TSTP Solution File: COL066-2 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL066-2 : TPTP v6.0.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n139.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 00:20:02 EDT 2014
% Result : Unsatisfiable 1.61s
% Output : Refutation 1.61s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL066-2 : TPTP v6.0.0. Bugfixed v1.2.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n139.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 : Fri Jun 6 00:56:23 CDT 2014
% % CPUTime : 1.61
% Processing problem /tmp/CiME_18409_n139.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " z,y,x,w,q,b : constant; apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z));
% apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z));
% apply(apply(w,X),Y) = apply(apply(X,Y),Y);
% ";
%
% let s1 = status F "
% z lr_lex;
% y lr_lex;
% x lr_lex;
% w lr_lex;
% q lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
%
% let p1 = precedence F "
% apply > b > q > w > x > y > z";
%
% let s2 = status F "
% z mul;
% y mul;
% x mul;
% w mul;
% q mul;
% apply mul;
% b mul;
% ";
%
% let p2 = precedence F "
% apply > b = q = w = x = y = z";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) = apply(apply(x,y),apply(apply(x,y),z));"
% ;
% (*
% 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(apply(q,X),Y),Z) =
% apply(Y,apply(X,Z)),
% apply(apply(w,X),Y) = apply(apply(X,Y),Y) }
% (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [z] = 1;
% [y] = 2;
% [x] = 3;
% [w] = 4;
% [q] = 5;
% [b] = 6;
% [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(apply(apply(apply(apply(apply(q,q),
% apply(w,apply(q,
% apply(q,q)))),x),y),y),z)
% = apply(apply(x,y),apply(apply(x,y),z)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] apply(apply(X,Y),Y) <-> apply(apply(w,X),Y)
% The conjecture has been reduced.
% Conjecture is now:
% apply(apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y),z) =
% apply(apply(x,y),apply(apply(x,y),z))
%
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 1
% New rule produced : [2] apply(apply(w,X),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 2
% New rule produced : [3] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced : [4] apply(apply(apply(q,X),Y),Z) -> apply(Y,apply(X,Z))
% The conjecture has been reduced.
% Conjecture is now:
% apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) =
% apply(apply(x,y),apply(apply(x,y),z))
%
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] apply(apply(w,w),X) <-> apply(apply(X,X),X)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced : [6] apply(apply(X,X),X) <-> apply(apply(w,w),X)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] apply(X,apply(X,Y)) <-> apply(apply(apply(w,b),X),Y)
% Current number of equations to process: 12
% Current number of ordered equations: 3
% Current number of rules: 7
% New rule produced : [8] apply(X,apply(Y,Y)) <-> apply(apply(w,apply(b,X)),Y)
% Current number of equations to process: 12
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced : [9] apply(apply(apply(w,b),X),Y) <-> apply(X,apply(X,Y))
% Current number of equations to process: 12
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] apply(apply(w,apply(b,X)),Y) <-> apply(X,apply(Y,Y))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] apply(X,apply(X,Y)) <-> apply(apply(apply(w,q),X),Y)
% Current number of equations to process: 53
% Current number of ordered equations: 3
% Current number of rules: 11
% New rule produced : [12] apply(Y,apply(X,Y)) <-> apply(apply(w,apply(q,X)),Y)
% Current number of equations to process: 53
% Current number of ordered equations: 2
% Current number of rules: 12
% New rule produced : [13] apply(apply(apply(w,q),X),Y) <-> apply(X,apply(X,Y))
% Current number of equations to process: 53
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced : [14] apply(apply(w,apply(q,X)),Y) <-> apply(Y,apply(X,Y))
% The conjecture has been reduced.
