TSTP Solution File: GRP485-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP485-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n147.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 00:23:17 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 : GRP485-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n147.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 14:18:18 CDT 2014
% % CPUTime : 1.13
% Processing problem /tmp/CiME_2580_n147.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,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(double_divide(A,B),C),double_divide(B,identity))),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 "
% a2 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% identity lr_lex;
% double_divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > double_divide > inverse > identity > a2";
%
% let s2 = status F "
% a2 mul;
% inverse mul;
% multiply mul;
% identity mul;
% double_divide mul;
% ";
%
% let p2 = precedence F "
% multiply > double_divide > inverse > identity = a2";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(identity,a2) = a2;"
% ;
% (*
% 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(
% double_divide(A,B),C),
% double_divide(B,identity))),
% 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(identity,a2) = a2 }
% (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(inverse(a2)) = a2
%
% 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(double_divide(A,B),C),
% inverse(B))),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(A,double_divide(identity,inverse(B))),inverse(identity))
% -> inverse(double_divide(A,B))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] double_divide(inverse(A),inverse(identity)) -> inverse(inverse(A))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% double_divide(double_divide(A,double_divide(double_divide(inverse(A),B),
% inverse(identity))),inverse(identity)) -> B
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 7
% New rule produced :
% [8]
% double_divide(double_divide(A,double_divide(inverse(double_divide(A,B)),
% inverse(B))),inverse(identity)) -> identity
% 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(A,double_divide(double_divide(identity,B),
% inverse(inverse(A)))),inverse(identity)) -> B
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10]
% double_divide(double_divide(A,inverse(inverse(inverse(A)))),inverse(identity))
% -> identity
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11]
% double_divide(double_divide(inverse(inverse(A)),B),inverse(identity)) ->
% double_divide(double_divide(A,B),inverse(identity))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] inverse(identity) -> identity
% Rule
% [4]
% double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),
% inverse(B))),inverse(identity)) -> C collapsed.
% Rule
% [5]
% double_divide(double_divide(A,double_divide(identity,inverse(B))),inverse(identity))
% -> inverse(double_divide(A,B)) collapsed.
% Rule [6] double_divide(inverse(A),inverse(identity)) -> inverse(inverse(A))
% collapsed.
% Rule
% [7]
% double_divide(double_divide(A,double_divide(double_divide(inverse(A),B),
% inverse(identity))),inverse(identity)) -> B
% collapsed.
% Rule
% [8]
% double_divide(double_divide(A,double_divide(inverse(double_divide(A,B)),
% inverse(B))),inverse(identity)) -> identity
% collapsed.
% Rule
% [9]
% double_divide(double_divide(A,double_divide(double_divide(identity,B),
% inverse(inverse(A)))),inverse(identity)) -> B
% collapsed.
% Rule
% [10]
% double_divide(double_divide(A,inverse(inverse(inverse(A)))),inverse(identity))
% -> identity collapsed.
% Rule
% [11]
% double_divide(double_divide(inverse(inverse(A)),B),inverse(identity)) ->
% double_divide(double_divide(A,B),inverse(identity)) collapsed.
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [13]
% inverse(double_divide(A,double_divide(double_divide(double_divide(A,B),C),
% inverse(B)))) -> C
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [14] inverse(double_divide(A,inverse(inverse(inverse(A))))) -> identity
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [15]
% inverse(double_divide(inverse(inverse(A)),B)) -> inverse(double_divide(A,B))
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [16]
% inverse(double_divide(A,double_divide(identity,inverse(B)))) ->
% inverse(double_divide(A,B))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [17] inverse(double_divide(A,inverse(double_divide(inverse(A),B)))) -> B
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [18]
% inverse(double_divide(A,double_divide(inverse(double_divide(A,B)),inverse(B))))
% -> identity
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [19]
% inverse(double_divide(A,double_divide(double_divide(identity,B),inverse(
% inverse(A)))))
% -> B
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [20]
% double_divide(double_divide(double_divide(inverse(A),C),B),inverse(C)) ->
% inverse(double_divide(A,B))
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [21] double_divide(identity,inverse(B)) -> B
% Rule
% [16]
% inverse(double_divide(A,double_divide(identity,inverse(B)))) ->
% inverse(double_divide(A,B)) collapsed.
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [22] inverse(inverse(inverse(inverse(A)))) -> inverse(inverse(A))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [23]
% double_divide(double_divide(inverse(inverse(A)),B),inverse(double_divide(A,B)))
% -> identity
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [24] inverse(double_divide(identity,A)) -> A
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [25]
% double_divide(double_divide(A,inverse(double_divide(inverse(A),B))),B) ->
% identity
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [26]
% inverse(double_divide(double_divide(inverse(inverse(A)),B),C)) ->
% inverse(double_divide(double_divide(A,B),C))
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [27]
% inverse(double_divide(double_divide(B,inverse(inverse(inverse(B)))),A)) -> A
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [28] inverse(double_divide(inverse(A),inverse(double_divide(A,B)))) -> B
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [29]
% double_divide(inverse(double_divide(inverse(A),B)),inverse(B)) ->
% inverse(inverse(A))
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [30]
% inverse(double_divide(A,double_divide(B,inverse(inverse(double_divide(
% inverse(A),B)))))) ->
% identity
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [31]
% double_divide(double_divide(A,double_divide(double_divide(identity,B),
% inverse(inverse(A)))),B) -> identity
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [32]
% inverse(double_divide(A,B)) <->
% double_divide(double_divide(identity,B),inverse(inverse(inverse(A))))
% Current number of equations to process: 34
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [33]
% double_divide(double_divide(identity,B),inverse(inverse(inverse(A)))) <->
% inverse(double_divide(A,B))
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [34]
% double_divide(double_divide(double_divide(identity,A),B),inverse(A)) -> B
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [35] double_divide(inverse(inverse(A)),B) -> double_divide(A,B)
% Rule
% [15]
% inverse(double_divide(inverse(inverse(A)),B)) -> inverse(double_divide(A,B))
% collapsed.
