TSTP Solution File: GRP548-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP548-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n152.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 00:23:27 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 : GRP548-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n152.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 18:46:28 CDT 2014
% % CPUTime : 1.12
% Processing problem /tmp/CiME_64363_n152.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a,identity : constant; inverse : 1; multiply : 2; divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C;
% multiply(A,B) = divide(A,divide(identity,B));
% inverse(A) = divide(identity,A);
% identity = divide(A,A);
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% divide lr_lex;
% identity lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > divide > identity > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% inverse mul;
% multiply mul;
% divide mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > divide > identity = a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(a,b) = multiply(b,a);"
% ;
% (*
% 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 = { divide(divide(identity,divide(A,B)),divide(
% divide(B,C),A))
% = C,
% multiply(A,B) = divide(A,divide(identity,B)),
% inverse(A) = divide(identity,A),
% identity = divide(A,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(a,b) = multiply(b,a) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] divide(A,A) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 1
% New rule produced : [2] inverse(A) -> divide(identity,A)
% 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) -> divide(A,divide(identity,B))
% The conjecture has been reduced.
% Conjecture is now:
% divide(a,divide(identity,b)) = divide(b,divide(identity,a))
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4] divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) -> C
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] divide(identity,divide(divide(A,B),A)) -> B
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] divide(identity,divide(identity,A)) -> A
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7] divide(divide(B,A),B) -> divide(identity,divide(A,identity))
% Rule [5] divide(identity,divide(divide(A,B),A)) -> B collapsed.
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 6
% Rule [7] divide(divide(B,A),B) -> divide(identity,divide(A,identity)) is composed into
% [7] divide(divide(B,A),B) -> divide(identity,A)
% New rule produced : [8] divide(B,identity) -> B
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [9] divide(A,divide(A,B)) -> B
% Rule [6] divide(identity,divide(identity,A)) -> A collapsed.
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [10] divide(divide(identity,A),divide(B,A)) -> divide(identity,B)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [11] divide(identity,divide(B,A)) <-> divide(A,B)
% Current number of equations to process: 15
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [12] divide(A,B) <-> divide(identity,divide(B,A))
% Rule [7] divide(divide(B,A),B) -> divide(identity,A) collapsed.
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [13] divide(divide(A,B),divide(identity,B)) -> A
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [14]
% divide(identity,divide(divide(identity,A),divide(identity,divide(A,B)))) -> B
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [15] divide(A,divide(divide(B,C),divide(B,A))) -> C
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [16] divide(divide(identity,divide(A,B)),divide(B,A)) -> identity
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [17] divide(divide(identity,divide(A,B)),C) <-> divide(divide(B,C),A)
% Current number of equations to process: 8
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [18] divide(divide(B,C),A) <-> divide(divide(identity,divide(A,B)),C)
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [19] divide(identity,B) <-> divide(A,divide(B,divide(identity,A)))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 12
% Current number of ordered equations: 3
% Current number of rules: 16
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 8 rules have been used:
% [1]
% divide(A,A) -> identity; trace = in the starting set
% [3] multiply(A,B) -> divide(A,divide(identity,B)); trace = in the starting set
% [4] divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) -> C; trace = in the starting set
% [5] divide(identity,divide(divide(A,B),A)) -> B; trace = Cp of 4 and 1
% [6] divide(identity,divide(identity,A)) -> A; trace = Cp of 5 and 1
% [9] divide(A,divide(A,B)) -> B; trace = Cp of 6 and 4
% [10] divide(divide(identity,A),divide(B,A)) -> divide(identity,B); trace = Cp of 6 and 4
% [19] divide(identity,B) <-> divide(A,divide(B,divide(identity,A))); trace = Cp of 10 and 9
% % 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
%------------------------------------------------------------------------------