TSTP Solution File: RNG023-7 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : RNG023-7 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n123.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 00:31:44 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 : RNG023-7 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n123.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 17:32:08 CDT 2014
% % CPUTime : 1.12
% Processing problem /tmp/CiME_60481_n123.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " add : AC; y,x,additive_identity : constant; commutator : 2; associator : 3; additive_inverse : 1; multiply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% additive_identity add X = X;
% X add additive_identity = X;
% multiply(additive_identity,X) = additive_identity;
% multiply(X,additive_identity) = additive_identity;
% additive_inverse(X) add X = additive_identity;
% X add additive_inverse(X) = additive_identity;
% additive_inverse(additive_inverse(X)) = X;
% multiply(X,Y add Z) = multiply(X,Y) add multiply(X,Z);
% multiply(X add Y,Z) = multiply(X,Z) add multiply(Y,Z);
% multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y));
% multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y));
% associator(X,Y,Z) = multiply(multiply(X,Y),Z) add additive_inverse(multiply(X,multiply(Y,Z)));
% commutator(X,Y) = multiply(Y,X) add additive_inverse(multiply(X,Y));
% multiply(additive_inverse(X),additive_inverse(Y)) = multiply(X,Y);
% multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y));
% multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y));
% multiply(X,Y add additive_inverse(Z)) = multiply(X,Y) add additive_inverse(multiply(X,Z));
% multiply(X add additive_inverse(Y),Z) = multiply(X,Z) add additive_inverse(multiply(Y,Z));
% multiply(additive_inverse(X),Y add Z) = additive_inverse(multiply(X,Y)) add additive_inverse(multiply(X,Z));
% multiply(X add Y,additive_inverse(Z)) = additive_inverse(multiply(X,Z)) add additive_inverse(multiply(Y,Z));
% ";
%
% let s1 = status F "
% y lr_lex;
% x lr_lex;
% commutator lr_lex;
% associator lr_lex;
% additive_inverse lr_lex;
% additive_identity lr_lex;
% multiply mul;
% add mul;
% ";
%
% let p1 = precedence F "
% associator > commutator > multiply > additive_inverse > add > additive_identity > x > y";
%
% let s2 = status F "
% y mul;
% x mul;
% commutator mul;
% associator mul;
% additive_inverse mul;
% multiply mul;
% add mul;
% additive_identity mul;
% ";
%
% let p2 = precedence F "
% associator > commutator > multiply > additive_inverse > add > additive_identity = x = y";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " associator(x,x,y) = additive_identity;"
% ;
% (*
% 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 = { additive_identity add X = X,
% additive_identity add X = X,
% multiply(additive_identity,X) =
% additive_identity,
% multiply(X,additive_identity) =
% additive_identity,
% additive_inverse(X) add X = additive_identity,
% additive_inverse(X) add X = additive_identity,
% additive_inverse(additive_inverse(X)) = X,
% multiply(X,Y add Z) =
% multiply(X,Y) add multiply(X,Z),
% multiply(X add Y,Z) =
% multiply(X,Z) add multiply(Y,Z),
% multiply(multiply(X,Y),Y) =
% multiply(X,multiply(Y,Y)),
% multiply(multiply(X,X),Y) =
% multiply(X,multiply(X,Y)),
% associator(X,Y,Z) =
% additive_inverse(multiply(X,multiply(Y,Z))) add
% multiply(multiply(X,Y),Z),
% commutator(X,Y) =
% additive_inverse(multiply(X,Y)) add multiply(Y,X),
% multiply(additive_inverse(X),additive_inverse(Y))
% = multiply(X,Y),
% multiply(additive_inverse(X),Y) =
% additive_inverse(multiply(X,Y)),
% multiply(X,additive_inverse(Y)) =
% additive_inverse(multiply(X,Y)),
% multiply(X,additive_inverse(Z) add Y) =
% additive_inverse(multiply(X,Z)) add multiply(X,Y),
% multiply(additive_inverse(Y) add X,Z) =
% additive_inverse(multiply(Y,Z)) add multiply(X,Z),
% multiply(additive_inverse(X),Y add Z) =
% additive_inverse(multiply(X,Y)) add additive_inverse(
% multiply(X,Z)),
% multiply(X add Y,additive_inverse(Z)) =
% additive_inverse(multiply(X,Z)) add additive_inverse(
% multiply(Y,Z)) }
% (20 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 = { associator(x,x,y) = additive_identity }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] additive_inverse(additive_inverse(X)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 17
% Current number of rules: 1
% New rule produced : [2] additive_identity add X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 16
% Current number of rules: 2
% New rule produced : [3] multiply(X,additive_identity) -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 15
% Current number of rules: 3
% New rule produced : [4] multiply(additive_identity,X) -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 4
% New rule produced : [5] additive_inverse(X) add X -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 5
% New rule produced :
% [6] multiply(X,additive_inverse(Y)) -> additive_inverse(multiply(X,Y))
% Current number of equations to process: 2
% Current number of ordered equations: 10
% Current number of rules: 6
% New rule produced :
% [7] multiply(additive_inverse(X),Y) -> additive_inverse(multiply(X,Y))
% Current number of equations to process: 1
% Current number of ordered equations: 9
% Current number of rules: 7
% New rule produced :
% [8] multiply(multiply(X,Y),Y) -> multiply(X,multiply(Y,Y))
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 8
% New rule produced :
% [9] multiply(multiply(X,X),Y) -> multiply(X,multiply(X,Y))
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 9
% New rule produced :
% [10] commutator(X,Y) -> additive_inverse(multiply(X,Y)) add multiply(Y,X)
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 10
% New rule produced :
% [11] multiply(X,Y add Z) -> multiply(X,Y) add multiply(X,Z)
% Current number of equations to process: 1
% Current number of ordered equations: 4
% Current number of rules: 11
% New rule produced :
% [12] multiply(X add Y,Z) -> multiply(X,Z) add multiply(Y,Z)
% Current number of equations to process: 1
% Current number of ordered equations: 2
% Current number of rules: 12
% New rule produced :
% [13]
% additive_inverse(multiply(X,Y) add multiply(X,Z)) ->
% additive_inverse(multiply(X,Y)) add additive_inverse(multiply(X,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 13
% New rule produced :
% [14]
% additive_inverse(multiply(X,Z) add multiply(Y,Z)) ->
% additive_inverse(multiply(X,Z)) add additive_inverse(multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [15]
% associator(X,Y,Z) ->
% additive_inverse(multiply(X,multiply(Y,Z))) add multiply(multiply(X,Y),Z)
% 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: 15
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 1 rules have been used:
% [15]
% associator(X,Y,Z) ->
% additive_inverse(multiply(X,multiply(Y,Z))) add multiply(multiply(X,Y),Z); trace = in the starting set
% % 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
%------------------------------------------------------------------------------