TSTP Solution File: COL033-1 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL033-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n162.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 00:19:46 EDT 2014
% Result : Unsatisfiable 1.36s
% Output : Refutation 1.36s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL033-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n162.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 18:10:38 CDT 2014
% % CPUTime : 1.36
% Processing problem /tmp/CiME_65472_n162.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " m,l,b : constant; f : 1; 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(l,X),Y) = apply(X,apply(Y,Y));
% apply(m,X) = apply(X,X);
% ";
%
% let s1 = status F "
% f lr_lex;
% m lr_lex;
% l lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
%
% let p1 = precedence F "
% apply > f > b > l > m";
%
% let s2 = status F "
% f mul;
% m mul;
% l mul;
% apply mul;
% b mul;
% ";
%
% let p2 = precedence F "
% apply > f > b = l = m";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " apply(Y,f(Y)) = apply(f(Y),apply(Y,f(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(apply(l,X),Y) = apply(X,apply(Y,Y)),
% apply(m,X) = apply(X,X) } (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [m] = 1;
% [l] = 2;
% [b] = 3;
% [f](x1) = 4 + x1;
% [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(Y,f(Y)) = apply(f(Y),apply(Y,f(Y))) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] (eq)(X,X) -> (true)
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 1
% New rule produced :
% [2] (eq)(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 5
% 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: 4
% 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: 3
% Current number of rules: 4
% New rule produced : [5] apply(X,apply(Y,Y)) <-> apply(apply(l,X),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 5
% New rule produced : [6] apply(apply(l,X),Y) <-> apply(X,apply(Y,Y))
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 6
% New rule produced : [7] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced :
% [8] (eq)(apply(f(m),f(m)),apply(f(m),apply(m,f(m)))) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [9] (eq)(apply(m,f(m)),apply(f(m),apply(f(m),f(m)))) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 9
% Rule [5] apply(X,apply(Y,Y)) <-> apply(apply(l,X),Y) is composed into
% [5] apply(X,apply(Y,Y)) <-> apply(X,apply(m,Y))
% New rule produced : [10] apply(apply(l,X),Y) -> apply(X,apply(m,Y))
% Rule [6] apply(apply(l,X),Y) <-> apply(X,apply(Y,Y)) collapsed.
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [11] apply(l,apply(X,X)) <-> apply(apply(m,l),X)
% Current number of equations to process: 11
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced : [12] apply(apply(m,l),X) <-> apply(l,apply(X,X))
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [13] (eq)(apply(f(m),f(m)),apply(f(m),apply(f(m),f(m)))) -> (false)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 12
% Rule [11] apply(l,apply(X,X)) <-> apply(apply(m,l),X) is composed into
% [11] apply(l,apply(X,X)) <-> apply(l,apply(m,X))
% New rule produced : [14] apply(apply(m,l),X) -> apply(l,apply(m,X))
% Rule [12] apply(apply(m,l),X) <-> apply(l,apply(X,X)) collapsed.
