%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL002-4 : TPTP v6.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n121.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 00:19:33 EDT 2014
% Result : Unsatisfiable 1.12s
% Output : Refutation 1.12s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL002-4 : TPTP v6.0.0. Bugfixed v3.1.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n121.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 15:25:43 CDT 2014
% % CPUTime : 1.12
% Processing problem /tmp/CiME_63953_n121.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " fixed_pt,i,c,b,s : constant; weak_fixed_point : 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(apply(b,X),Y),Z) = apply(X,apply(Y,Z));
% apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y);
% apply(i,X) = X;
% weak_fixed_point(X) = apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i));
% ";
%
% let s1 = status F "
% fixed_pt lr_lex;
% weak_fixed_point lr_lex;
% i lr_lex;
% c lr_lex;
% b lr_lex;
% apply lr_lex;
% s lr_lex;
% ";
%
% let p1 = precedence F "
% weak_fixed_point > apply > s > b > c > i > fixed_pt";
%
% let s2 = status F "
% fixed_pt mul;
% weak_fixed_point mul;
% i mul;
% c mul;
% b mul;
% apply mul;
% s mul;
% ";
%
% let p2 = precedence F "
% weak_fixed_point > apply > s = b = c = i = fixed_pt";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " weak_fixed_point(fixed_pt) = apply(fixed_pt,weak_fixed_point(fixed_pt));"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
%
% let Red_Conjectures = normalize_equations Defining_rules Conjectures;
% *)
% #time on;
%
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
%
% #time off;
%
%
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
%
% F : signature = <signature>
% X : variable_set = <variable set>
%
% Axioms : (F,X) equations = { apply(apply(apply(s,X),Y),Z) =
% apply(apply(X,Z),apply(Y,Z)),
% apply(apply(apply(b,X),Y),Z) =
% apply(X,apply(Y,Z)),
% apply(apply(apply(c,X),Y),Z) =
% apply(apply(X,Z),Y),
% apply(i,X) = X,
% weak_fixed_point(X) =
% apply(apply(apply(s,apply(b,X)),i),apply(
% apply(s,
% apply(b,X)),i)) }
% (5 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [fixed_pt] = 1;
% [i] = 2;
% [c] = 3;
% [b] = 4;
% [s] = 5;
% [weak_fixed_point](x1) = 6 + 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 = { weak_fixed_point(fixed_pt) =
% apply(fixed_pt,weak_fixed_point(fixed_pt)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] apply(i,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 1
% New rule produced : [2] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 2
% New rule produced : [3] apply(apply(apply(c,X),Y),Z) -> apply(apply(X,Z),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(X,Z),apply(Y,Z)) <-> apply(apply(apply(s,X),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 4
% New rule produced :
% [5] apply(apply(apply(s,X),Y),Z) <-> apply(apply(X,Z),apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [6]
% apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)) ->
% weak_fixed_point(X)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] apply(X,apply(Y,X)) <-> apply(apply(apply(s,i),Y),X)
% Current number of equations to process: 2
% Current number of ordered equations: 3
% Current number of rules: 7
% New rule produced : [8] apply(apply(X,Y),Y) <-> apply(apply(apply(s,X),i),Y)
% Current number of equations to process: 2
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced : [9] apply(apply(apply(s,X),i),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] apply(apply(apply(s,i),Y),X) <-> apply(X,apply(Y,X))
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] apply(X,apply(Y,apply(Z,Y))) <-> apply(apply(apply(s,apply(b,X)),Z),Y)
% Current number of equations to process: 12
% Current number of ordered equations: 3
% Current number of rules: 11
% New rule produced :
% [12] apply(Y,apply(apply(X,Y),Z)) <-> apply(apply(apply(apply(s,b),X),Y),Z)
% Current number of equations to process: 12