% Rule
% [23]
% double_divide(double_divide(inverse(inverse(A)),B),inverse(double_divide(A,B)))
% -> identity collapsed.
% Rule
% [26]
% inverse(double_divide(double_divide(inverse(inverse(A)),B),C)) ->
% inverse(double_divide(double_divide(A,B),C)) collapsed.
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [36] double_divide(double_divide(A,B),inverse(inverse(A))) -> B
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [37] double_divide(A,inverse(inverse(inverse(A)))) -> identity
% Rule [14] inverse(double_divide(A,inverse(inverse(inverse(A))))) -> identity
% collapsed.
% Rule
% [27]
% inverse(double_divide(double_divide(B,inverse(inverse(inverse(B)))),A)) -> A
% collapsed.
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [38]
% double_divide(B,inverse(double_divide(inverse(B),A))) ->
% double_divide(identity,A)
% Rule [17] inverse(double_divide(A,inverse(double_divide(inverse(A),B)))) -> B
% collapsed.
% Rule
% [25]
% double_divide(double_divide(A,inverse(double_divide(inverse(A),B))),B) ->
% identity collapsed.
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [39] double_divide(double_divide(identity,B),B) -> identity
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [40]
% double_divide(B,double_divide(double_divide(double_divide(B,C),A),inverse(C)))
% -> double_divide(identity,A)
% Rule
% [13]
% inverse(double_divide(A,double_divide(double_divide(double_divide(A,B),C),
% inverse(B)))) -> C collapsed.
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [41]
% double_divide(A,double_divide(inverse(double_divide(A,B)),inverse(B))) ->
% identity
% Rule
% [18]
% inverse(double_divide(A,double_divide(inverse(double_divide(A,B)),inverse(B))))
% -> identity collapsed.
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [42]
% inverse(double_divide(A,double_divide(B,inverse(inverse(A))))) -> inverse(B)
% Rule
% [19]
% inverse(double_divide(A,double_divide(double_divide(identity,B),inverse(
% inverse(A)))))
% -> B collapsed.
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [43]
% double_divide(B,double_divide(double_divide(identity,A),inverse(inverse(B))))
% -> double_divide(identity,A)
% Rule
% [31]
% double_divide(double_divide(A,double_divide(double_divide(identity,B),
% inverse(inverse(A)))),B) -> identity collapsed.
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 23
% Rule [32]
% inverse(double_divide(A,B)) <->
% double_divide(double_divide(identity,B),inverse(inverse(inverse(A)))) is composed into
% [32]
% inverse(double_divide(A,B)) <->
% double_divide(double_divide(identity,B),inverse(A))
% New rule produced : [44] inverse(inverse(inverse(A))) -> inverse(A)
% Rule [22] inverse(inverse(inverse(inverse(A)))) -> inverse(inverse(A))
% collapsed.
% Rule
% [33]
% double_divide(double_divide(identity,B),inverse(inverse(inverse(A)))) <->
% inverse(double_divide(A,B)) collapsed.
% Rule [37] double_divide(A,inverse(inverse(inverse(A)))) -> identity
% collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [45]
% double_divide(double_divide(inverse(A),inverse(double_divide(A,B))),B) ->
% identity
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 22
% Rule [29]
% double_divide(inverse(double_divide(inverse(A),B)),inverse(B)) ->
% inverse(inverse(A)) is composed into [29]
% double_divide(inverse(double_divide(
% inverse(A),B)),
% inverse(B)) -> A
% New rule produced : [46] inverse(inverse(A)) -> A
% Rule
% [30]
% inverse(double_divide(A,double_divide(B,inverse(inverse(double_divide(
% inverse(A),B)))))) ->
% identity collapsed.
% Rule [35] double_divide(inverse(inverse(A)),B) -> double_divide(A,B)
% collapsed.
% Rule [36] double_divide(double_divide(A,B),inverse(inverse(A))) -> B
% collapsed.
% Rule
% [42]
% inverse(double_divide(A,double_divide(B,inverse(inverse(A))))) -> inverse(B)
% collapsed.
% Rule
% [43]
% double_divide(B,double_divide(double_divide(identity,A),inverse(inverse(B))))
% -> double_divide(identity,A) collapsed.
% Rule [44] inverse(inverse(inverse(A))) -> inverse(A) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 17
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 8 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(double_divide(A,B),C),
% inverse(B))),inverse(identity)) -> C; trace = in the starting set
% [17] inverse(double_divide(A,inverse(double_divide(inverse(A),B)))) -> B; trace = Cp of 4 and 1
% [18] inverse(double_divide(A,double_divide(inverse(double_divide(A,B)),
% inverse(B)))) -> identity; trace = Cp of 4 and 1
% [29] double_divide(inverse(double_divide(inverse(A),B)),inverse(B)) ->
% inverse(inverse(A)); trace = Cp of 18 and 17
% [46] inverse(inverse(A)) -> A; trace = Cp of 29 and 2
% % 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
%------------------------------------------------------------------------------