% Conjecture is now:
% apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) =
% apply(apply(x,y),apply(apply(x,y),z))
%
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] apply(X,apply(X,X)) <-> apply(apply(w,apply(w,b)),X)
% Current number of equations to process: 117
% Current number of ordered equations: 2
% Current number of rules: 15
% New rule produced : [16] apply(apply(apply(w,w),b),X) -> apply(b,apply(b,X))
% Current number of equations to process: 117
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced : [17] apply(apply(w,apply(w,b)),X) <-> apply(X,apply(X,X))
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] apply(X,apply(X,X)) <-> apply(apply(w,apply(w,q)),X)
% Current number of equations to process: 159
% Current number of ordered equations: 2
% Current number of rules: 18
% New rule produced : [19] apply(apply(apply(w,w),q),X) -> apply(q,apply(q,X))
% Current number of equations to process: 159
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced : [20] apply(apply(w,apply(w,q)),X) <-> apply(X,apply(X,X))
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [21] apply(apply(w,apply(w,w)),b) -> apply(b,apply(b,b))
% Current number of equations to process: 207
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] apply(apply(w,apply(w,w)),q) -> apply(q,apply(q,q))
% Current number of equations to process: 209
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23] apply(apply(apply(w,X),Y),Y) -> apply(apply(w,apply(X,Y)),Y)
% Current number of equations to process: 211
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24] apply(apply(apply(X,Y),Y),Y) <-> apply(apply(w,apply(w,X)),Y)
% Current number of equations to process: 231
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [25] apply(apply(w,apply(w,X)),Y) <-> apply(apply(apply(X,Y),Y),Y)
% Current number of equations to process: 231
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26] apply(apply(apply(X,X),X),X) <-> apply(apply(w,apply(w,w)),X)
% Current number of equations to process: 284
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [27] apply(apply(w,apply(w,w)),X) <-> apply(apply(apply(X,X),X),X)
% Current number of equations to process: 284
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(X,X)),X)
% Current number of equations to process: 305
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced :
% [29] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,X)),X)
% Current number of equations to process: 305
% Current number of ordered equations: 0
% Current number of rules: 29
% Rule [7] apply(X,apply(X,Y)) <-> apply(apply(apply(w,b),X),Y) is composed into
% [7] apply(X,apply(X,Y)) <-> apply(apply(apply(w,q),X),Y)
% New rule produced :
% [30] apply(apply(apply(w,b),X),Y) -> apply(apply(apply(w,q),X),Y)
% Rule [9] apply(apply(apply(w,b),X),Y) <-> apply(X,apply(X,Y)) collapsed.
% Current number of equations to process: 317
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [31] apply(apply(w,apply(b,X)),X) -> apply(apply(w,apply(q,X)),X)
% Current number of equations to process: 331
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [32] apply(apply(w,apply(q,X)),X) <-> apply(apply(w,apply(w,b)),X)
% Current number of equations to process: 333
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [33] apply(apply(w,apply(w,b)),X) <-> apply(apply(w,apply(q,X)),X)
% Current number of equations to process: 335
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [34] apply(apply(w,apply(q,X)),X) <-> apply(apply(w,apply(w,q)),X)
% Current number of equations to process: 344
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [35] apply(apply(w,apply(w,q)),X) <-> apply(apply(w,apply(q,X)),X)
% Current number of equations to process: 346
% Current number of ordered equations: 0
% Current number of rules: 34
% Rule [32] apply(apply(w,apply(q,X)),X) <-> apply(apply(w,apply(w,b)),X) is composed into
% [32] apply(apply(w,apply(q,X)),X) <-> apply(apply(w,apply(w,q)),X)
% Rule [15] apply(X,apply(X,X)) <-> apply(apply(w,apply(w,b)),X) is composed into
% [15] apply(X,apply(X,X)) <-> apply(apply(w,apply(w,q)),X)
% New rule produced :
% [36] apply(apply(w,apply(w,b)),X) -> apply(apply(w,apply(w,q)),X)
% Rule [17] apply(apply(w,apply(w,b)),X) <-> apply(X,apply(X,X)) collapsed.
