TSTP Solution File: COL030-1 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL030-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n126.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 00:19:45 EDT 2014
% Result : Unsatisfiable 11.16s
% Output : Refutation 11.16s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL030-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n126.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 18:02:38 CDT 2014
% % CPUTime : 11.16
% Processing problem /tmp/CiME_34065_n126.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " l,s : constant; f : 1; apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z));
% apply(apply(l,X),Y) = apply(X,apply(Y,Y));
% ";
%
% let s1 = status F "
% f lr_lex;
% l lr_lex;
% apply lr_lex;
% s lr_lex;
% ";
%
% let p1 = precedence F "
% apply > f > s > l";
%
% let s2 = status F "
% f mul;
% l mul;
% apply mul;
% s mul;
% ";
%
% let p2 = precedence F "
% apply > f > s = l";
%
% 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(s,X),Y),Z) =
% apply(apply(X,Z),apply(Y,Z)),
% apply(apply(l,X),Y) = apply(X,apply(Y,Y)) }
% (2 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [l] = 1;
% [s] = 2;
% [f](x1) = 3 + 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: 5
% 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: 4
% Current number of rules: 2
% New rule produced : [3] apply(X,apply(Y,Y)) <-> apply(apply(l,X),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 3
% New rule produced : [4] apply(apply(l,X),Y) <-> apply(X,apply(Y,Y))
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 4
% New rule produced :
% [5] apply(apply(X,Z),apply(Y,Z)) <-> apply(apply(apply(s,X),Y),Z)
% Current number of equations to process: 4
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [6] apply(apply(apply(s,X),Y),Z) <-> apply(apply(X,Z),apply(Y,Z))
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% (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: 20
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8] apply(apply(X,X),apply(Y,Y)) <-> apply(apply(apply(l,l),X),Y)
% Current number of equations to process: 24
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [9] apply(apply(apply(l,l),X),Y) <-> apply(apply(X,X),apply(Y,Y))
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10] apply(apply(apply(s,X),Y),Y) -> apply(apply(l,apply(X,Y)),Y)
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] apply(X,apply(apply(l,apply(Y,Y)),Y)) -> apply(apply(l,X),apply(Y,Y))
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] apply(X,apply(apply(Y,Y),apply(Y,Y))) <-> apply(apply(l,apply(l,X)),Y)
% Current number of equations to process: 70
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [13] apply(apply(l,apply(l,X)),Y) <-> apply(X,apply(apply(Y,Y),apply(Y,Y)))
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] apply(X,apply(apply(apply(s,Y),Y),Z)) -> apply(apply(l,X),apply(Y,Z))
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] apply(X,apply(apply(Y,X),apply(Y,X))) <-> apply(apply(apply(s,l),Y),X)
% Current number of equations to process: 134
% Current number of ordered equations: 1
% Current number of rules: 15
% New rule produced :
% [16] apply(apply(apply(s,l),Y),X) <-> apply(X,apply(apply(Y,X),apply(Y,X)))
% Current number of equations to process: 134
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17] apply(X,apply(apply(apply(l,l),Y),Y)) -> apply(apply(l,X),apply(Y,Y))
% Current number of equations to process: 171
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 190
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(apply(l,l),X),
% f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 211
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(apply(l,l),X),
% f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 227
% Current number of ordered equations: 2
% Current number of rules: 20
% New rule produced :
% [21]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(apply(l,l),X),
% f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 227
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [22]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(apply(l,l),X),
% f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 227
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(apply(l,l),X),
% f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 240
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [24]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(apply(l,l),X),
% f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(apply(l,l),X),
