TSTP Solution File: LCL134-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LCL134-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n034.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 16127.75MB
% OS : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Tue Jun 10 00:27:11 EDT 2014
% Result : Unsatisfiable 1.13s
% Output : Refutation 1.13s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : LCL134-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n034.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 16127.75MB
% % OS : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Fri Jun 6 01:31:23 CDT 2014
% % CPUTime : 1.13
% Processing problem /tmp/CiME_62605_n034.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " x,truth : constant; not : 1; implies : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% implies(truth,X) = X;
% implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth;
% implies(implies(X,Y),Y) = implies(implies(Y,X),X);
% implies(implies(not(X),not(Y)),implies(Y,X)) = truth;
% ";
%
% let s1 = status F "
% x lr_lex;
% not lr_lex;
% implies lr_lex;
% truth lr_lex;
% ";
%
% let p1 = precedence F "
% implies > not > truth > x";
%
% let s2 = status F "
% x mul;
% not mul;
% implies mul;
% truth mul;
% ";
%
% let p2 = precedence F "
% implies > not > truth = x";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " implies(x,truth) = truth;"
% ;
% (*
% 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 = { implies(truth,X) = X,
% implies(implies(X,Y),implies(implies(Y,Z),
% implies(X,Z))) = truth,
% implies(implies(X,Y),Y) =
% implies(implies(Y,X),X),
% implies(implies(not(X),not(Y)),implies(Y,X)) =
% truth } (4 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { implies(x,truth) = truth } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] implies(truth,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced : [2] implies(implies(X,Y),Y) <-> implies(implies(Y,X),X)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 2
% New rule produced : [3] implies(implies(not(X),not(Y)),implies(Y,X)) -> truth
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) -> truth
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] implies(implies(X,truth),truth) -> implies(X,X)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] implies(implies(not(X),not(truth)),X) -> truth
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] implies(X,implies(implies(X,Y),Y)) -> truth
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8] implies(implies(implies(implies(X,Y),Y),X),truth) -> truth
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9] implies(implies(X,truth),implies(Y,implies(X,Y))) -> truth
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] implies(implies(X,not(not(X))),truth) -> truth
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 10
% Rule [5] implies(implies(X,truth),truth) -> implies(X,X) is composed into
% [5] implies(implies(X,truth),truth) -> truth
% New rule produced : [11] implies(X,X) -> truth
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] implies(X,implies(implies(Y,X),X)) -> truth
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] implies(X,truth) -> truth
% Rule [5] implies(implies(X,truth),truth) -> truth collapsed.
% Rule [8] implies(implies(implies(implies(X,Y),Y),X),truth) -> truth
% collapsed.
% Rule [9] implies(implies(X,truth),implies(Y,implies(X,Y))) -> truth
% collapsed.
% Rule [10] implies(implies(X,not(not(X))),truth) -> truth collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 9
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 6 rules have been used:
% [1]
% implies(truth,X) -> X; trace = in the starting set
% [2] implies(implies(X,Y),Y) <-> implies(implies(Y,X),X); trace = in the starting set
% [4] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) -> truth; trace = in the starting set
% [5] implies(implies(X,truth),truth) -> truth; trace = Cp of 2 and 1
% [7] implies(X,implies(implies(X,Y),Y)) -> truth; trace = Cp of 4 and 1
% [13] implies(X,truth) -> truth; trace = Cp of 7 and 5
% % 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
%------------------------------------------------------------------------------