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [15]
% (eq)(apply(X,apply(m,f(apply(l,X)))),apply(f(apply(l,X)),apply(X,apply(m,
% f(apply(l,X))))))
% -> (false)
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [16]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [17]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 19
% Current number of ordered equations: 2
% Current number of rules: 15
% New rule produced :
% [18]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 19
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [19]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [20]
% (eq)(apply(X,apply(f(apply(l,X)),f(apply(l,X)))),apply(f(apply(l,X)),
% apply(X,apply(m,f(apply(l,X))))))
% -> (false)
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [21]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 23
% Current number of ordered equations: 2
% Current number of rules: 19
% New rule produced :
% [22]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 23
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [23]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [24]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [25]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [26]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [27]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [28]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 30
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [29]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [30]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [31]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [32]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [33]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 37
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [34]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [35]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 39
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [36]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [37]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 40
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [38]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [39] apply(apply(X,X),apply(m,X)) -> apply(m,apply(X,X))
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [40] apply(apply(X,X),apply(X,X)) <-> apply(m,apply(m,X))
% Current number of equations to process: 52
% Current number of ordered equations: 1
% Current number of rules: 38
% New rule produced : [41] apply(m,apply(m,X)) <-> apply(apply(X,X),apply(X,X))
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [42] apply(X,apply(m,apply(l,X))) -> apply(m,apply(l,X))
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [43] apply(apply(apply(m,b),X),Y) -> apply(b,apply(X,Y))
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [44] apply(l,apply(m,apply(m,l))) -> apply(m,apply(m,l))
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [45] apply(apply(m,X),apply(X,X)) -> apply(m,apply(m,X))
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [46]
% (eq)(apply(X,apply(m,f(apply(l,X)))),apply(f(apply(l,X)),apply(X,apply(
% f(apply(l,X)),
% f(apply(l,X))))))
% -> (false)
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [47]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,apply(
% f(apply(m,l)),
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [48]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,apply(
% f(apply(l,l)),
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [49]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,apply(
% f(apply(l,l)),
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [50]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(l,l)),apply(l,apply(
% f(apply(m,l)),
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [51]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,apply(
% f(apply(l,l)),
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 102
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [52]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,apply(
% f(apply(m,l)),
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [53]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,apply(
% f(apply(m,l)),
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [54]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(l,l)),apply(l,apply(
% f(apply(m,l)),
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 105
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [55]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(l,l)),apply(l,apply(
% f(apply(l,l)),
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [56]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,apply(
% f(apply(l,l)),
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 107
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [57]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,apply(
% f(apply(m,l)),
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 107
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [58]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,apply(
% f(apply(m,l)),
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 110
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [59]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,apply(
% f(apply(l,l)),
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 110
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [60]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,apply(
% f(apply(l,l)),
% f(apply(m,l))))))
% -> (false)
% Current number of equations to process: 109