% f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 277
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 291
% Current number of ordered equations: 3
% Current number of rules: 27
% New rule produced :
% [28]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 291
% Current number of ordered equations: 2
% Current number of rules: 28
% New rule produced :
% [29]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 291
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [30]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 291
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 379
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 398
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 416
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [34]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 430
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [35]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 441
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [36]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 441
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [37]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 468
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [38]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 468
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [39]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(l,apply(X,X))))))
% -> (false)
% Current number of equations to process: 488
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [40]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false)
% Current number of equations to process: 499
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [41]
% apply(apply(X,apply(Y,Y)),apply(Z,Y)) <->
% apply(apply(apply(s,apply(l,X)),Z),Y)
% Current number of equations to process: 494
% Current number of ordered equations: 3
% Current number of rules: 41
% New rule produced :
% [42]
% apply(apply(X,Y),apply(Z,apply(Y,Y))) <->
% apply(apply(apply(s,X),apply(l,Z)),Y)
% Current number of equations to process: 494
% Current number of ordered equations: 2
% Current number of rules: 42
% New rule produced :
% [43]
% apply(apply(apply(s,apply(l,X)),Z),Y) <->
% apply(apply(X,apply(Y,Y)),apply(Z,Y))
% Current number of equations to process: 494
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced :
% [44]
% apply(apply(apply(s,X),apply(l,Z)),Y) <->
% apply(apply(X,Y),apply(Z,apply(Y,Y)))
% Current number of equations to process: 494
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [45]
% apply(apply(X,Z),apply(apply(Y,Y),Z)) <->
% apply(apply(apply(l,apply(s,X)),Y),Z)
% Current number of equations to process: 619
% Current number of ordered equations: 3
% Current number of rules: 45
% New rule produced :
% [46]
% apply(apply(apply(X,X),Z),apply(Y,Z)) <->
% apply(apply(apply(apply(l,s),X),Y),Z)
% Current number of equations to process: 619
% Current number of ordered equations: 2
% Current number of rules: 46
% New rule produced :
% [47]
% apply(apply(apply(apply(l,s),X),Y),Z) <->
% apply(apply(apply(X,X),Z),apply(Y,Z))
% Current number of equations to process: 619
% Current number of ordered equations: 1
% Current number of rules: 47
% New rule produced :
% [48]
% apply(apply(apply(l,apply(s,X)),Y),Z) <->
% apply(apply(X,Z),apply(apply(Y,Y),Z))
% Current number of equations to process: 619
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [49]
% apply(apply(Y,Z),apply(apply(X,Y),Z)) <->
% apply(apply(apply(apply(s,s),X),Y),Z)
% Current number of equations to process: 814
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced :
% [50]
% apply(apply(apply(apply(s,s),X),Y),Z) <->
% apply(apply(Y,Z),apply(apply(X,Y),Z))
% Current number of equations to process: 814
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [51]
% apply(apply(apply(apply(l,s),X),Y),Y) <->
% apply(apply(l,apply(apply(X,X),Y)),Y)
% Current number of equations to process: 935
% Current number of ordered equations: 1
% Current number of rules: 51
% New rule produced :
% [52]
% apply(apply(l,apply(apply(X,X),Y)),Y) <->
% apply(apply(apply(apply(l,s),X),Y),Y)
% Current number of equations to process: 935
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [53]
% apply(apply(apply(l,l),X),apply(Y,Y)) <->
% apply(apply(l,apply(l,apply(X,X))),Y)
% Current number of equations to process: 1012
% Current number of ordered equations: 1
% Current number of rules: 53
% New rule produced :
% [54]
% apply(apply(l,apply(l,apply(X,X))),Y) <->
% apply(apply(apply(l,l),X),apply(Y,Y))
% Current number of equations to process: 1012
