TSTP Solution File: COL017-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL017-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n169.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 00:19:42 EDT 2014
% Result : Unsatisfiable 1.17s
% Output : Refutation 1.17s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL017-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n169.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jun 5 17:27:48 CDT 2014
% % CPUTime : 1.17
% Processing problem /tmp/CiME_65009_n169.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " combinator,t,m,b : constant; apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z));
% apply(m,X) = apply(X,X);
% apply(apply(t,X),Y) = apply(Y,X);
% ";
%
% let s1 = status F "
% combinator lr_lex;
% t lr_lex;
% m lr_lex;
% apply lr_lex;
% b lr_lex;
% ";
%
% let p1 = precedence F "
% apply > b > m > t > combinator";
%
% let s2 = status F "
% combinator mul;
% t mul;
% m mul;
% apply mul;
% b mul;
% ";
%
% let p2 = precedence F "
% apply > b = m = t = combinator";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " Y = apply(combinator,Y);"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
%
% let Red_Conjectures = normalize_equations Defining_rules Conjectures;
% *)
% #time on;
%
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
%
% #time off;
%
%
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
%
% F : signature = <signature>
% X : variable_set = <variable set>
%
% Axioms : (F,X) equations = { apply(apply(apply(b,X),Y),Z) =
% apply(X,apply(Y,Z)),
% apply(m,X) = apply(X,X),
% apply(apply(t,X),Y) = apply(Y,X) }
% (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [combinator] = 1;
% [t] = 2;
% [m] = 3;
% [b] = 4;
% [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 = { Y = apply(combinator,Y) } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] (eq)(Y,apply(combinator,Y)) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 1
% New rule produced : [2] (eq)(X,X) -> (true)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 2
% New rule produced : [3] apply(X,X) <-> apply(m,X)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 3
% New rule produced : [4] apply(m,X) <-> apply(X,X)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 4
% New rule produced : [5] apply(apply(t,X),Y) -> apply(Y,X)
% 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(b,X),Y),Z) -> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] (eq)(combinator,apply(m,combinator)) -> (false)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] apply(X,X) <-> apply(m,apply(t,X))
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced : [9] apply(m,apply(t,X)) <-> apply(X,X)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] apply(apply(m,t),X) -> apply(X,t)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 10
% Rule [8] apply(X,X) <-> apply(m,apply(t,X)) is composed into [8]
% apply(X,X) <->
% apply(m,X)
% New rule produced : [11] apply(m,apply(t,X)) -> apply(m,X)
% Rule [9] apply(m,apply(t,X)) <-> apply(X,X) collapsed.
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [12] apply(m,apply(m,t)) -> apply(t,t)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [13] apply(apply(apply(m,b),X),Y) -> apply(b,apply(X,Y))
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [14] apply(X,apply(apply(b,X),Y)) <-> apply(apply(m,apply(b,X)),Y)
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced :
% [15] apply(apply(m,apply(b,X)),Y) <-> apply(X,apply(apply(b,X),Y))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [16] apply(apply(m,apply(m,b)),X) -> apply(b,apply(apply(m,b),X))
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [17] apply(apply(X,Y),Y) <-> apply(apply(m,apply(b,apply(t,Y))),X)
% Current number of equations to process: 16
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [18] apply(apply(m,apply(b,apply(t,Y))),X) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [19] apply(X,X) <-> apply(apply(m,apply(b,apply(t,X))),t)
% Current number of equations to process: 27
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced : [20] apply(apply(m,apply(b,apply(t,X))),t) <-> apply(X,X)
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 19
% Rule [19] apply(X,X) <-> apply(apply(m,apply(b,apply(t,X))),t) is composed into
% [19] apply(X,X) <-> apply(m,X)
% New rule produced : [21] apply(apply(m,apply(b,apply(t,X))),t) -> apply(m,X)
% Rule [20] apply(apply(m,apply(b,apply(t,X))),t) <-> apply(X,X) collapsed.
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [22] apply(apply(m,apply(b,apply(m,t))),t) -> apply(m,t)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [23] apply(apply(m,apply(b,apply(m,t))),X) -> apply(apply(X,t),t)
% Rule [22] apply(apply(m,apply(b,apply(m,t))),t) -> apply(m,t) collapsed.
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [24] apply(m,apply(m,apply(b,apply(m,t)))) -> apply(t,t)
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [25] apply(m,apply(m,apply(b,apply(t,t)))) -> apply(t,t)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [26] apply(apply(m,apply(b,apply(t,X))),X) -> apply(apply(m,X),X)
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [27] apply(apply(X,X),X) <-> apply(apply(m,apply(b,apply(t,X))),m)
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [28] apply(apply(m,apply(b,apply(t,X))),m) <-> apply(apply(X,X),X)
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [29] apply(X,apply(Y,apply(apply(b,X),Y))) <-> apply(m,apply(apply(b,X),Y))
% Current number of equations to process: 43
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [30] apply(m,apply(apply(b,X),Y)) <-> apply(X,apply(Y,apply(apply(b,X),Y)))
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [31]
% (eq)(apply(X,apply(apply(b,combinator),X)),apply(m,apply(apply(b,combinator),X)))
% -> (false)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [32]
% (eq)(apply(apply(b,combinator),apply(m,apply(b,combinator))),apply(m,
% apply(m,
% apply(b,combinator))))
% -> (false)
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 29
% Rule [32]
% (eq)(apply(apply(b,combinator),apply(m,apply(b,combinator))),apply(m,
% apply(m,
% apply(b,combinator))))
% -> (false) is composed into [32]
% (eq)(apply(apply(b,combinator),apply(m,
% apply(b,combinator))),
% apply(m,apply(m,apply(b,combinator)))) ->
% (true)
% Rule [31]
% (eq)(apply(X,apply(apply(b,combinator),X)),apply(m,apply(apply(b,combinator),X)))
% -> (false) is composed into [31]
% (eq)(apply(X,apply(apply(b,combinator),X)),
% apply(m,apply(apply(b,combinator),X))) ->
% (true)
% Rule [7] (eq)(combinator,apply(m,combinator)) -> (false) is composed into
% [7] (eq)(combinator,apply(m,combinator)) -> (true)
% Rule [1] (eq)(Y,apply(combinator,Y)) -> (false) is composed into [1]
% (eq)(Y,
% apply(combinator,Y))
% -> (true)
% New rule produced : [33] (false) -> (true)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 30
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 9 rules have been used:
% [1]
% (eq)(Y,apply(combinator,Y)) -> (false); trace = in the starting set
% [2] (eq)(X,X) -> (true); trace = in the starting set
% [3] apply(X,X) <-> apply(m,X); trace = in the starting set
% [5] apply(apply(t,X),Y) -> apply(Y,X); trace = in the starting set
% [6] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z)); trace = in the starting set
% [8] apply(X,X) <-> apply(m,X); trace = Cp of 5 and 3
% [29] apply(X,apply(Y,apply(apply(b,X),Y))) <-> apply(m,apply(apply(b,X),Y)); trace = Cp of 8 and 6
% [31] (eq)(apply(X,apply(apply(b,combinator),X)),apply(m,apply(apply(b,combinator),X)))
% -> (false); trace = Cp of 29 and 1
% [33] (false) -> (true); trace = Cp of 31 and 2
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.060000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------