TSTP Solution File: COL019-1 by CiME---2.01
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL019-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n112.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 1.23s
% Output : Refutation 1.23s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL019-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n112.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 17:33:48 CDT 2014
% % CPUTime : 1.23
% Processing problem /tmp/CiME_19945_n112.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " combinator,t,b,s : constant; 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(t,X),Y) = apply(Y,X);
% ";
%
% let s1 = status F "
% combinator lr_lex;
% t lr_lex;
% b lr_lex;
% apply lr_lex;
% s lr_lex;
% ";
%
% let p1 = precedence F "
% apply > s > b > t > combinator";
%
% let s2 = status F "
% combinator mul;
% t mul;
% b mul;
% apply mul;
% s mul;
% ";
%
% let p2 = precedence F "
% apply > s = b = 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(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(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;
% [b] = 3;
% [s] = 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(apply(t,X),Y) -> apply(Y,X)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 3
% New rule produced : [4] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 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: 0
% 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: 0
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] apply(apply(X,Y),Y) <-> apply(apply(apply(s,t),X),Y)
% Current number of equations to process: 4
% Current number of ordered equations: 1
% Current number of rules: 7
% New rule produced : [8] apply(apply(apply(s,t),X),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [9] apply(X,X) <-> apply(apply(apply(s,t),t),X)
% Current number of equations to process: 14
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] apply(apply(apply(s,t),t),X) <-> apply(X,X)
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] apply(X,X) <-> apply(apply(apply(s,t),t),apply(t,X))
% Current number of equations to process: 38
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced : [12] apply(apply(apply(s,t),t),apply(t,X)) <-> apply(X,X)
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13] apply(apply(X,Y),X) <-> apply(apply(apply(s,t),apply(t,Y)),X)
% Current number of equations to process: 49
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced :
% [14] apply(apply(apply(s,t),apply(t,Y)),X) <-> apply(apply(X,Y),X)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] apply(X,apply(X,Y)) <-> apply(apply(apply(apply(s,t),b),X),Y)
% Current number of equations to process: 71
% Current number of ordered equations: 3
% Current number of rules: 15
% New rule produced :
% [16] apply(X,apply(Y,Y)) <-> apply(apply(apply(s,t),apply(b,X)),Y)
% Current number of equations to process: 71
% Current number of ordered equations: 2
% Current number of rules: 16
% New rule produced :
% [17] apply(apply(apply(apply(s,t),b),X),Y) <-> apply(X,apply(X,Y))
% Current number of equations to process: 71
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [18] apply(apply(apply(s,t),apply(b,X)),Y) <-> apply(X,apply(Y,Y))
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19]
% (eq)(apply(X,X),apply(apply(apply(s,t),apply(b,combinator)),X)) -> (false)
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% (eq)(apply(X,X),apply(apply(apply(s,t),apply(b,combinator)),apply(t,X))) ->
% (false)
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,Y))) -> (false)
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22]
% (eq)(apply(apply(apply(s,X),X),apply(b,combinator)),apply(apply(apply(s,
% apply(s,t)),X),
% apply(b,combinator))) ->
% (false)
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23]
% (eq)(apply(apply(b,combinator),apply(b,combinator)),apply(apply(apply(s,t),
% apply(s,t)),
% apply(b,combinator))) ->
% (false)
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24]
% (eq)(apply(apply(apply(s,t),t),X),apply(apply(apply(s,t),apply(b,combinator)),X))
% -> (false)
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% (eq)(apply(apply(apply(s,t),t),apply(t,X)),apply(apply(apply(s,t),apply(b,combinator)),X))
% -> (false)
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [26]
% (eq)(apply(apply(apply(s,t),apply(b,apply(X,X))),X),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(X,X))) -> (false)
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [27]
% (eq)(apply(X,X),apply(apply(apply(s,t),apply(b,combinator)),apply(t,apply(t,X))))
% -> (false)
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [28]
% (eq)(apply(apply(b,combinator),apply(b,combinator)),apply(apply(apply(s,
% apply(s,t)),t),
% apply(b,combinator))) ->