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [55]
% apply(apply(X,apply(Y,Y)),apply(Y,Y)) <->
% apply(apply(l,apply(apply(l,X),Y)),Y)
% Current number of equations to process: 1067
% Current number of ordered equations: 1
% Current number of rules: 55
% New rule produced :
% [56]
% apply(apply(l,apply(apply(l,X),Y)),Y) <->
% apply(apply(X,apply(Y,Y)),apply(Y,Y))
% Current number of equations to process: 1067
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [57]
% apply(apply(X,Y),apply(X,apply(Y,Y))) <->
% apply(apply(apply(apply(s,s),l),X),Y)
% Current number of equations to process: 1157
% Current number of ordered equations: 1
% Current number of rules: 57
% New rule produced :
% [58]
% apply(apply(apply(apply(s,s),l),X),Y) <->
% apply(apply(X,Y),apply(X,apply(Y,Y)))
% Current number of equations to process: 1157
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [59]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(l,apply(X,X)))))))
% -> (false)
% Current number of equations to process: 1260
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [60]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X))))))
% -> (false)
% Current number of equations to process: 1284
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [61]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(l,apply(X,X)))))))
% -> (false)
% Current number of equations to process: 1301
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [62]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X))))))
% -> (false)
% Current number of equations to process: 1323
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [63]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(l,apply(X,X)))))))
% -> (false)
% Current number of equations to process: 1343
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [64]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X))))))
% -> (false)
% Current number of equations to process: 1364
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [65]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(l,apply(X,X)))))))
% -> (false)
% Current number of equations to process: 1377
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [66]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X))))))
% -> (false)
% Current number of equations to process: 1396
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [67]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(l,apply(X,X)))))))
% -> (false)
% Current number of equations to process: 1407
% Current number of ordered equations: 1
% Current number of rules: 67
% New rule produced :
% [68]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X))))))
% -> (false)
% Current number of equations to process: 1407
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [69]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X))))))
% -> (false)
% Current number of equations to process: 1441
% Current number of ordered equations: 1
% Current number of rules: 69
% New rule produced :
% [70]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(l,apply(X,X)))))))
% -> (false)
% Current number of equations to process: 1441
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [71]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X))))))
% -> (false)
% Current number of equations to process: 1468
% Current number of ordered equations: 1
% Current number of rules: 71
% New rule produced :
% [72]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(l,apply(X,X)))))))
% -> (false)
% Current number of equations to process: 1468
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [73]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(l,apply(X,X)))))))
% -> (false)
% Current number of equations to process: 1482
% Current number of ordered equations: 1
% Current number of rules: 73
% New rule produced :
% [74]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X))))))
% -> (false)
% Current number of equations to process: 1482
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [75]
% apply(apply(X,apply(Y,Y)),apply(apply(l,Z),Y)) ->
% apply(apply(apply(s,X),Z),apply(Y,Y))
% Current number of equations to process: 1488
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [76]
% apply(apply(apply(l,X),Y),apply(Z,apply(Y,Y))) ->
% apply(apply(apply(s,X),Z),apply(Y,Y))
% Current number of equations to process: 1488
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [77]
% apply(apply(X,apply(Z,Z)),apply(Y,apply(Z,Z))) <->
% apply(apply(l,apply(apply(s,X),Y)),Z)
% Current number of equations to process: 1613