% Rule [33] apply(apply(w,apply(w,b)),X) <-> apply(apply(w,apply(q,X)),X)
% collapsed.
% Current number of equations to process: 363
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [37] apply(apply(w,apply(X,Y)),Y) <-> apply(apply(w,apply(w,X)),Y)
% Rule [29] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,X)),X)
% collapsed.
% Rule [32] apply(apply(w,apply(q,X)),X) <-> apply(apply(w,apply(w,q)),X)
% collapsed.
% Rule [34] apply(apply(w,apply(q,X)),X) <-> apply(apply(w,apply(w,q)),X)
% collapsed.
% Current number of equations to process: 371
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [38] apply(apply(w,apply(w,X)),Y) <-> apply(apply(w,apply(X,Y)),Y)
% Rule [28] apply(apply(w,apply(w,X)),X) <-> apply(apply(w,apply(X,X)),X)
% collapsed.
% Rule [35] apply(apply(w,apply(w,q)),X) <-> apply(apply(w,apply(q,X)),X)
% collapsed.
% Current number of equations to process: 371
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [39] apply(apply(w,apply(w,w)),X) <-> apply(apply(w,apply(X,X)),X)
% Current number of equations to process: 406
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [40] apply(apply(w,apply(X,X)),X) <-> apply(apply(w,apply(w,w)),X)
% Current number of equations to process: 406
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [41] apply(apply(X,apply(Y,Z)),Z) <-> apply(apply(w,apply(apply(b,X),Y)),Z)
% Current number of equations to process: 419
% Current number of ordered equations: 1
% Current number of rules: 33
% New rule produced :
% [42] apply(apply(w,apply(apply(b,X),Y)),Z) <-> apply(apply(X,apply(Y,Z)),Z)
% Current number of equations to process: 419
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [43] apply(X,apply(X,X)) <-> apply(apply(w,apply(apply(b,w),b)),X)
% Current number of equations to process: 489
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [44] apply(apply(w,apply(apply(b,w),b)),X) <-> apply(X,apply(X,X))
% Current number of equations to process: 489
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [45] apply(X,apply(X,X)) <-> apply(apply(w,apply(apply(b,w),q)),X)
% Current number of equations to process: 488
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [46] apply(apply(w,apply(apply(b,w),q)),X) <-> apply(X,apply(X,X))
% Current number of equations to process: 488
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [47] apply(apply(w,apply(apply(w,b),w)),q) -> apply(q,apply(q,q))
% Current number of equations to process: 487
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [48] apply(apply(w,apply(apply(w,b),w)),b) -> apply(b,apply(b,b))
% Current number of equations to process: 486
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [49] apply(apply(w,apply(w,apply(b,w))),b) -> apply(b,apply(b,b))
% Current number of equations to process: 560
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [50] apply(apply(w,apply(w,apply(b,w))),q) -> apply(q,apply(q,q))
% Current number of equations to process: 610
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [51] apply(apply(X,apply(Y,Z)),Z) <-> apply(apply(w,apply(apply(q,Y),X)),Z)
% Current number of equations to process: 630
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced :
% [52] apply(apply(w,apply(apply(q,Y),X)),Z) <-> apply(apply(X,apply(Y,Z)),Z)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 630
% Current number of ordered equations: 0
% Current number of rules: 44
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 4 rules have been used:
% [1]
% apply(apply(X,Y),Y) <-> apply(apply(w,X),Y); trace = in the starting set
% [4] apply(apply(apply(q,X),Y),Z) -> apply(Y,apply(X,Z)); trace = in the starting set
% [14] apply(apply(w,apply(q,X)),Y) <-> apply(Y,apply(X,Y)); trace = Cp of 4 and 1
% [52] apply(apply(w,apply(apply(q,Y),X)),Z) <-> apply(apply(X,apply(Y,Z)),Z); trace = Cp of 4 and 1
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.500000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------