TSTP Solution File: GRP590-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP590-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n109.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 00:23:33 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 : GRP590-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n109.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 21:12:13 CDT 2014
% % CPUTime : 1.14
% Processing problem /tmp/CiME_29622_n109.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; multiply : 2; inverse : 1; double_divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C;
% multiply(A,B) = inverse(double_divide(B,A));
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% double_divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > double_divide > inverse > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% multiply mul;
% inverse mul;
% double_divide mul;
% ";
%
% let p2 = precedence F "
% multiply > double_divide > inverse > b2 = a2";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(multiply(inverse(b2),b2),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(inverse(double_divide(double_divide(A,B),
% inverse(double_divide(A,
% inverse(C))))),B)
% = C,
% multiply(A,B) = inverse(double_divide(B,A)) }
% (2 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(multiply(inverse(b2),b2),a2) = a2 }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] multiply(A,B) -> inverse(double_divide(B,A))
% The conjecture has been reduced.
% Conjecture is now:
% inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) = a2
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced :
% [2]
% double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,
% inverse(C))))),B)
% -> C
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(
% double_divide(B,C),
% inverse(
% double_divide(B,
% inverse(A))))),
% inverse(V_3))))),C) -> V_3
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4]
% double_divide(inverse(double_divide(double_divide(inverse(double_divide(
% double_divide(A,
% inverse(B)),
% inverse(double_divide(A,
% inverse(C))))),V_3),
% inverse(C))),V_3) -> 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(inverse(double_divide(A,inverse(A))),inverse(B)) -> 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(inverse(double_divide(A,inverse(A)))),inverse(B)) -> B
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7] double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) -> B
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,
% inverse(A))),B),
% inverse(C))),B) -> C
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% double_divide(inverse(inverse(inverse(inverse(double_divide(A,inverse(A)))))),
% inverse(B)) -> B
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10]
% double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,
% inverse(B))),C),
% inverse(B))),C) -> A
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(A))))) -> B
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12]
% double_divide(inverse(inverse(inverse(double_divide(A,inverse(A))))),
% inverse(B)) -> B
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% double_divide(inverse(double_divide(A,inverse(double_divide(B,inverse(A))))),C)
% -> double_divide(B,C)
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) -> A
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15]
% double_divide(inverse(A),inverse(inverse(inverse(double_divide(B,inverse(B))))))
% -> A
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% double_divide(inverse(double_divide(double_divide(inverse(inverse(double_divide(A,
% inverse(A)))),B),
% inverse(C))),B) -> C
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% double_divide(inverse(double_divide(double_divide(A,inverse(B)),inverse(B))),
% inverse(double_divide(A,inverse(C)))) -> C
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,
% inverse(A))),
% inverse(C))))),inverse(B)) -> C
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19]
% double_divide(inverse(A),inverse(inverse(double_divide(double_divide(B,
% inverse(C)),inverse(
% double_divide(B,
% inverse(A)))))))
% -> C
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [20]
% double_divide(inverse(inverse(inverse(inverse(inverse(double_divide(A,
% inverse(A))))))),
% inverse(B)) -> B
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21]
% double_divide(inverse(A),inverse(inverse(inverse(inverse(inverse(double_divide(B,
