TSTP Solution File: GRP584-1 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP584-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n121.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 00:23:31 EDT 2014
% Result : Unsatisfiable 1.13s
% Output : Refutation 1.13s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP584-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n121.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 21:03:13 CDT 2014
% % CPUTime : 1.13
% Processing problem /tmp/CiME_23188_n121.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a,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(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C;
% 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 "
% b lr_lex;
% a lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% double_divide lr_lex;
% identity lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > double_divide > inverse > identity > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% inverse mul;
% multiply mul;
% double_divide mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% multiply > double_divide > inverse > 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 = { double_divide(double_divide(A,double_divide(
% double_divide(identity,B),
% double_divide(C,
% double_divide(B,A)))),
% double_divide(identity,identity)) = C,
% 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(a,b) = multiply(b,a) }
% (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(double_divide(b,a)) = inverse(double_divide(a,b))
%
% 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(identity,B),
% double_divide(C,double_divide(B,A)))),inverse(identity))
% -> C
% 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(double_divide(identity,A),
% inverse(B))),inverse(identity)) -> B
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% double_divide(inverse(inverse(A)),inverse(identity)) ->
% double_divide(identity,A)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% double_divide(double_divide(inverse(identity),double_divide(inverse(identity),
% inverse(A))),inverse(identity))
% -> A
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% double_divide(double_divide(inverse(inverse(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: 8
% New rule produced :
% [9]
% double_divide(double_divide(A,double_divide(inverse(identity),double_divide(B,
% double_divide(identity,A)))),
% inverse(identity)) -> B
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [10]
% double_divide(double_divide(identity,double_divide(double_divide(identity,A),
% double_divide(B,inverse(A)))),inverse(identity))
% -> B
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11]
% double_divide(double_divide(A,double_divide(identity,double_divide(B,
% double_divide(inverse(identity),A)))),
% inverse(identity)) -> B
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12]
% double_divide(double_divide(identity,double_divide(inverse(identity),
% double_divide(A,inverse(identity)))),
% inverse(identity)) -> A
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% double_divide(double_divide(identity,inverse(double_divide(identity,A))),
% inverse(identity)) -> A
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% double_divide(double_divide(identity,double_divide(identity,double_divide(A,
% inverse(inverse(identity))))),
% inverse(identity)) -> A
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15]
% double_divide(double_divide(identity,inverse(inverse(identity))),inverse(identity))
% -> identity
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% double_divide(double_divide(identity,double_divide(inverse(identity),A)),
% inverse(identity)) ->
% double_divide(identity,double_divide(inverse(identity),double_divide(A,
% inverse(identity))))
% Rule
% [12]
% double_divide(double_divide(identity,double_divide(inverse(identity),
% double_divide(A,inverse(identity)))),
% inverse(identity)) -> A collapsed.
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [17] inverse(identity) -> identity
% Rule
% [4]
% double_divide(double_divide(A,double_divide(double_divide(identity,B),
% double_divide(C,double_divide(B,A)))),inverse(identity))
% -> C collapsed.
% Rule
% [5]
% double_divide(double_divide(inverse(A),double_divide(double_divide(identity,A),
% inverse(B))),inverse(identity)) -> B
% collapsed.
% Rule
% [6]
% double_divide(inverse(inverse(A)),inverse(identity)) ->
% double_divide(identity,A) collapsed.
% Rule
% [7]
% double_divide(double_divide(inverse(identity),double_divide(inverse(identity),
% inverse(A))),inverse(identity))
% -> A collapsed.
% Rule
% [8]
% double_divide(double_divide(inverse(inverse(identity)),double_divide(identity,
% inverse(A))),inverse(identity))
% -> A collapsed.
% Rule
% [9]
% double_divide(double_divide(A,double_divide(inverse(identity),double_divide(B,
% double_divide(identity,A)))),
% inverse(identity)) -> B collapsed.
% Rule
% [10]
% double_divide(double_divide(identity,double_divide(double_divide(identity,A),
% double_divide(B,inverse(A)))),inverse(identity))
% -> B collapsed.
