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(m,b),b),combinator),X),Y),Z))
% -> (false) is composed into [68]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(
% apply(
% apply(m,b),b),combinator),X),Y),Z))
% -> (true)
% Rule [67]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),V_3)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,V_3))) -> (false) is composed into
% [67]
% (eq)(apply(X,apply(apply(apply(b,Y),Z),V_3)),apply(apply(apply(b,combinator),
% apply(apply(b,X),Y)),
% apply(Z,V_3))) -> (true)
% Rule [66]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Z)) -> (false) is composed into
% [66]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),
% apply(b,X)),Y),Z)) -> (true)
% Rule [65]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(b,combinator),apply(apply(
% apply(
% apply(b,b),X),Y),X)),Y))
% -> (false) is composed into [65]
% (eq)(apply(m,apply(X,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(
% apply(
% apply(b,b),X),Y),X)),Y))
% -> (true)
% Rule [64]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,V_3)),apply(apply(apply(b,combinator),X),
% apply(apply(apply(b,Y),Z),V_3)))
% -> (false) is composed into [64]
% (eq)(apply(apply(apply(b,X),Y),apply(Z,V_3)),
% apply(apply(apply(b,combinator),X),apply(
% apply(
% apply(b,Y),Z),V_3)))
% -> (true)
% Rule [63]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),apply(b,combinator)),
% apply(apply(apply(b,m),m),apply(b,combinator))) -> (false) is composed into
% [63]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),m),apply(b,combinator)),
% apply(apply(apply(b,m),m),apply(b,combinator))) -> (true)
% Rule [62]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),
% apply(X,Y)),X),Y)) -> (false) is composed into
% [62]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),
% apply(X,Y)),X),Y)) -> (true)
% Rule [61]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(X,Y))) -> (false) is composed into
% [61]
% (eq)(apply(m,apply(X,Y)),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(X,Y))) -> (true)
% Rule [60]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),m),b),b),combinator),b),
% apply(m,apply(apply(b,combinator),b))) -> (false) is composed into
% [60]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),m),b),b),combinator),b),
% apply(m,apply(apply(b,combinator),b))) -> (true)
% Rule [59]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(
% apply(
% apply(
% apply(b,m),b),combinator),
% apply(X,Y)))
% -> (false) is composed into [59]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(apply(apply(apply(b,m),b),combinator),
% apply(X,Y))) -> (true)
% Rule [58]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),m),Y))
% -> (false) is composed into [58]
% (eq)(apply(X,apply(Y,Y)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),m),Y))
% -> (true)
% Rule [57]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Y))
% -> (false) is composed into [57]
% (eq)(apply(X,apply(m,Y)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Y))
% -> (true)
% Rule [56]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(m,b),apply(b,combinator)),X),Y),Z))
% -> (false) is composed into [56]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(
% apply(
% apply(m,b),
% apply(b,combinator)),X),Y),Z))
% -> (true)
% Rule [55]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(apply(
% apply(b,m),
% apply(b,combinator)),b))
% -> (false) is composed into [55]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),
% apply(apply(apply(b,m),apply(b,combinator)),b))
% -> (true)
% Rule [54]
% (eq)(apply(apply(apply(apply(b,m),b),combinator),combinator),apply(m,
% apply(
% apply(b,combinator),combinator)))
% -> (false) is composed into [54]
% (eq)(apply(apply(apply(apply(b,m),b),combinator),combinator),
% apply(m,apply(apply(b,combinator),combinator)))
% -> (true)
% Rule [53]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),apply(apply(
% apply(b,m),
% apply(b,combinator)),combinator))
% -> (false) is composed into [53]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),
