TSTP Solution File: GRP573-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP573-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n164.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 00:23:30 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 : GRP573-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n164.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 20:41:08 CDT 2014
% % CPUTime : 1.12
% Processing problem /tmp/CiME_28051_n164.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a1,identity : constant; inverse : 1; multiply : 2; double_divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B;
% multiply(A,B) = double_divide(double_divide(B,A),identity);
% inverse(A) = double_divide(A,identity);
% identity = double_divide(A,inverse(A));
% ";
%
% let s1 = status F "
% a1 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% identity lr_lex;
% double_divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > double_divide > inverse > identity > a1";
%
% let s2 = status F "
% a1 mul;
% inverse mul;
% multiply mul;
% identity mul;
% double_divide mul;
% ";
%
% let p2 = precedence F "
% multiply > double_divide > inverse > identity = a1";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(inverse(a1),a1) = 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 = { double_divide(double_divide(A,double_divide(
% double_divide(B,
% double_divide(C,A)),
% double_divide(C,identity))),
% double_divide(identity,identity)) = B,
% multiply(A,B) =
% double_divide(double_divide(B,A),identity),
% inverse(A) = double_divide(A,identity),
% identity = double_divide(A,inverse(A)) }
% (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 = { multiply(inverse(a1),a1) = identity }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] double_divide(A,identity) -> inverse(A)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced : [2] double_divide(A,inverse(A)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 2
% New rule produced : [3] multiply(A,B) -> inverse(double_divide(B,A))
% The conjecture has been reduced.
% Conjecture is now:
% inverse(identity) = identity
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4]
% double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),
% inverse(C))),inverse(identity)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [5]
% double_divide(double_divide(inverse(A),double_divide(inverse(B),inverse(A))),
% inverse(identity)) -> B
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] double_divide(inverse(inverse(inverse(A))),inverse(identity)) -> A
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% double_divide(double_divide(identity,double_divide(double_divide(A,inverse(B)),
% inverse(B))),inverse(identity)) -> A
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% double_divide(double_divide(inverse(identity),A),inverse(identity)) ->
% inverse(inverse(A))
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% double_divide(double_divide(identity,double_divide(identity,inverse(A))),
% inverse(identity)) -> A
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10]
% double_divide(identity,double_divide(double_divide(A,inverse(B)),inverse(B)))
% <->
% double_divide(double_divide(identity,double_divide(A,inverse(identity))),
% inverse(identity))
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 10
% Rule [10]
% double_divide(identity,double_divide(double_divide(A,inverse(B)),
% inverse(B))) <->
% double_divide(double_divide(identity,double_divide(A,inverse(identity))),
% inverse(identity)) is composed into [10]
% double_divide(identity,double_divide(
% double_divide(A,
% inverse(B)),
% inverse(B)))
% <->
% double_divide(identity,double_divide(
% double_divide(A,
% inverse(a1)),
% inverse(a1)))
% New rule produced :
% [11]
% double_divide(double_divide(identity,double_divide(A,inverse(identity))),
% inverse(identity)) <->
% double_divide(identity,double_divide(double_divide(A,inverse(B)),inverse(B)))
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] inverse(inverse(inverse(inverse(identity)))) -> identity
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% double_divide(inverse(inverse(identity)),inverse(identity)) ->
% inverse(inverse(identity))
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 13
% Rule [10]
% double_divide(identity,double_divide(double_divide(A,inverse(B)),
% inverse(B))) <->
% double_divide(identity,double_divide(double_divide(A,inverse(a1)),
% inverse(a1))) is composed into [10]
% double_divide(identity,
% double_divide(
% double_divide(A,
% inverse(B)),
% inverse(B))) ->
% inverse(inverse(
% inverse(A)))
% New rule produced :
% [14]
% double_divide(identity,double_divide(double_divide(A,inverse(a1)),inverse(a1)))
% -> inverse(inverse(inverse(A)))
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] inverse(inverse(double_divide(inverse(A),inverse(identity)))) -> A
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% double_divide(inverse(identity),A) ->
% inverse(inverse(inverse(inverse(inverse(A)))))
% Rule
% [8]
% double_divide(double_divide(inverse(identity),A),inverse(identity)) ->
% inverse(inverse(A)) collapsed.
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [17] inverse(inverse(identity)) -> identity
% Rule [12] inverse(inverse(inverse(inverse(identity)))) -> identity collapsed.
% Rule
% [13]
% double_divide(inverse(inverse(identity)),inverse(identity)) ->
% inverse(inverse(identity)) collapsed.
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [18] inverse(identity) -> identity
% Rule
% [4]
% double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),
% inverse(C))),inverse(identity)) -> B collapsed.
% Rule
% [5]
% double_divide(double_divide(inverse(A),double_divide(inverse(B),inverse(A))),
% inverse(identity)) -> B collapsed.
% Rule [6] double_divide(inverse(inverse(inverse(A))),inverse(identity)) -> A
% collapsed.
% Rule
% [7]
% double_divide(double_divide(identity,double_divide(double_divide(A,inverse(B)),
% inverse(B))),inverse(identity)) -> A
% collapsed.
% Rule
% [9]
% double_divide(double_divide(identity,double_divide(identity,inverse(A))),
% inverse(identity)) -> A collapsed.
% Rule
% [11]
% double_divide(double_divide(identity,double_divide(A,inverse(identity))),
% inverse(identity)) <->
% double_divide(identity,double_divide(double_divide(A,inverse(B)),inverse(B)))
% collapsed.
% Rule [15] inverse(inverse(double_divide(inverse(A),inverse(identity)))) -> A
% collapsed.
% Rule
% [16]
% double_divide(inverse(identity),A) ->
% inverse(inverse(inverse(inverse(inverse(A))))) collapsed.
% Rule [17] inverse(inverse(identity)) -> identity collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 6
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 9 rules have been used:
% [1]
% double_divide(A,identity) -> inverse(A); trace = in the starting set
% [2] double_divide(A,inverse(A)) -> identity; trace = in the starting set
% [3] multiply(A,B) -> inverse(double_divide(B,A)); trace = in the starting set
% [4] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),
% inverse(C))),inverse(identity)) -> B; trace = in the starting set
% [5] double_divide(double_divide(inverse(A),double_divide(inverse(B),inverse(A))),
% inverse(identity)) -> B; trace = Cp of 4 and 2
% [6] double_divide(inverse(inverse(inverse(A))),inverse(identity)) -> A; trace = Cp of 5 and 2
% [7] double_divide(double_divide(identity,double_divide(double_divide(A,
% inverse(B)),inverse(B))),
% inverse(identity)) -> A; trace = Cp of 4 and 1
% [8] double_divide(double_divide(inverse(identity),A),inverse(identity)) ->
% inverse(inverse(A)); trace = Cp of 6 and 5
% [18] inverse(identity) -> identity; trace = Cp of 8 and 7
% % 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
%------------------------------------------------------------------------------