% (false)
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [29]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(s,t),apply(b,combinator)),
% apply(t,apply(X,Y)))) -> (false)
% Current number of equations to process: 151
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% (eq)(apply(X,apply(Y,apply(apply(b,X),Y))),apply(apply(apply(s,t),apply(b,combinator)),
% apply(apply(b,X),Y))) -> (false)
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31]
% (eq)(apply(apply(apply(s,apply(t,X)),apply(t,X)),Y),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(Y,X))) -> (false)
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32]
% (eq)(apply(apply(apply(s,apply(s,X)),Y),X),apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,apply(Y,X)))) -> (false)
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33]
% (eq)(apply(apply(apply(s,X),X),Y),apply(combinator,apply(apply(X,Y),apply(X,Y))))
% -> (false)
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [34]
% (eq)(apply(apply(apply(apply(s,t),s),X),Y),apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,Y))) -> (false)
% Current number of equations to process: 156
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [35]
% (eq)(apply(apply(apply(s,t),apply(s,X)),X),apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,X))) -> (false)
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [36]
% (eq)(apply(apply(X,X),apply(X,X)),apply(apply(apply(s,t),apply(b,apply(
% apply(s,t),
% apply(b,combinator)))),X))
% -> (false)
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [37]
% (eq)(apply(apply(apply(s,t),apply(b,apply(X,X))),X),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(t,apply(X,X)))) ->
% (false)
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [38]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(s,t),apply(b,combinator)),
% apply(apply(apply(s,t),t),X))) -> (false)
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [39]
% (eq)(apply(apply(apply(s,t),apply(t,X)),apply(s,X)),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(X,apply(s,X)))) ->
% (false)
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [40]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(s,t),apply(b,apply(
% apply(s,t),
% apply(b,combinator)))),X))
% -> (false)
% Current number of equations to process: 164
% Current number of ordered equations: 0
% Current number of rules: 40
% Rule [40]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(s,t),apply(b,
% apply(apply(s,t),
% apply(b,combinator)))),X))
% -> (false) is composed into [40]
% (eq)(apply(apply(apply(s,X),X),X),apply(
% apply(
% apply(s,t),
% apply(b,
% apply(
% apply(s,t),
% apply(b,combinator)))),X))
% -> (true)
% Rule [39]
% (eq)(apply(apply(apply(s,t),apply(t,X)),apply(s,X)),apply(apply(
% apply(s,t),
% apply(b,combinator)),
% apply(X,apply(s,X))))
% -> (false) is composed into [39]
% (eq)(apply(apply(apply(s,t),apply(t,X)),
% apply(s,X)),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(X,apply(s,X)))) ->
% (true)
% Rule [38]
% (eq)(apply(apply(apply(s,X),X),X),apply(apply(apply(s,t),apply(b,combinator)),
% apply(apply(apply(s,t),t),X))) ->
% (false) is composed into [38]
% (eq)(apply(apply(apply(s,X),X),X),apply(
% apply(
% apply(s,t),
% apply(b,combinator)),
% apply(
% apply(
% apply(s,t),t),X)))
% -> (true)
% Rule [37]
% (eq)(apply(apply(apply(s,t),apply(b,apply(X,X))),X),apply(apply(
% apply(s,t),
% apply(b,combinator)),
% apply(t,apply(X,X))))
% -> (false) is composed into [37]
% (eq)(apply(apply(apply(s,t),apply(b,
% apply(X,X))),X),
% apply(apply(apply(s,t),apply(b,combinator)),
% apply(t,apply(X,X)))) -> (true)
% Rule [36]
% (eq)(apply(apply(X,X),apply(X,X)),apply(apply(apply(s,t),apply(b,
% apply(apply(s,t),
% apply(b,combinator)))),X))
% -> (false) is composed into [36]
% (eq)(apply(apply(X,X),apply(X,X)),apply(
% apply(
% apply(s,t),
% apply(b,
% apply(
% apply(s,t),
% apply(b,combinator)))),X))
% -> (true)
% Rule [35]
% (eq)(apply(apply(apply(s,t),apply(s,X)),X),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(X,X))) -> (false) is composed into
% [35]
% (eq)(apply(apply(apply(s,t),apply(s,X)),X),apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,X))) -> (true)
% Rule [34]
% (eq)(apply(apply(apply(apply(s,t),s),X),Y),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(X,Y))) -> (false) is composed into
% [34]
% (eq)(apply(apply(apply(apply(s,t),s),X),Y),apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,Y))) -> (true)
% Rule [33]
% (eq)(apply(apply(apply(s,X),X),Y),apply(combinator,apply(apply(X,Y),
% apply(X,Y)))) ->
% (false) is composed into [33]
% (eq)(apply(apply(apply(s,X),X),Y),apply(combinator,
% apply(
% apply(X,Y),
% apply(X,Y))))
% -> (true)
% Rule [32]
% (eq)(apply(apply(apply(s,apply(s,X)),Y),X),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(X,apply(Y,X)))) ->
