TSTP Solution File: LCL161-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LCL161-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n070.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 00:27:14 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 : LCL161-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n070.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 : Fri Jun 6 02:26:54 CDT 2014
% % CPUTime : 1.12
% Processing problem /tmp/CiME_29928_n070.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " xor : infix commutative; and_star : AC; x,falsehood,truth : constant; implies : 2; not : 1;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% not(X) = X xor truth;
% X xor falsehood = X;
% X xor X = falsehood;
% X and_star truth = X;
% X and_star falsehood = falsehood;
% (truth xor X) and_star X = falsehood;
% X xor (truth xor Y) = (X xor truth) xor Y;
% (((truth xor X) and_star Y) xor truth) and_star Y = (((truth xor Y) and_star X) xor truth) and_star X;
% not(truth) = falsehood;
% implies(X,Y) = truth xor (X and_star (truth xor Y));
% ";
%
% let s1 = status F "
% x lr_lex;
% implies lr_lex;
% falsehood lr_lex;
% truth lr_lex;
% not lr_lex;
% and_star mul;
% xor mul;
% ";
%
% let p1 = precedence F "
% implies > xor > not > and_star > truth > falsehood > x";
%
% let s2 = status F "
% x mul;
% implies mul;
% and_star mul;
% falsehood mul;
% xor mul;
% truth mul;
% not mul;
% ";
%
% let p2 = precedence F "
% implies > xor > not > and_star > truth = falsehood = x";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " implies(truth,x) = x;"
% ;
% (*
% 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 = { not(X) = truth xor X,
% falsehood xor X = X,
% X xor X = falsehood,
% truth and_star X = X,
% falsehood and_star X = falsehood,
% (truth xor X) and_star X = falsehood,
% (truth xor Y) xor X = (truth xor X) xor Y,
% (((truth xor X) and_star Y) xor truth) and_star Y
% =
% (((truth xor Y) and_star X) xor truth) and_star X,
% not(truth) = falsehood,
% implies(X,Y) =
% ((truth xor Y) and_star X) xor truth }
% (10 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(truth,x) = x } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] not(truth) -> falsehood
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 1
% New rule produced : [2] X xor X -> falsehood
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 2
% New rule produced : [3] falsehood xor X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 3
% New rule produced : [4] truth and_star X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 4
% New rule produced : [5] falsehood and_star X -> falsehood
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 5
% New rule produced : [6] truth xor X -> not(X)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] not(X) and_star X -> falsehood
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 7
% New rule produced : [8] not(X) xor Y <-> not(Y) xor X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 8
% New rule produced : [9] implies(X,Y) -> not(not(Y) and_star X)
% The conjecture has been reduced.
% Conjecture is now:
% not(not(x)) = x
%
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 9
% New rule produced :
% [10] not(not(X) and_star Y) and_star Y <-> not(not(Y) and_star X) and_star X
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 10
% New rule produced : [11] not(falsehood) -> truth
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 11
% New rule produced : [12] not(not(X)) -> X
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 12
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 4 rules have been used:
% [1]
% not(truth) -> falsehood; trace = in the starting set
% [8] not(X) xor Y <-> not(Y) xor X; trace = in the starting set
% [9] implies(X,Y) -> not(not(Y) and_star X); trace = in the starting set
% [12] not(not(X)) -> X; trace = Cp of 8 and 1
% % 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
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