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [61]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,apply(
% f(apply(m,l)),
% f(apply(l,l))))))
% -> (false)
% Current number of equations to process: 109
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [62]
% (eq)(apply(X,apply(f(apply(l,X)),f(apply(l,X)))),apply(f(apply(l,X)),
% apply(X,apply(f(apply(l,X)),
% f(apply(l,X)))))) ->
% (false)
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [63]
% (eq)(apply(X,apply(Y,f(apply(apply(b,X),Y)))),apply(f(apply(apply(b,X),Y)),
% apply(X,apply(Y,f(apply(
% apply(b,X),Y))))))
% -> (false)
% Current number of equations to process: 108
% Current number of ordered equations: 0
% Current number of rules: 61
% Rule [63]
% (eq)(apply(X,apply(Y,f(apply(apply(b,X),Y)))),apply(f(apply(apply(b,X),Y)),
% apply(X,apply(Y,f(
% apply(
% apply(b,X),Y))))))
% -> (false) is composed into [63]
% (eq)(apply(X,apply(Y,f(apply(apply(b,X),Y)))),
% apply(f(apply(apply(b,X),Y)),apply(X,
% apply(Y,
% f(apply(
% apply(b,X),Y))))))
% -> (true)
% Rule [62]
% (eq)(apply(X,apply(f(apply(l,X)),f(apply(l,X)))),apply(f(apply(l,X)),
% apply(X,apply(f(
% apply(l,X)),
% f(apply(l,X))))))
% -> (false) is composed into [62]
% (eq)(apply(X,apply(f(apply(l,X)),f(apply(l,X)))),
% apply(f(apply(l,X)),apply(X,apply(f(
% apply(l,X)),
% f(apply(l,X))))))
% -> (true)
% Rule [61]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,
% apply(f(
% apply(m,l)),
% f(apply(l,l))))))
% -> (false) is composed into [61]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(f(
% apply(m,l)),
% f(apply(l,l))))))
% -> (true)
% Rule [60]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,
% apply(f(
% apply(l,l)),
% f(apply(m,l))))))
% -> (false) is composed into [60]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(f(
% apply(l,l)),
% f(apply(m,l))))))
% -> (true)
% Rule [59]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,
% apply(f(
% apply(l,l)),
% f(apply(m,l))))))
% -> (false) is composed into [59]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(f(
% apply(l,l)),
% f(apply(m,l))))))
% -> (true)
% Rule [58]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,
% apply(f(
% apply(m,l)),
% f(apply(l,l))))))
% -> (false) is composed into [58]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(f(
% apply(m,l)),
% f(apply(l,l))))))
% -> (true)
% Rule [57]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,
% apply(f(
% apply(m,l)),
% f(apply(l,l))))))
% -> (false) is composed into [57]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(f(
% apply(m,l)),
% f(apply(l,l))))))
% -> (true)
% Rule [56]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,
% apply(f(
% apply(l,l)),
% f(apply(m,l))))))
% -> (false) is composed into [56]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(f(
% apply(l,l)),
% f(apply(m,l))))))
% -> (true)
% Rule [55]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(l,l)),apply(l,
% apply(f(
% apply(l,l)),
% f(apply(m,l))))))
% -> (false) is composed into [55]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(l,l)),apply(l,apply(f(
% apply(l,l)),
% f(apply(m,l))))))
% -> (true)
% Rule [54]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(l,l)),apply(l,
% apply(f(
% apply(m,l)),
% f(apply(l,l))))))
% -> (false) is composed into [54]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(l,l)),apply(l,apply(f(
% apply(m,l)),
% f(apply(l,l))))))
% -> (true)
% Rule [53]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,
% apply(f(
% apply(m,l)),
% f(apply(m,l))))))
% -> (false) is composed into [53]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(f(
% apply(m,l)),
% f(apply(m,l))))))
% -> (true)
% Rule [52]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,
% apply(f(
% apply(m,l)),
% f(apply(m,l))))))
% -> (false) is composed into [52]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(f(
% apply(m,l)),
% f(apply(m,l))))))
% -> (true)
% Rule [51]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,
% apply(f(
% apply(l,l)),
% f(apply(l,l))))))
% -> (false) is composed into [51]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(f(
% apply(l,l)),
% f(apply(l,l))))))
% -> (true)
% Rule [50]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(l,l)),apply(l,
% apply(f(
% apply(m,l)),
% f(apply(m,l))))))
% -> (false) is composed into [50]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(l,l)),apply(l,apply(f(
% apply(m,l)),
% f(apply(m,l))))))
% -> (true)
% Rule [49]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,
% apply(f(
% apply(l,l)),
% f(apply(l,l))))))
% -> (false) is composed into [49]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(f(
% apply(l,l)),
% f(apply(l,l))))))
% -> (true)
% Rule [48]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,
% apply(f(
% apply(l,l)),
% f(apply(l,l))))))
% -> (false) is composed into [48]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(f(
% apply(l,l)),
% f(apply(l,l))))))
% -> (true)
% Rule [47]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,
% apply(f(
% apply(m,l)),
% f(apply(m,l))))))
% -> (false) is composed into [47]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(f(
% apply(m,l)),
% f(apply(m,l))))))
% -> (true)
% Rule [46]
% (eq)(apply(X,apply(m,f(apply(l,X)))),apply(f(apply(l,X)),apply(X,
% apply(f(
% apply(l,X)),
% f(apply(l,X))))))
% -> (false) is composed into [46]
% (eq)(apply(X,apply(m,f(apply(l,X)))),
% apply(f(apply(l,X)),apply(X,apply(f(
% apply(l,X)),
% f(apply(l,X))))))
% -> (true)