% Rule
% [11]
% double_divide(double_divide(A,double_divide(identity,double_divide(B,
% double_divide(inverse(identity),A)))),
% inverse(identity)) -> B collapsed.
% Rule
% [13]
% double_divide(double_divide(identity,inverse(double_divide(identity,A))),
% inverse(identity)) -> A collapsed.
% Rule
% [14]
% double_divide(double_divide(identity,double_divide(identity,double_divide(A,
% inverse(inverse(identity))))),
% inverse(identity)) -> A collapsed.
% Rule
% [15]
% double_divide(double_divide(identity,inverse(inverse(identity))),inverse(identity))
% -> identity collapsed.
% Rule
% [16]
% double_divide(double_divide(identity,double_divide(inverse(identity),A)),
% inverse(identity)) ->
% double_divide(identity,double_divide(inverse(identity),double_divide(A,
% inverse(identity))))
% collapsed.
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [18]
% inverse(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,
% double_divide(B,A)))))
% -> C
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [19] double_divide(identity,A) -> inverse(inverse(inverse(A)))
% Rule
% [18]
% inverse(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,
% double_divide(B,A)))))
% -> C collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [20]
% inverse(double_divide(A,double_divide(inverse(inverse(inverse(B))),double_divide(C,
% double_divide(B,A)))))
% -> C
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [21]
% inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(A)))))))) ->
% A
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [22]
% inverse(double_divide(A,inverse(inverse(inverse(double_divide(B,inverse(
% inverse(
% inverse(A)))))))))
% -> B
% Current number of equations to process: 13
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [23]
% inverse(double_divide(inverse(A),double_divide(inverse(inverse(inverse(A))),
% inverse(B)))) -> B
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [24]
% inverse(inverse(inverse(inverse(double_divide(inverse(inverse(inverse(A))),
% double_divide(B,inverse(A))))))) -> B
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [25]
% double_divide(inverse(inverse(inverse(inverse(inverse(inverse(inverse(A))))))),A)
% -> identity
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [26]
% inverse(double_divide(double_divide(A,inverse(inverse(inverse(B)))),inverse(
% inverse(A))))
% -> B
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [27]
% inverse(double_divide(inverse(A),inverse(inverse(inverse(inverse(A)))))) ->
% identity
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [28]
% inverse(double_divide(A,double_divide(inverse(inverse(A)),inverse(B)))) -> B
% Rule
% [23]
% inverse(double_divide(inverse(A),double_divide(inverse(inverse(inverse(A))),
% inverse(B)))) -> B collapsed.
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [29]
% double_divide(double_divide(inverse(A),double_divide(inverse(inverse(
% inverse(A))),
% inverse(B))),B) -> identity
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [30]
% inverse(inverse(inverse(inverse(double_divide(inverse(inverse(A)),double_divide(B,A))))))
% -> B
% Rule
% [24]
% inverse(inverse(inverse(inverse(double_divide(inverse(inverse(inverse(A))),
% double_divide(B,inverse(A))))))) -> B
% collapsed.
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [31]
% inverse(double_divide(double_divide(A,B),inverse(inverse(A)))) ->
% inverse(inverse(inverse(inverse(inverse(B)))))
% Rule
% [26]
% inverse(double_divide(double_divide(A,inverse(inverse(inverse(B)))),inverse(
% inverse(A))))
% -> B collapsed.
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [32] inverse(double_divide(A,inverse(inverse(inverse(A))))) -> identity
% Rule
% [27]
% inverse(double_divide(inverse(A),inverse(inverse(inverse(inverse(A)))))) ->
% identity collapsed.
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [33]
% double_divide(double_divide(A,double_divide(inverse(inverse(A)),inverse(B))),B)
% -> identity
% Rule
% [29]
% double_divide(double_divide(inverse(A),double_divide(inverse(inverse(
% inverse(A))),
% inverse(B))),B) -> identity collapsed.
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [34]
% inverse(double_divide(A,double_divide(inverse(inverse(A)),B))) ->
% inverse(inverse(inverse(inverse(inverse(inverse(inverse(B)))))))
% Rule
% [28]
% inverse(double_divide(A,double_divide(inverse(inverse(A)),inverse(B)))) -> B
% collapsed.