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [78]
% apply(apply(l,apply(apply(s,X),Y)),Z) <->
% apply(apply(X,apply(Z,Z)),apply(Y,apply(Z,Z)))
% Current number of equations to process: 1613
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [79]
% apply(apply(X,apply(Y,Z)),apply(Z,apply(Y,Z))) <->
% apply(apply(apply(s,apply(s,X)),Y),Z)
% Current number of equations to process: 1765
% Current number of ordered equations: 1
% Current number of rules: 79
% New rule produced :
% [80]
% apply(apply(apply(s,apply(s,X)),Y),Z) <->
% apply(apply(X,apply(Y,Z)),apply(Z,apply(Y,Z)))
% Current number of equations to process: 1765
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [81]
% apply(apply(apply(apply(l,l),X),X),apply(Y,Y)) ->
% apply(apply(apply(l,l),apply(X,X)),Y)
% Current number of equations to process: 1943
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [82]
% apply(apply(apply(l,l),apply(X,X)),Y) <->
% apply(apply(apply(l,apply(X,X)),X),apply(Y,Y))
% Current number of equations to process: 1979
% Current number of ordered equations: 1
% Current number of rules: 82
% New rule produced :
% [83]
% apply(apply(apply(l,apply(X,X)),X),apply(Y,Y)) <->
% apply(apply(apply(l,l),apply(X,X)),Y)
% Current number of equations to process: 1979
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [84]
% apply(apply(apply(l,l),apply(X,Y)),Z) <->
% apply(apply(apply(apply(s,X),X),Y),apply(Z,Z))
% Current number of equations to process: 2025
% Current number of ordered equations: 1
% Current number of rules: 84
% New rule produced :
% [85]
% apply(apply(apply(apply(s,X),X),Y),apply(Z,Z)) <->
% apply(apply(apply(l,l),apply(X,Y)),Z)
% Current number of equations to process: 2025
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [86]
% apply(apply(X,X),apply(apply(Y,Y),apply(Y,Y))) <->
% apply(apply(l,apply(apply(l,l),X)),Y)
% Current number of equations to process: 2105
% Current number of ordered equations: 3
% Current number of rules: 86
% New rule produced :
% [87]
% apply(apply(apply(X,X),apply(X,X)),apply(Y,Y)) <->
% apply(apply(apply(l,apply(l,l)),X),Y)
% Current number of equations to process: 2105
% Current number of ordered equations: 2
% Current number of rules: 87
% New rule produced :
% [88]
% apply(apply(apply(l,apply(l,l)),X),Y) <->
% apply(apply(apply(X,X),apply(X,X)),apply(Y,Y))
% Current number of equations to process: 2105
% Current number of ordered equations: 1
% Current number of rules: 88
% New rule produced :
% [89]
% apply(apply(l,apply(apply(l,l),X)),Y) <->
% apply(apply(X,X),apply(apply(Y,Y),apply(Y,Y)))
% Current number of equations to process: 2105
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [90]
% apply(apply(l,apply(X,X)),apply(Y,Y)) <->
% apply(apply(l,apply(apply(l,l),X)),Y)
% Current number of equations to process: 2120
% Current number of ordered equations: 1
% Current number of rules: 90
% New rule produced :
% [91]
% apply(apply(l,apply(apply(l,l),X)),Y) <->
% apply(apply(l,apply(X,X)),apply(Y,Y))
% Current number of equations to process: 2120
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [92]
% apply(apply(Y,Y),apply(apply(X,Y),apply(X,Y))) <->
% apply(apply(apply(s,apply(l,l)),X),Y)
% Current number of equations to process: 2424
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [93]
% apply(apply(apply(s,apply(l,l)),X),Y) <->
% apply(apply(Y,Y),apply(apply(X,Y),apply(X,Y)))
% Current number of equations to process: 2424
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [94]
% apply(apply(l,apply(s,apply(s,s))),apply(s,s)) ->
% apply(apply(apply(l,l),apply(s,s)),s)
% Current number of equations to process: 2558
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [95]
% apply(apply(apply(s,X),apply(l,apply(Y,Y))),Y) ->
% apply(apply(l,apply(X,Y)),apply(Y,Y))
% Current number of equations to process: 2565
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [96]
% apply(X,apply(apply(l,apply(apply(s,Y),Y)),Z)) <->
% apply(apply(l,X),apply(Y,apply(Z,Z)))
% Current number of equations to process: 2600
% Current number of ordered equations: 2
% Current number of rules: 96
% New rule produced :
% [97]
% apply(apply(l,X),apply(Y,apply(Z,Z))) <->
% apply(X,apply(apply(l,apply(apply(s,Y),Y)),Z))
% Current number of equations to process: 2600
% Current number of ordered equations: 1
% Current number of rules: 97
% New rule produced :
% [98]
% apply(apply(l,X),apply(Y,apply(apply(s,Y),Y))) ->
% apply(apply(l,X),apply(apply(s,Y),Y))
% Current number of equations to process: 2600
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [99]
