TSTP Solution File: COL015-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL015-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n148.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 00:19:41 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 : COL015-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n148.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 17:22:08 CDT 2014
% % CPUTime : 1.12
% Processing problem /tmp/CiME_16508_n148.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " combinator,q,m : constant; apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(m,X) = apply(X,X);
% apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z));
% ";
%
% let s1 = status F "
% combinator lr_lex;
% q lr_lex;
% apply lr_lex;
% m lr_lex;
% ";
%
% let p1 = precedence F "
% apply > m > q > combinator";
%
% let s2 = status F "
% combinator mul;
% q mul;
% apply mul;
% m mul;
% ";
%
% let p2 = precedence F "
% apply > m = q = 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(m,X) = apply(X,X),
% apply(apply(apply(q,X),Y),Z) =
% apply(Y,apply(X,Z)) } (2 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [combinator] = 1;
% [q] = 2;
% [m] = 3;
% [apply](x1,x2) = 1 + x1 + x2;
% Chosen ordering : RPO
% 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(Y,apply(X,Z)) <-> apply(apply(apply(q,X),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 5
% New rule produced : [6] apply(apply(apply(q,X),Y),Z) <-> apply(Y,apply(X,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% 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] (eq)(apply(X,Y),apply(apply(apply(q,X),combinator),Y)) -> (false)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9] (eq)(apply(m,X),apply(apply(apply(q,X),combinator),X)) -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [10] (eq)(apply(q,X),apply(apply(apply(m,q),combinator),X)) -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] (eq)(apply(X,X),apply(apply(apply(q,m),combinator),X)) -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12]
% (eq)(apply(apply(apply(q,X),Y),Z),apply(apply(apply(q,Y),combinator),
% apply(X,Z))) -> (false)
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(q,X),q),Y),combinator),Z))
% -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced :
% [14]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(q,Y),apply(apply(q,X),combinator)),Z))
% -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] (eq)(apply(m,q),apply(apply(apply(m,q),combinator),q)) -> (false)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (false)
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% (eq)(apply(apply(apply(q,X),q),Y),apply(apply(apply(m,q),combinator),
% apply(X,Y))) -> (false)
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 17
% Rule [17]
% (eq)(apply(apply(apply(q,X),q),Y),apply(apply(apply(m,q),combinator),
% apply(X,Y))) -> (false) is composed into
% [17]
% (eq)(apply(apply(apply(q,X),q),Y),apply(apply(apply(m,q),combinator),
% apply(X,Y))) -> (true)
% Rule [16] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (false) is composed into
% [16] (eq)(apply(m,X),apply(combinator,apply(X,X))) -> (true)
% Rule [15] (eq)(apply(m,q),apply(apply(apply(m,q),combinator),q)) -> (false) is composed into
% [15] (eq)(apply(m,q),apply(apply(apply(m,q),combinator),q)) -> (true)
% Rule [14]
% (eq)(apply(X,apply(Y,Z)),apply(apply(apply(q,Y),apply(apply(q,X),combinator)),Z))
% -> (false) is composed into [14]
% (eq)(apply(X,apply(Y,Z)),apply(apply(
% apply(q,Y),
% apply(
% apply(q,X),combinator)),Z))
% -> (true)
% Rule [13]
% (eq)(apply(apply(X,Y),Z),apply(apply(apply(apply(apply(q,X),q),Y),combinator),Z))
% -> (false) is composed into [13]
% (eq)(apply(apply(X,Y),Z),apply(apply(
% apply(
% apply(
% apply(q,X),q),Y),combinator),Z))
% -> (true)
% Rule [12]
% (eq)(apply(apply(apply(q,X),Y),Z),apply(apply(apply(q,Y),combinator),
% apply(X,Z))) -> (false) is composed into
% [12]
% (eq)(apply(apply(apply(q,X),Y),Z),apply(apply(apply(q,Y),combinator),
% apply(X,Z))) -> (true)
% Rule [11] (eq)(apply(X,X),apply(apply(apply(q,m),combinator),X)) -> (false) is composed into
% [11] (eq)(apply(X,X),apply(apply(apply(q,m),combinator),X)) -> (true)
% Rule [10] (eq)(apply(q,X),apply(apply(apply(m,q),combinator),X)) -> (false) is composed into
% [10] (eq)(apply(q,X),apply(apply(apply(m,q),combinator),X)) -> (true)
% Rule [9] (eq)(apply(m,X),apply(apply(apply(q,X),combinator),X)) -> (false) is composed into
% [9] (eq)(apply(m,X),apply(apply(apply(q,X),combinator),X)) -> (true)
% Rule [8] (eq)(apply(X,Y),apply(apply(apply(q,X),combinator),Y)) -> (false) is composed into
% [8] (eq)(apply(X,Y),apply(apply(apply(q,X),combinator),Y)) -> (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 : [18] (false) -> (true)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 18
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [1]
% (eq)(Y,apply(combinator,Y)) -> (false); trace = in the starting set
% [3] apply(X,X) <-> apply(m,X); trace = in the starting set
% [4] apply(m,X) <-> apply(X,X); trace = in the starting set
% [5] apply(Y,apply(X,Z)) <-> apply(apply(apply(q,X),Y),Z); trace = in the starting set
% [8] (eq)(apply(X,Y),apply(apply(apply(q,X),combinator),Y)) -> (false); trace = Cp of 5 and 1
% [11] (eq)(apply(X,X),apply(apply(apply(q,m),combinator),X)) -> (false); trace = Cp of 8 and 4
% [18] (false) -> (true); trace = Cp of 11 and 3
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.010000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------