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [35]
% double_divide(C,double_divide(inverse(inverse(C)),inverse(B))) ->
% inverse(inverse(inverse(inverse(inverse(inverse(inverse(B)))))))
% Rule
% [33]
% double_divide(double_divide(A,double_divide(inverse(inverse(A)),inverse(B))),B)
% -> identity collapsed.
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [36]
% double_divide(inverse(inverse(B)),double_divide(A,B)) ->
% inverse(inverse(inverse(inverse(A))))
% Rule
% [30]
% inverse(inverse(inverse(inverse(double_divide(inverse(inverse(A)),double_divide(B,A))))))
% -> B collapsed.
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [37]
% double_divide(double_divide(B,A),inverse(inverse(B))) ->
% inverse(inverse(inverse(inverse(A))))
% Rule
% [31]
% inverse(double_divide(double_divide(A,B),inverse(inverse(A)))) ->
% inverse(inverse(inverse(inverse(inverse(B))))) collapsed.
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 14
% Rule [19] double_divide(identity,A) -> inverse(inverse(inverse(A))) is composed into
% [19] double_divide(identity,A) -> inverse(A)
% New rule produced : [38] inverse(inverse(A)) -> A
% Rule
% [20]
% inverse(double_divide(A,double_divide(inverse(inverse(inverse(B))),double_divide(C,
% double_divide(B,A)))))
% -> C collapsed.
% Rule
% [21]
% inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(A)))))))) ->
% A collapsed.
% Rule
% [22]
% inverse(double_divide(A,inverse(inverse(inverse(double_divide(B,inverse(
% inverse(
% inverse(A)))))))))
% -> B collapsed.
% Rule
% [25]
% double_divide(inverse(inverse(inverse(inverse(inverse(inverse(inverse(A))))))),A)
% -> identity collapsed.
% Rule [32] inverse(double_divide(A,inverse(inverse(inverse(A))))) -> identity
% collapsed.
% Rule
% [34]
% inverse(double_divide(A,double_divide(inverse(inverse(A)),B))) ->
% inverse(inverse(inverse(inverse(inverse(inverse(inverse(B))))))) collapsed.
% Rule
% [35]
% double_divide(C,double_divide(inverse(inverse(C)),inverse(B))) ->
% inverse(inverse(inverse(inverse(inverse(inverse(inverse(B))))))) collapsed.
% Rule
% [36]
% double_divide(inverse(inverse(B)),double_divide(A,B)) ->
% inverse(inverse(inverse(inverse(A)))) collapsed.
% Rule
% [37]
% double_divide(double_divide(B,A),inverse(inverse(B))) ->
% inverse(inverse(inverse(inverse(A)))) collapsed.
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [39]
% inverse(double_divide(A,double_divide(inverse(B),double_divide(C,double_divide(B,A)))))
% -> C
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [40] double_divide(inverse(A),A) -> identity
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [41] double_divide(B,double_divide(A,B)) -> A
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [42] double_divide(double_divide(B,A),B) -> A
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [43] inverse(double_divide(A,double_divide(A,B))) -> inverse(B)
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [44] double_divide(C,double_divide(C,inverse(B))) -> inverse(B)
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [45] inverse(double_divide(A,inverse(double_divide(B,inverse(A))))) -> B
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [46] inverse(double_divide(B,A)) <-> inverse(double_divide(A,B))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 14
% 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(identity,B),
% double_divide(C,double_divide(B,A)))),
% inverse(identity)) -> C; trace = in the starting set
% [10] double_divide(double_divide(identity,double_divide(double_divide(identity,A),
% double_divide(B,inverse(A)))),
% inverse(identity)) -> B; trace = Cp of 4 and 1
% [21] inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(A))))))))
% -> A; trace = Cp of 10 and 2
% [39] inverse(double_divide(A,double_divide(inverse(B),double_divide(C,
% double_divide(B,A)))))
% -> C; trace = in the starting set
% [40] double_divide(inverse(A),A) -> identity; trace = Cp of 21 and 2
% [46] inverse(double_divide(B,A)) <-> inverse(double_divide(A,B)); trace = Cp of 40 and 39
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.020000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------