TSTP Solution File: GRP552-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP552-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n168.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 1.14s
% Output : Refutation 1.14s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP552-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n168.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 19:05:43 CDT 2014
% % CPUTime : 1.14
% Processing problem /tmp/CiME_43125_n168.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,A),divide(divide(divide(B,A),C),B)) = 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,A),divide(divide(
% divide(B,A),C),B))
% = 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,A),divide(divide(divide(B,A),C),B)) -> C
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [5] divide(divide(identity,A),divide(identity,B)) <-> divide(B,A)
% Current number of equations to process: 4
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [6] divide(B,A) <-> divide(divide(identity,A),divide(identity,B))
% Rule [4] divide(divide(identity,A),divide(divide(divide(B,A),C),B)) -> C
% collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [7]
% divide(divide(identity,A),divide(divide(identity,B),divide(identity,divide(
% divide(B,A),C))))
% -> C
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [8] divide(identity,divide(identity,A)) <-> divide(A,identity)
% Current number of equations to process: 4
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced :
% [9] divide(A,identity) <-> divide(identity,divide(identity,A))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [10]
% divide(identity,divide(identity,divide(identity,A))) -> divide(identity,A)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [11]
% divide(identity,divide(divide(identity,A),divide(identity,divide(divide(A,identity),B))))
% -> B
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [12] divide(divide(identity,A),divide(divide(identity,B),A)) -> B
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [13]
% divide(divide(identity,A),divide(B,identity)) <->
% divide(divide(identity,C),divide(identity,divide(divide(C,A),B)))
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [14]
% divide(divide(identity,C),divide(identity,divide(divide(C,A),B))) <->
% divide(divide(identity,A),divide(B,identity))
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [15]
% divide(divide(identity,divide(identity,A)),divide(identity,divide(identity,B)))
% -> divide(A,B)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [16] divide(identity,divide(A,identity)) -> divide(identity,A)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [17]
% divide(divide(identity,A),divide(B,identity)) <->
% divide(divide(identity,B),A)
% Current number of equations to process: 9
% Current number of ordered equations: 3
% Current number of rules: 16
% New rule produced :
% [18]
% divide(B,divide(identity,A)) <->
% divide(divide(A,identity),divide(identity,B))
% Current number of equations to process: 9
% Current number of ordered equations: 2
% Current number of rules: 17
% New rule produced :
% [19]
% divide(divide(identity,B),A) <->
% divide(divide(identity,A),divide(B,identity))
% Current number of equations to process: 9
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [20]
% divide(divide(A,identity),divide(identity,B)) <->
% divide(B,divide(identity,A))
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [21]
% divide(divide(identity,A),divide(identity,B)) <->
% divide(B,divide(identity,divide(identity,A)))
% Current number of equations to process: 12
% Current number of ordered equations: 3
% Current number of rules: 20
% New rule produced :
% [22]
% divide(divide(identity,A),divide(identity,B)) <->
% divide(divide(identity,divide(identity,B)),A)
% Current number of equations to process: 12
% Current number of ordered equations: 2
% Current number of rules: 21
% New rule produced :
% [23]
% divide(B,divide(identity,divide(identity,A))) <->
% divide(divide(identity,A),divide(identity,B))
% Current number of equations to process: 12
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [24]
% divide(divide(identity,divide(identity,B)),A) <->
% divide(divide(identity,A),divide(identity,B))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 23
% Rule [22]
% divide(divide(identity,A),divide(identity,B)) <->
% divide(divide(identity,divide(identity,B)),A) is composed into [22]
% divide(
% divide(identity,A),
% divide(identity,B))
% <->
% divide(B,A)
% Rule [21]
% divide(divide(identity,A),divide(identity,B)) <->
% divide(B,divide(identity,divide(identity,A))) is composed into [21]
% divide(
% divide(identity,A),
% divide(identity,B))
% <->
% divide(B,A)
% Rule [9] divide(A,identity) <-> divide(identity,divide(identity,A)) is composed into
% [9] divide(A,identity) -> A
% New rule produced : [25] divide(identity,divide(identity,A)) -> A
% Rule [8] divide(identity,divide(identity,A)) <-> divide(A,identity)
% collapsed.
% Rule
% [10]
% divide(identity,divide(identity,divide(identity,A))) -> divide(identity,A)
% collapsed.
% Rule
% [15]
% divide(divide(identity,divide(identity,A)),divide(identity,divide(identity,B)))
% -> divide(A,B) collapsed.
% Rule
% [23]
% divide(B,divide(identity,divide(identity,A))) <->
% divide(divide(identity,A),divide(identity,B)) collapsed.
% Rule
% [24]
% divide(divide(identity,divide(identity,B)),A) <->
% divide(divide(identity,A),divide(identity,B)) collapsed.
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [26]
% divide(identity,divide(A,divide(identity,divide(divide(identity,A),B)))) -> B
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [27]
% divide(identity,divide(divide(identity,A),divide(identity,divide(A,B)))) -> B
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [28] divide(A,divide(A,B)) -> B
% Rule [25] divide(identity,divide(identity,A)) -> A collapsed.
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [29]
% divide(divide(identity,B),divide(identity,divide(B,A))) -> divide(identity,A)
% Rule
% [27]
% divide(identity,divide(divide(identity,A),divide(identity,divide(A,B)))) -> B
% collapsed.
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [30] divide(divide(identity,B),divide(A,B)) -> divide(identity,A)
% Rule [12] divide(divide(identity,A),divide(divide(identity,B),A)) -> B
% collapsed.
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [31] divide(A,divide(identity,divide(divide(B,A),C))) -> divide(B,C)
% Rule
% [26]
% divide(identity,divide(A,divide(identity,divide(divide(identity,A),B)))) -> B
% collapsed.
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [32] divide(divide(identity,A),B) <-> divide(divide(identity,B),A)
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [33] divide(A,divide(identity,B)) <-> divide(B,divide(identity,A))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 23
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 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,A),divide(divide(divide(B,A),C),B)) -> C; trace = in the starting set
% [5] divide(divide(identity,A),divide(identity,B)) <-> divide(B,A); trace = Cp of 4 and 1
% [8] divide(identity,divide(identity,A)) <-> divide(A,identity); trace = Cp of 5 and 1
% [18] divide(B,divide(identity,A)) <->
% divide(divide(A,identity),divide(identity,B)); trace = Cp of 8 and 5
% [33] divide(A,divide(identity,B)) <-> divide(B,divide(identity,A)); trace = Cp of 18 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.030000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------