% apply(apply(apply(b,m),apply(b,combinator)),combinator))
% -> (true)
% Rule [52]
% (eq)(apply(apply(apply(b,m),X),Y),apply(combinator,apply(apply(apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (false) is composed into [52]
% (eq)(apply(apply(apply(b,m),X),Y),apply(combinator,
% apply(
% apply(
% apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (true)
% Rule [51]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(apply(
% apply(b,m),X),Y)))
% -> (false) is composed into [51]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(combinator,apply(apply(apply(b,m),X),Y)))
% -> (true)
% Rule [50]
% (eq)(apply(m,apply(X,Y)),apply(combinator,apply(apply(apply(apply(
% apply(b,b),X),Y),X),Y)))
% -> (false) is composed into [50]
% (eq)(apply(m,apply(X,Y)),apply(combinator,
% apply(apply(
% apply(
% apply(
% apply(b,b),X),Y),X),Y)))
% -> (true)
% Rule [49]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),
% apply(X,X)),apply(m,X))) ->
% (false) is composed into [49]
% (eq)(apply(apply(apply(b,m),m),X),apply(
% apply(
% apply(b,combinator),
% apply(X,X)),
% apply(m,X)))
% -> (true)
% Rule [48]
% (eq)(apply(apply(apply(b,m),m),X),apply(apply(apply(b,combinator),
% apply(m,X)),apply(X,X))) ->
% (false) is composed into [48]
% (eq)(apply(apply(apply(b,m),m),X),apply(
% apply(
% apply(b,combinator),
% apply(m,X)),
% apply(X,X)))
% -> (true)
% Rule [47]
% (eq)(apply(apply(apply(b,m),X),X),apply(apply(apply(b,combinator),
% apply(X,X)),apply(m,X))) ->
% (false) is composed into [47]
% (eq)(apply(apply(apply(b,m),X),X),apply(
% apply(
% apply(b,combinator),
% apply(X,X)),
% apply(m,X)))
% -> (true)
% Rule [46]
% (eq)(apply(apply(apply(b,m),X),X),apply(apply(apply(b,combinator),
% apply(m,X)),apply(X,X))) ->
% (false) is composed into [46]
% (eq)(apply(apply(apply(b,m),X),X),apply(
% apply(
% apply(b,combinator),
% apply(m,X)),
% apply(X,X)))
% -> (true)
% Rule [45]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(combinator,
% apply(m,apply(X,Y))))
% -> (false) is composed into [45]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(combinator,apply(m,apply(X,Y)))) ->
% (true)
% Rule [44]
% (eq)(apply(X,apply(Y,Z)),apply(combinator,apply(apply(apply(b,X),Y),Z)))
% -> (false) is composed into [44]
% (eq)(apply(X,apply(Y,Z)),apply(combinator,
% apply(apply(
% apply(b,X),Y),Z)))
% -> (true)
% Rule [43]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,m),X)),Y))
% -> (false) is composed into [43]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(apply(apply(b,combinator),apply(
% apply(b,m),X)),Y))
% -> (true)
% Rule [42]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),V_3),apply(apply(
% apply(b,combinator),X),
% apply(Y,apply(Z,V_3))))
% -> (false) is composed into [42]
% (eq)(apply(apply(apply(b,X),apply(apply(b,Y),Z)),V_3),
% apply(apply(apply(b,combinator),X),apply(Y,
% apply(Z,V_3))))
% -> (true)
% Rule [41]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),V_3),apply(apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(Z,V_3))) ->
% (false) is composed into [41]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),Z),V_3),
% apply(apply(apply(b,combinator),apply(X,Y)),
% apply(Z,V_3))) -> (true)
% Rule [40]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(apply(apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (false) is composed into [40]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(
% apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (true)
% Rule [39]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),b),combinator),X),
% apply(m,apply(apply(b,combinator),X))) -> (false) is composed into
% [39]
% (eq)(apply(apply(apply(apply(apply(apply(b,b),b),X),b),combinator),X),
% apply(m,apply(apply(b,combinator),X))) -> (true)
% Rule [38]
% (eq)(apply(apply(b,combinator),apply(X,Y)),apply(apply(apply(apply(
% apply(b,b),m),
% apply(b,combinator)),X),Y))
% -> (false) is composed into [38]
% (eq)(apply(apply(b,combinator),apply(X,Y)),
% apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),X),Y)) ->
% (true)
% Rule [37]
% (eq)(apply(apply(apply(b,b),X),Y),apply(apply(apply(b,combinator),