% apply(X,apply(apply(apply(s,apply(s,Y)),Z),Y)) ->
% apply(apply(l,X),apply(Y,apply(Z,Y)))
% Current number of equations to process: 2844
% Current number of ordered equations: 2
% Current number of rules: 99
% New rule produced :
% [100]
% apply(apply(l,apply(X,Z)),apply(Y,Z)) <->
% apply(apply(apply(s,X),apply(apply(s,Y),Y)),Z)
% Current number of equations to process: 2844
% Current number of ordered equations: 1
% Current number of rules: 100
% New rule produced :
% [101]
% apply(apply(apply(s,X),apply(apply(s,Y),Y)),Z) <->
% apply(apply(l,apply(X,Z)),apply(Y,Z))
% Current number of equations to process: 2844
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [102]
% apply(apply(l,apply(X,Y)),apply(Y,Y)) <->
% apply(apply(apply(s,X),apply(apply(l,l),Y)),Y)
% Current number of equations to process: 3136
% Current number of ordered equations: 1
% Current number of rules: 102
% New rule produced :
% [103]
% apply(apply(apply(s,X),apply(apply(l,l),Y)),Y) <->
% apply(apply(l,apply(X,Y)),apply(Y,Y))
% Current number of equations to process: 3136
% Current number of ordered equations: 0
% Current number of rules: 103
% New rule produced :
% [104]
% apply(X,apply(apply(apply(l,l),apply(l,l)),l)) ->
% apply(apply(l,apply(l,X)),apply(l,l))
% Current number of equations to process: 3313
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [105]
% apply(apply(l,apply(X,Y)),apply(X,Y)) <->
% apply(apply(apply(apply(s,s),apply(s,X)),X),Y)
% Current number of equations to process: 3380
% Current number of ordered equations: 1
% Current number of rules: 105
% New rule produced :
% [106]
% apply(apply(apply(apply(s,s),apply(s,X)),X),Y) <->
% apply(apply(l,apply(X,Y)),apply(X,Y))
% Current number of equations to process: 3380
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [107]
% apply(apply(l,apply(X,X)),apply(X,X)) <->
% apply(apply(apply(apply(s,s),apply(l,l)),X),X)
% Current number of equations to process: 3617
% Current number of ordered equations: 1
% Current number of rules: 107
% New rule produced :
% [108]
% apply(apply(apply(apply(s,s),apply(l,l)),X),X) <->
% apply(apply(l,apply(X,X)),apply(X,X))
% Current number of equations to process: 3617
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [109]
% apply(apply(apply(l,X),Y),apply(apply(l,Z),Y)) ->
% apply(apply(apply(s,X),Z),apply(Y,Y))
% Current number of equations to process: 3699
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [110]
% apply(apply(apply(s,X),Y),apply(Z,Z)) <->
% apply(apply(apply(s,apply(l,X)),apply(l,Y)),Z)
% Current number of equations to process: 3803
% Current number of ordered equations: 1
% Current number of rules: 110
% New rule produced :
% [111]
% apply(apply(apply(s,apply(l,X)),apply(l,Y)),Z) <->
% apply(apply(apply(s,X),Y),apply(Z,Z))
% Current number of equations to process: 3803
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [112]
% apply(apply(apply(l,apply(l,l)),X),Y) <->
% apply(apply(apply(l,apply(X,X)),X),apply(Y,Y))
% Current number of equations to process: 3979
% Current number of ordered equations: 1
% Current number of rules: 112
% New rule produced :
% [113]
% apply(apply(apply(l,apply(X,X)),X),apply(Y,Y)) <->
% apply(apply(apply(l,apply(l,l)),X),Y)
% Current number of equations to process: 3979
% Current number of ordered equations: 0
% Current number of rules: 113
% Rule [97]
% apply(apply(l,X),apply(Y,apply(Z,Z))) <->
% apply(X,apply(apply(l,apply(apply(s,Y),Y)),Z)) is composed into
% [97]
% apply(apply(l,X),apply(Y,apply(Z,Z))) <->
% apply(apply(l,X),apply(apply(l,Y),Z))
% New rule produced :
% [114]
% apply(X,apply(apply(l,apply(apply(s,Y),Y)),Z)) ->
% apply(apply(l,X),apply(apply(l,Y),Z))
% Rule
% [96]
% apply(X,apply(apply(l,apply(apply(s,Y),Y)),Z)) <->
% apply(apply(l,X),apply(Y,apply(Z,Z))) collapsed.
% Current number of equations to process: 4072
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [115]
% apply(apply(apply(s,X),apply(apply(s,Y),Y)),X) ->
% apply(apply(apply(l,l),X),apply(Y,X))
% Current number of equations to process: 4172
% Current number of ordered equations: 0
% Current number of rules: 114
% Rule [102]
% apply(apply(l,apply(X,Y)),apply(Y,Y)) <->
% apply(apply(apply(s,X),apply(apply(l,l),Y)),Y) is composed into
% [102]
% apply(apply(l,apply(X,Y)),apply(Y,Y)) <->
% apply(apply(l,apply(l,apply(X,Y))),Y)
% New rule produced :
% [116]
% apply(apply(apply(s,X),apply(apply(l,l),Y)),Y) ->
% apply(apply(l,apply(l,apply(X,Y))),Y)
% Rule
% [103]
% apply(apply(apply(s,X),apply(apply(l,l),Y)),Y) <->
% apply(apply(l,apply(X,Y)),apply(Y,Y)) collapsed.