% Rule [38]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [38]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [37]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [37]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [36]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [36]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [35]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [35]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [34]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [34]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [33]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [33]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [32]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [32]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [31]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [31]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [30]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [30]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [29]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [29]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [28]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [28]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(l,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [27]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [27]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [26]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [26]
% (eq)(apply(l,apply(f(apply(l,l)),f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [25]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),apply(f(apply(l,l)),
% apply(l,apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [25]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [24]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),apply(f(apply(m,l)),
% apply(l,apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [24]
% (eq)(apply(l,apply(f(apply(m,l)),f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [23]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,
% apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [23]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [22]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,
% apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [22]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [21]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,
% apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [21]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [20]
% (eq)(apply(X,apply(f(apply(l,X)),f(apply(l,X)))),apply(f(apply(l,X)),
% apply(X,apply(m,
% f(apply(l,X))))))
% -> (false) is composed into [20]
% (eq)(apply(X,apply(f(apply(l,X)),f(apply(l,X)))),
% apply(f(apply(l,X)),apply(X,apply(m,
% f(apply(l,X))))))
% -> (true)
% Rule [19]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(l,l)),apply(l,
% apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [19]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [18]
% (eq)(apply(l,apply(m,f(apply(l,l)))),apply(f(apply(m,l)),apply(l,
% apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [18]
% (eq)(apply(l,apply(m,f(apply(l,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [17]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(l,l)),apply(l,
% apply(m,
% f(apply(l,l))))))
% -> (false) is composed into [17]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(l,l)),apply(l,apply(m,
% f(apply(l,l))))))
% -> (true)
% Rule [16]
% (eq)(apply(l,apply(m,f(apply(m,l)))),apply(f(apply(m,l)),apply(l,
% apply(m,
% f(apply(m,l))))))
% -> (false) is composed into [16]
% (eq)(apply(l,apply(m,f(apply(m,l)))),
% apply(f(apply(m,l)),apply(l,apply(m,
% f(apply(m,l))))))
% -> (true)
% Rule [15]
% (eq)(apply(X,apply(m,f(apply(l,X)))),apply(f(apply(l,X)),apply(X,
% apply(m,
% f(apply(l,X))))))
% -> (false) is composed into [15]
% (eq)(apply(X,apply(m,f(apply(l,X)))),
% apply(f(apply(l,X)),apply(X,apply(m,
% f(apply(l,X))))))
% -> (true)
% Rule [13] (eq)(apply(f(m),f(m)),apply(f(m),apply(f(m),f(m)))) -> (false) is composed into
% [13] (eq)(apply(f(m),f(m)),apply(f(m),apply(f(m),f(m)))) -> (true)
% Rule [9] (eq)(apply(m,f(m)),apply(f(m),apply(f(m),f(m)))) -> (false) is composed into
% [9] (eq)(apply(m,f(m)),apply(f(m),apply(f(m),f(m)))) -> (true)
% Rule [8] (eq)(apply(f(m),f(m)),apply(f(m),apply(m,f(m)))) -> (false) is composed into
% [8] (eq)(apply(f(m),f(m)),apply(f(m),apply(m,f(m)))) -> (true)
% Rule [2] (eq)(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) -> (false) is composed into
% [2] (eq)(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) -> (true)
% New rule produced : [64] (false) -> (true)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 62
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [2]
% (eq)(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) -> (false); trace = in the starting set
% [3] apply(X,X) <-> apply(m,X); trace = in the starting set
% [6] apply(apply(l,X),Y) <-> apply(X,apply(Y,Y)); trace = in the starting set
% [7] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z)); trace = in the starting set
% [42] apply(X,apply(m,apply(l,X))) -> apply(m,apply(l,X)); trace = Cp of 6 and 3
% [63] (eq)(apply(X,apply(Y,f(apply(apply(b,X),Y)))),apply(f(apply(apply(b,X),Y)),
% apply(X,apply(Y,f(
% apply(
% apply(b,X),Y))))))
% -> (false); trace = Cp of 7 and 2
% [64] (false) -> (true); trace = Cp of 63 and 42
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.260000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------