% (false) is composed into [32]
% (eq)(apply(apply(apply(s,apply(s,X)),Y),X),
% apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,apply(Y,X)))) -> (true)
% Rule [31]
% (eq)(apply(apply(apply(s,apply(t,X)),apply(t,X)),Y),apply(apply(
% apply(s,t),
% apply(b,combinator)),
% apply(Y,X))) ->
% (false) is composed into [31]
% (eq)(apply(apply(apply(s,apply(t,X)),apply(t,X)),Y),
% apply(apply(apply(s,t),apply(b,combinator)),
% apply(Y,X))) -> (true)
% Rule [30]
% (eq)(apply(X,apply(Y,apply(apply(b,X),Y))),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(apply(b,X),Y))) ->
% (false) is composed into [30]
% (eq)(apply(X,apply(Y,apply(apply(b,X),Y))),
% apply(apply(apply(s,t),apply(b,combinator)),
% apply(apply(b,X),Y))) -> (true)
% Rule [29]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(s,t),apply(b,combinator)),
% apply(t,apply(X,Y)))) -> (false) is composed into
% [29]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(s,t),apply(b,combinator)),
% apply(t,apply(X,Y)))) -> (true)
% Rule [28]
% (eq)(apply(apply(b,combinator),apply(b,combinator)),apply(apply(
% apply(s,
% apply(s,t)),t),
% apply(b,combinator)))
% -> (false) is composed into [28]
% (eq)(apply(apply(b,combinator),apply(b,combinator)),
% apply(apply(apply(s,apply(s,t)),t),apply(b,combinator)))
% -> (true)
% Rule [27]
% (eq)(apply(X,X),apply(apply(apply(s,t),apply(b,combinator)),apply(t,
% apply(t,X))))
% -> (false) is composed into [27]
% (eq)(apply(X,X),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(t,apply(t,X)))) ->
% (true)
% Rule [26]
% (eq)(apply(apply(apply(s,t),apply(b,apply(X,X))),X),apply(apply(
% apply(s,t),
% apply(b,combinator)),
% apply(X,X))) ->
% (false) is composed into [26]
% (eq)(apply(apply(apply(s,t),apply(b,apply(X,X))),X),
% apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,X))) -> (true)
% Rule [25]
% (eq)(apply(apply(apply(s,t),t),apply(t,X)),apply(apply(apply(s,t),
% apply(b,combinator)),X))
% -> (false) is composed into [25]
% (eq)(apply(apply(apply(s,t),t),apply(t,X)),
% apply(apply(apply(s,t),apply(b,combinator)),X))
% -> (true)
% Rule [24]
% (eq)(apply(apply(apply(s,t),t),X),apply(apply(apply(s,t),apply(b,combinator)),X))
% -> (false) is composed into [24]
% (eq)(apply(apply(apply(s,t),t),X),apply(
% apply(
% apply(s,t),
% apply(b,combinator)),X))
% -> (true)
% Rule [23]
% (eq)(apply(apply(b,combinator),apply(b,combinator)),apply(apply(
% apply(s,t),
% apply(s,t)),
% apply(b,combinator)))
% -> (false) is composed into [23]
% (eq)(apply(apply(b,combinator),apply(b,combinator)),
% apply(apply(apply(s,t),apply(s,t)),apply(b,combinator)))
% -> (true)
% Rule [22]
% (eq)(apply(apply(apply(s,X),X),apply(b,combinator)),apply(apply(
% apply(s,
% apply(s,t)),X),
% apply(b,combinator)))
% -> (false) is composed into [22]
% (eq)(apply(apply(apply(s,X),X),apply(b,combinator)),
% apply(apply(apply(s,apply(s,t)),X),apply(b,combinator)))
% -> (true)
% Rule [21]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,Y))) -> (false) is composed into
% [21]
% (eq)(apply(apply(apply(s,X),X),Y),apply(apply(apply(s,t),apply(b,combinator)),
% apply(X,Y))) -> (true)
% Rule [20]
% (eq)(apply(X,X),apply(apply(apply(s,t),apply(b,combinator)),apply(t,X)))
% -> (false) is composed into [20]
% (eq)(apply(X,X),apply(apply(apply(s,t),
% apply(b,combinator)),
% apply(t,X))) -> (true)
% Rule [19]
% (eq)(apply(X,X),apply(apply(apply(s,t),apply(b,combinator)),X)) ->
% (false) is composed into [19]
% (eq)(apply(X,X),apply(apply(apply(s,t),
% apply(b,combinator)),X))
% -> (true)
% Rule [1] (eq)(Y,apply(combinator,Y)) -> (false) is composed into [1]
% (eq)(Y,
% apply(combinator,Y))
% -> (true)
% New rule produced : [41] (false) -> (true)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 164
% Current number of ordered equations: 0
% Current number of rules: 41
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 10 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(apply(t,X),Y) -> apply(Y,X); trace = in the starting set
% [4] apply(apply(apply(b,X),Y),Z) -> apply(X,apply(Y,Z)); trace = in the starting set
% [5] apply(apply(X,Z),apply(Y,Z)) <-> apply(apply(apply(s,X),Y),Z); trace = in the starting set
% [7] apply(apply(X,Y),Y) <-> apply(apply(apply(s,t),X),Y); trace = Cp of 5 and 3
% [16] apply(X,apply(Y,Y)) <-> apply(apply(apply(s,t),apply(b,X)),Y); trace = Cp of 7 and 4
% [19] (eq)(apply(X,X),apply(apply(apply(s,t),apply(b,combinator)),X)) ->
% (false); trace = Cp of 16 and 1
% [22] (eq)(apply(apply(apply(s,X),X),apply(b,combinator)),apply(apply(
% apply(s,
% apply(s,t)),X),
% apply(b,combinator)))
% -> (false); trace = Cp of 19 and 5
% [41] (false) -> (true); trace = Cp of 22 and 2
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.110000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------