% Current number of ordered equations: 2
% Current number of rules: 12
% New rule produced :
% [13] apply(apply(apply(apply(s,b),X),Y),Z) <-> apply(Y,apply(apply(X,Y),Z))
% Current number of equations to process: 12
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced :
% [14] apply(apply(apply(s,apply(b,X)),Z),Y) <-> apply(X,apply(Y,apply(Z,Y)))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] apply(apply(Y,Z),apply(X,Y)) <-> apply(apply(apply(apply(s,c),X),Y),Z)
% Current number of equations to process: 10
% Current number of ordered equations: 3
% Current number of rules: 15
% New rule produced :
% [16] apply(apply(X,apply(Y,Z)),Z) <-> apply(apply(apply(s,apply(c,X)),Y),Z)
% Current number of equations to process: 10
% Current number of ordered equations: 2
% Current number of rules: 16
% New rule produced :
% [17] apply(apply(apply(apply(s,c),X),Y),Z) <-> apply(apply(Y,Z),apply(X,Y))
% Current number of equations to process: 10
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [18] apply(apply(apply(s,apply(c,X)),Y),Z) <-> apply(apply(X,apply(Y,Z)),Z)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19]
% apply(apply(Y,Z),apply(apply(X,Y),Z)) <->
% apply(apply(apply(apply(s,s),X),Y),Z)
% Current number of equations to process: 9
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [20]
% apply(apply(apply(apply(s,s),X),Y),Z) <->
% apply(apply(Y,Z),apply(apply(X,Y),Z))
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% apply(apply(X,apply(Y,Z)),apply(V_3,Z)) <->
% apply(apply(apply(s,apply(apply(b,X),Y)),V_3),Z)
% Current number of equations to process: 7
% Current number of ordered equations: 3
% Current number of rules: 21
% New rule produced :
% [22]
% apply(apply(X,Y),apply(Z,apply(V_3,Y))) <->
% apply(apply(apply(s,X),apply(apply(b,Z),V_3)),Y)
% Current number of equations to process: 7
% Current number of ordered equations: 2
% Current number of rules: 22
% New rule produced :
% [23]
% apply(apply(apply(s,apply(apply(b,X),Y)),V_3),Z) <->
% apply(apply(X,apply(Y,Z)),apply(V_3,Z))
% Current number of equations to process: 7
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [24]
% apply(apply(apply(s,X),apply(apply(b,Z),V_3)),Y) <->
% apply(apply(X,Y),apply(Z,apply(V_3,Y)))
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% apply(apply(X,Y),apply(apply(Z,Y),V_3)) <->
% apply(apply(apply(s,X),apply(apply(c,Z),V_3)),Y)
% Current number of equations to process: 5
% Current number of ordered equations: 3
% Current number of rules: 25
% New rule produced :
% [26]
% apply(apply(apply(X,Y),Z),apply(V_3,Y)) <->
% apply(apply(apply(s,apply(apply(c,X),Z)),V_3),Y)
% Current number of equations to process: 5
% Current number of ordered equations: 2
% Current number of rules: 26
% New rule produced :
% [27]
% apply(apply(apply(s,apply(apply(c,X),Z)),V_3),Y) <->
% apply(apply(apply(X,Y),Z),apply(V_3,Y))
% Current number of equations to process: 5
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [28]
% apply(apply(apply(s,X),apply(apply(c,Z),V_3)),Y) <->
% apply(apply(X,Y),apply(apply(Z,Y),V_3))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% 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: 4
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [30]
% 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: 4
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [31] apply(X,weak_fixed_point(X)) -> weak_fixed_point(X)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 31
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 3 rules have been used:
% [5]
% apply(apply(apply(s,X),Y),Z) <-> apply(apply(X,Z),apply(Y,Z)); trace = in the starting set
% [6] apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)) ->
% weak_fixed_point(X); trace = in the starting set
% [31] apply(X,weak_fixed_point(X)) -> weak_fixed_point(X); trace = Cp of 6 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.020000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------