% Current number of equations to process: 4226
% Current number of ordered equations: 0
% Current number of rules: 114
% New rule produced :
% [117]
% apply(apply(apply(apply(s,s),apply(s,X)),X),X) ->
% apply(apply(apply(l,l),X),apply(X,X))
% Current number of equations to process: 4283
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [118]
% apply(apply(apply(l,l),X),apply(X,X)) <->
% apply(apply(apply(apply(s,s),apply(l,l)),X),X)
% Current number of equations to process: 4321
% Current number of ordered equations: 1
% Current number of rules: 116
% New rule produced :
% [119]
% apply(apply(apply(apply(s,s),apply(l,l)),X),X) <->
% apply(apply(apply(l,l),X),apply(X,X))
% Current number of equations to process: 4322
% Current number of ordered equations: 0
% Current number of rules: 117
% Rule [118]
% apply(apply(apply(l,l),X),apply(X,X)) <->
% apply(apply(apply(apply(s,s),apply(l,l)),X),X) is composed into
% [118]
% apply(apply(apply(l,l),X),apply(X,X)) <->
% apply(apply(l,apply(apply(l,l),X)),X)
% Rule [107]
% apply(apply(l,apply(X,X)),apply(X,X)) <->
% apply(apply(apply(apply(s,s),apply(l,l)),X),X) is composed into
% [107]
% apply(apply(l,apply(X,X)),apply(X,X)) <->
% apply(apply(l,apply(apply(l,l),X)),X)
% New rule produced :
% [120]
% apply(apply(apply(apply(s,s),apply(l,l)),X),X) ->
% apply(apply(l,apply(apply(l,l),X)),X)
% Rule
% [108]
% apply(apply(apply(apply(s,s),apply(l,l)),X),X) <->
% apply(apply(l,apply(X,X)),apply(X,X)) collapsed.
% Rule
% [119]
% apply(apply(apply(apply(s,s),apply(l,l)),X),X) <->
% apply(apply(apply(l,l),X),apply(X,X)) collapsed.
% Current number of equations to process: 4434
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [121]
% apply(apply(l,apply(apply(s,l),l)),apply(l,l)) ->
% apply(apply(apply(l,l),apply(l,l)),l)
% Current number of equations to process: 4468
% Current number of ordered equations: 0
% Current number of rules: 117
% Rule [110]
% apply(apply(apply(s,X),Y),apply(Z,Z)) <->
% apply(apply(apply(s,apply(l,X)),apply(l,Y)),Z) is composed into
% [110]
% apply(apply(apply(s,X),Y),apply(Z,Z)) <->
% apply(apply(l,apply(apply(s,X),Y)),Z)
% New rule produced :
% [122]
% apply(apply(apply(s,apply(l,X)),apply(l,Y)),Z) ->
% apply(apply(l,apply(apply(s,X),Y)),Z)
% Rule
% [111]
% apply(apply(apply(s,apply(l,X)),apply(l,Y)),Z) <->
% apply(apply(apply(s,X),Y),apply(Z,Z)) collapsed.
% Current number of equations to process: 4479
% Current number of ordered equations: 0
% Current number of rules: 117
% New rule produced :
% [123]
% (eq)(apply(apply(X,f(apply(apply(s,X),Y))),apply(Y,f(apply(apply(s,X),Y)))),
% apply(f(apply(apply(s,X),Y)),apply(apply(X,f(apply(apply(s,X),Y))),apply(Y,
% f(
% apply(
% apply(s,X),Y))))))
% -> (false)
% Current number of equations to process: 4533
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [124]
% (eq)(apply(apply(X,f(apply(apply(s,X),X))),apply(X,f(apply(apply(s,X),X)))),
% apply(apply(l,f(apply(apply(s,X),X))),apply(X,f(apply(apply(s,X),X))))) ->
% (false)
% Current number of equations to process: 4545
% Current number of ordered equations: 0
% Current number of rules: 119
% Rule [124]
% (eq)(apply(apply(X,f(apply(apply(s,X),X))),apply(X,f(apply(apply(s,X),X)))),
% apply(apply(l,f(apply(apply(s,X),X))),apply(X,f(apply(apply(s,X),X)))))
% -> (false) is composed into [124]
% (eq)(apply(apply(X,f(apply(apply(s,X),X))),
% apply(X,f(apply(apply(s,X),X)))),
% apply(apply(l,f(apply(apply(s,X),X))),
% apply(X,f(apply(apply(s,X),X))))) -> (true)
% Rule [123]
% (eq)(apply(apply(X,f(apply(apply(s,X),Y))),apply(Y,f(apply(apply(s,X),Y)))),
% apply(f(apply(apply(s,X),Y)),apply(apply(X,f(apply(apply(s,X),Y))),
% apply(Y,f(apply(apply(s,X),Y)))))) ->
% (false) is composed into [123]
% (eq)(apply(apply(X,f(apply(apply(s,X),Y))),
% apply(Y,f(apply(apply(s,X),Y)))),apply(
% f(
% apply(
% apply(s,X),Y)),
% apply(
% apply(X,
% f(
% apply(
% apply(s,X),Y))),
% apply(Y,
% f(
% apply(
% apply(s,X),Y))))))
% -> (true)
% Rule [74]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X))))))
% -> (false) is composed into [74]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(l,apply(X,X))),apply(apply(X,X),
% apply(f(
% apply(l,
% apply(X,X))),
% f(apply(
% apply(l,l),X))))))
% -> (true)
% Rule [73]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(l,
% apply(X,X)))))))
% -> (false) is composed into [73]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(l,apply(X,X))),apply(apply(X,X),
% apply(f(
% apply(
% apply(l,l),X)),
% f(apply(l,
% apply(X,X)))))))
% -> (true)
% Rule [72]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(l,
% apply(X,X)))))))
% -> (false) is composed into [72]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(X,X),
% apply(f(
% apply(
% apply(l,l),X)),
% f(apply(l,
% apply(X,X)))))))
% -> (true)