% apply(apply(m,b),X)),Y)) ->
% (false) is composed into [37]
% (eq)(apply(apply(apply(b,b),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(
% apply(m,b),X)),Y))
% -> (true)
% Rule [36]
% (eq)(apply(X,apply(Y,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),m)),Y))
% -> (false) is composed into [36]
% (eq)(apply(X,apply(Y,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),m)),Y))
% -> (true)
% Rule [35]
% (eq)(apply(X,apply(m,Y)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Y))
% -> (false) is composed into [35]
% (eq)(apply(X,apply(m,Y)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),Y)),Y))
% -> (true)
% Rule [34]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(apply(b,b),m),
% apply(b,combinator)),b),combinator))
% -> (false) is composed into [34]
% (eq)(apply(m,apply(b,combinator)),apply(
% apply(
% apply(
% apply(
% apply(b,b),m),
% apply(b,combinator)),b),combinator))
% -> (true)
% Rule [33]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(b,m),b),combinator),
% apply(b,combinator))) -> (false) is composed into
% [33]
% (eq)(apply(m,apply(b,combinator)),apply(apply(apply(apply(b,m),b),combinator),
% apply(b,combinator))) -> (true)
% Rule [32]
% (eq)(apply(apply(apply(b,m),b),combinator),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) ->
% (false) is composed into [32]
% (eq)(apply(apply(apply(b,m),b),combinator),
% apply(apply(m,apply(b,combinator)),apply(b,combinator)))
% -> (true)
% Rule [31]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(combinator,apply(X,apply(Y,Z))))
% -> (false) is composed into [31]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(combinator,
% apply(X,
% apply(Y,Z))))
% -> (true)
% Rule [30]
% (eq)(apply(apply(m,apply(b,X)),Y),apply(apply(apply(b,combinator),X),
% apply(apply(b,X),Y))) -> (false) is composed into
% [30]
% (eq)(apply(apply(m,apply(b,X)),Y),apply(apply(apply(b,combinator),X),
% apply(apply(b,X),Y))) -> (true)
% Rule [29]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (false) is composed into
% [29]
% (eq)(apply(apply(apply(b,X),m),Y),apply(apply(apply(b,combinator),X),
% apply(Y,Y))) -> (true)
% Rule [28]
% (eq)(apply(apply(apply(m,b),X),Y),apply(apply(apply(b,combinator),b),
% apply(X,Y))) -> (false) is composed into
% [28]
% (eq)(apply(apply(apply(m,b),X),Y),apply(apply(apply(b,combinator),b),
% apply(X,Y))) -> (true)
% Rule [27]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (false) is composed into
% [27]
% (eq)(apply(apply(apply(b,X),Y),Y),apply(apply(apply(b,combinator),X),
% apply(m,Y))) -> (true)
% Rule [26]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(apply(
% apply(b,m),
% apply(b,combinator)),X))
% -> (false) is composed into [26]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),
% apply(apply(apply(b,m),apply(b,combinator)),X))
% -> (true)
% Rule [25]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),apply(
% apply(m,
% apply(b,combinator)),
% apply(X,Y)))
% -> (false) is composed into [25]
% (eq)(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),
% apply(apply(m,apply(b,combinator)),apply(X,Y)))
% -> (true)
% Rule [24]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),apply(apply(
% apply(b,combinator),m),
% apply(X,Y))) ->
% (false) is composed into [24]
% (eq)(apply(apply(apply(apply(apply(b,b),X),Y),X),Y),
% apply(apply(apply(b,combinator),m),apply(X,Y)))
% -> (true)
% Rule [23]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(apply(b,b),b),combinator),X),Y),Z))
% -> (false) is composed into [23]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(
% apply(
% apply(b,b),b),combinator),X),Y),Z))
% -> (true)
% Rule [22]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(apply(apply(b,b),apply(b,combinator)),X),Y),Z))
% -> (false) is composed into [22]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(
% apply(
% apply(b,b),
% apply(b,combinator)),X),Y),Z))
% -> (true)
% Rule [21]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),apply(m,apply(
% apply(b,combinator),b)))
% -> (false) is composed into [21]