% Rule [71]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X))))))
% -> (false) is composed into [71]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(X,X),
% apply(f(
% apply(l,
% apply(X,X))),
% f(apply(
% apply(l,l),X))))))
% -> (true)
% Rule [70]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(l,
% apply(X,X)))))))
% -> (false) is composed into [70]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(apply(l,l),X)),apply(apply(X,X),
% apply(f(
% apply(
% apply(l,l),X)),
% f(apply(l,
% apply(X,X)))))))
% -> (true)
% Rule [69]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X))))))
% -> (false) is composed into [69]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(apply(l,l),X)),apply(apply(X,X),
% apply(f(
% apply(l,
% apply(X,X))),
% f(apply(
% apply(l,l),X))))))
% -> (true)
% Rule [68]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X))))))
% -> (false) is composed into [68]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(X,X),
% apply(f(
% apply(l,
% apply(X,X))),
% f(apply(
% apply(l,l),X))))))
% -> (true)
% Rule [67]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(l,
% apply(X,X)))))))
% -> (false) is composed into [67]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(X,X),
% apply(f(
% apply(
% apply(l,l),X)),
% f(apply(l,
% apply(X,X)))))))
% -> (true)
% Rule [66]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X))))))
% -> (false) is composed into [66]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(l,apply(X,X))),apply(apply(X,X),
% apply(f(
% apply(
% apply(l,l),X)),
% f(apply(
% apply(l,l),X))))))
% -> (true)
% Rule [65]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(l,
% apply(X,X)))))))
% -> (false) is composed into [65]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(apply(l,l),X)),apply(apply(X,X),
% apply(f(
% apply(l,
% apply(X,X))),
% f(apply(l,
% apply(X,X)))))))
% -> (true)
% Rule [64]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X))))))
% -> (false) is composed into [64]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(X,X),
% apply(f(
% apply(
% apply(l,l),X)),
% f(apply(
% apply(l,l),X))))))
% -> (true)
% Rule [63]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(l,
% apply(X,X)))))))
% -> (false) is composed into [63]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(l,apply(X,X))),apply(apply(X,X),
% apply(f(
% apply(l,
% apply(X,X))),
% f(apply(l,
% apply(X,X)))))))
% -> (true)
% Rule [62]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X))))))
% -> (false) is composed into [62]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(X,X),
% apply(f(
% apply(
% apply(l,l),X)),
% f(apply(
% apply(l,l),X))))))
% -> (true)
% Rule [61]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(l,
% apply(X,X)))))))
% -> (false) is composed into [61]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(X,X),
% apply(f(
% apply(l,
% apply(X,X))),
% f(apply(l,
% apply(X,X)))))))
% -> (true)
% Rule [60]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(X,X),
% apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X))))))
% -> (false) is composed into [60]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(apply(l,l),X)),apply(apply(X,X),
% apply(f(
% apply(
% apply(l,l),X)),
% f(apply(
% apply(l,l),X))))))
% -> (true)
% Rule [59]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(X,X),
% apply(f(apply(l,
% apply(X,X))),
% f(apply(l,
% apply(X,X)))))))
% -> (false) is composed into [59]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(X,X),
% apply(f(
% apply(l,
% apply(X,X))),
% f(apply(l,
% apply(X,X)))))))
% -> (true)
% Rule [40]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false) is composed into [40]
% (eq)(apply(apply(X,X),apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [39]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [39]
% (eq)(apply(apply(X,X),apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [38]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false) is composed into [38]
% (eq)(apply(apply(X,X),apply(f(apply(
% apply(l,l),X)),
% f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [37]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [37]
% (eq)(apply(apply(X,X),apply(f(apply(
% apply(l,l),X)),
% f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [36]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false) is composed into [36]
% (eq)(apply(apply(X,X),apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [35]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false) is composed into [35]
% (eq)(apply(apply(X,X),apply(f(apply(
% apply(l,l),X)),
% f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [34]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false) is composed into [34]
% (eq)(apply(apply(X,X),apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [33]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [33]
% (eq)(apply(apply(X,X),apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [32]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false) is composed into [32]
% (eq)(apply(apply(X,X),apply(f(apply(l,
% apply(X,X))),
% f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [31]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [31]
% (eq)(apply(apply(X,X),apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [30]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [30]
% (eq)(apply(apply(X,X),apply(f(apply(l,
% apply(X,X))),
% f(apply(apply(l,l),X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [29]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false) is composed into [29]
% (eq)(apply(apply(X,X),apply(f(apply(l,
% apply(X,X))),
% f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [28]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [28]
% (eq)(apply(apply(X,X),apply(f(apply(l,
% apply(X,X))),
% f(apply(l,apply(X,X))))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [27]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [27]
% (eq)(apply(apply(X,X),apply(f(apply(
% apply(l,l),X)),
% f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [26]
% (eq)(apply(apply(X,X),apply(f(apply(apply(l,l),X)),f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(apply(l,l),X),f(apply(apply(l,l),X)))))
% -> (false) is composed into [26]
% (eq)(apply(apply(X,X),apply(f(apply(
% apply(l,l),X)),
% f(apply(apply(l,l),X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [25]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(
% apply(l,l),X),
% f(apply(apply(l,l),X)))))
% -> (false) is composed into [25]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [24]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [24]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [23]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(
% apply(l,l),X),
% f(apply(apply(l,l),X)))))
% -> (false) is composed into [23]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [22]
% (eq)(apply(apply(apply(l,l),X),f(apply(apply(l,l),X))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [22]
% (eq)(apply(apply(apply(l,l),X),f(apply(
% apply(l,l),X))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [21]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(
% apply(l,l),X),
% f(apply(apply(l,l),X)))))
% -> (false) is composed into [21]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(
% apply(l,l),X)))))
% -> (true)
% Rule [20]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(
% apply(l,l),X)),
% apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [20]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(apply(l,l),X)),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [19]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,apply(X,X)))),apply(f(apply(l,
% apply(X,X))),
% apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [19]
% (eq)(apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X)))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [18]
% (eq)(apply(apply(X,X),apply(f(apply(l,apply(X,X))),f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(apply(l,l),X),f(apply(l,
% apply(X,X))))))
% -> (false) is composed into [18]
% (eq)(apply(apply(X,X),apply(f(apply(l,
% apply(X,X))),
% f(apply(l,apply(X,X))))),
% apply(f(apply(l,apply(X,X))),apply(apply(
% apply(l,l),X),
% f(apply(l,
% apply(X,X))))))
% -> (true)
% Rule [7]
% (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 [7]
% (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 [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 : [125] (false) -> (true)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 4658
% Current number of ordered equations: 0
% Current number of rules: 120
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [1]
% (eq)(X,X) -> (true); trace = in the starting set
% [2] (eq)(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) -> (false); trace = in the starting set
% [3] apply(X,apply(Y,Y)) <-> apply(apply(l,X),Y); trace = in the starting set
% [6] apply(apply(apply(s,X),Y),Z) <-> apply(apply(X,Z),apply(Y,Z)); trace = in the starting set
% [123] (eq)(apply(apply(X,f(apply(apply(s,X),Y))),apply(Y,f(apply(apply(s,X),Y)))),
% apply(f(apply(apply(s,X),Y)),apply(apply(X,f(apply(apply(s,X),Y))),
% apply(Y,f(apply(apply(s,X),Y)))))) ->
% (false); trace = Cp of 6 and 2
% [124] (eq)(apply(apply(X,f(apply(apply(s,X),X))),apply(X,f(apply(apply(s,X),X)))),
% apply(apply(l,f(apply(apply(s,X),X))),apply(X,f(apply(apply(s,X),X)))))
% -> (false); trace = Cp of 123 and 3
% [125] (false) -> (true); trace = Cp of 124 and 1
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 10.020000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------