% (eq)(apply(apply(apply(m,b),apply(b,combinator)),b),
% apply(m,apply(apply(b,combinator),b))) ->
% (true)
% Rule [20]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),apply(m,apply(
% apply(b,combinator),combinator)))
% -> (false) is composed into [20]
% (eq)(apply(apply(m,apply(b,combinator)),combinator),
% apply(m,apply(apply(b,combinator),combinator)))
% -> (true)
% Rule [19]
% (eq)(apply(apply(b,combinator),X),apply(apply(apply(apply(b,m),b),combinator),X))
% -> (false) is composed into [19]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(
% apply(
% apply(b,m),b),combinator),X))
% -> (true)
% Rule [18]
% (eq)(apply(apply(apply(b,m),X),Y),apply(apply(apply(b,combinator),
% apply(X,Y)),apply(X,Y))) ->
% (false) is composed into [18]
% (eq)(apply(apply(apply(b,m),X),Y),apply(
% apply(
% apply(b,combinator),
% apply(X,Y)),
% apply(X,Y)))
% -> (true)
% Rule [17] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (false) is composed into
% [17] (eq)(apply(X,X),apply(combinator,apply(m,X))) -> (true)
% Rule [16] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (false) is composed into
% [16] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (true)
% Rule [15]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(b,combinator),apply(apply(b,X),Y)),Z))
% -> (false) is composed into [15]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(b,combinator),
% apply(
% apply(b,X),Y)),Z))
% -> (true)
% Rule [14]
% (eq)(apply(m,apply(b,combinator)),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) -> (false) is composed into
% [14]
% (eq)(apply(m,apply(b,combinator)),apply(apply(m,apply(b,combinator)),
% apply(b,combinator))) -> (true)
% Rule [13]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (false) is composed into
% [13]
% (eq)(apply(apply(apply(b,X),Y),Z),apply(apply(apply(b,combinator),X),
% apply(Y,Z))) -> (true)
% Rule [12]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(m,apply(
% apply(b,combinator),X)))
% -> (false) is composed into [12]
% (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),
% apply(m,apply(apply(b,combinator),X))) ->
% (true)
% Rule [11]
% (eq)(apply(apply(b,combinator),X),apply(apply(m,apply(b,combinator)),X))
% -> (false) is composed into [11]
% (eq)(apply(apply(b,combinator),X),apply(
% apply(m,
% apply(b,combinator)),X))
% -> (true)
% Rule [10] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (false) is composed into
% [10] (eq)(apply(X,X),apply(apply(apply(b,combinator),m),X)) -> (true)
% Rule [9] (eq)(apply(m,X),apply(apply(apply(b,combinator),X),X)) -> (false) is composed into
% [9] (eq)(apply(m,X),apply(apply(apply(b,combinator),X),X)) -> (true)
% Rule [8] (eq)(apply(X,Y),apply(apply(apply(b,combinator),X),Y)) -> (false) is composed into
% [8] (eq)(apply(X,Y),apply(apply(apply(b,combinator),X),Y)) -> (true)
% Rule [7] (eq)(combinator,apply(m,combinator)) -> (false) is composed into
% [7] (eq)(combinator,apply(m,combinator)) -> (true)
% Rule [1] (eq)(Y,apply(combinator,Y)) -> (false) is composed into [1]
% (eq)(Y,
% apply(combinator,Y))
% -> (true)
% New rule produced : [77] (false) -> (true)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 77
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 8 rules have been used:
% [1]
% (eq)(Y,apply(combinator,Y)) -> (false); trace = in the starting set
% [2] (eq)(X,X) -> (true); trace = in the starting set
% [3] apply(X,X) <-> apply(m,X); trace = in the starting set
% [5] apply(X,apply(Y,Z)) <-> apply(apply(apply(b,X),Y),Z); trace = in the starting set
% [8] (eq)(apply(X,Y),apply(apply(apply(b,combinator),X),Y)) -> (false); trace = Cp of 5 and 1
% [12] (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(m,apply(
% apply(b,combinator),X)))
% -> (false); trace = Cp of 8 and 3
% [26] (eq)(apply(apply(apply(b,X),apply(b,combinator)),X),apply(apply(
% apply(b,m),
% apply(b,combinator)),X))
% -> (false); trace = Cp of 12 and 5
% [77] (false) -> (true); trace = Cp of 26 and 2
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.100000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------