% inverse(B))))))))
% -> A
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [22]
% double_divide(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(A,
% inverse(A)))))))),
% inverse(B)) -> B
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [23]
% double_divide(inverse(double_divide(double_divide(inverse(inverse(inverse(
% double_divide(A,
% inverse(A))))),B),
% inverse(C))),B) -> C
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [24]
% double_divide(inverse(inverse(inverse(inverse(inverse(inverse(inverse(
% inverse(
% double_divide(A,
% inverse(A)))))))))),
% inverse(B)) -> B
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [25]
% inverse(double_divide(double_divide(V_3,inverse(C)),inverse(double_divide(V_3,
% inverse(A)))))
% <->
% double_divide(inverse(double_divide(double_divide(inverse(A),B),inverse(C))),B)
% Current number of equations to process: 32
% Current number of ordered equations: 1
% Current number of rules: 25
% Rule [25]
% inverse(double_divide(double_divide(V_3,inverse(C)),inverse(double_divide(V_3,
% inverse(A)))))
% <->
% double_divide(inverse(double_divide(double_divide(inverse(A),B),
% inverse(C))),B) is composed into [25]
% inverse(double_divide(
% double_divide(V_3,
% inverse(C)),
% inverse(
% double_divide(V_3,
% inverse(A)))))
% <->
% inverse(double_divide(
% double_divide(a2,
% inverse(C)),
% inverse(
% double_divide(a2,
% inverse(A)))))
% New rule produced :
% [26]
% double_divide(inverse(double_divide(double_divide(inverse(A),B),inverse(C))),B)
% <->
% inverse(double_divide(double_divide(V_3,inverse(C)),inverse(double_divide(V_3,
% inverse(A)))))
% Rule
% [4]
% double_divide(inverse(double_divide(double_divide(inverse(double_divide(
% double_divide(A,
% inverse(B)),
% inverse(double_divide(A,
% inverse(C))))),V_3),
% inverse(C))),V_3) -> B collapsed.
% Rule
% [8]
% double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,
% inverse(A))),B),
% inverse(C))),B) -> C collapsed.
% Rule
% [10]
% double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,
% inverse(B))),C),
% inverse(B))),C) -> A collapsed.
% Rule
% [16]
% double_divide(inverse(double_divide(double_divide(inverse(inverse(double_divide(A,
% inverse(A)))),B),
% inverse(C))),B) -> C collapsed.
% Rule
% [23]
% double_divide(inverse(double_divide(double_divide(inverse(inverse(inverse(
% double_divide(A,
% inverse(A))))),B),
% inverse(C))),B) -> C collapsed.
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 21
% Rule [25]
% inverse(double_divide(double_divide(V_3,inverse(C)),inverse(double_divide(V_3,
% inverse(A)))))
% <->
% inverse(double_divide(double_divide(a2,inverse(C)),inverse(double_divide(a2,
% inverse(A))))) is composed into
% [25]
% inverse(double_divide(double_divide(V_3,inverse(C)),inverse(double_divide(V_3,
% inverse(A))))) ->
% inverse(double_divide(C,inverse(A)))
% New rule produced :
% [27]
% inverse(double_divide(double_divide(a2,inverse(A)),inverse(double_divide(a2,
% inverse(B))))) ->
% inverse(double_divide(A,inverse(B)))
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [28]
% double_divide(inverse(A),inverse(inverse(B))) ->
% inverse(double_divide(A,inverse(B)))
% Rule
% [11]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(A))))) -> B
% collapsed.
% Rule
% [14]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) -> A
% collapsed.
% Rule
% [15]
% double_divide(inverse(A),inverse(inverse(inverse(double_divide(B,inverse(B))))))
% -> A collapsed.
% Rule
% [19]
% double_divide(inverse(A),inverse(inverse(double_divide(double_divide(B,
% inverse(C)),inverse(
% double_divide(B,
% inverse(A)))))))
% -> C collapsed.
% Rule
% [21]
% double_divide(inverse(A),inverse(inverse(inverse(inverse(inverse(double_divide(B,
% inverse(B))))))))
% -> A collapsed.
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [29] inverse(double_divide(A,inverse(double_divide(B,inverse(A))))) -> B
% Rule
% [13]
% double_divide(inverse(double_divide(A,inverse(double_divide(B,inverse(A))))),C)
% -> double_divide(B,C) collapsed.
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [30] inverse(double_divide(A,inverse(double_divide(B,inverse(B))))) -> A
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 19
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 6 rules have been used:
% [1]
% multiply(A,B) -> inverse(double_divide(B,A)); trace = in the starting set
% [2] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,
% inverse(C))))),B)
% -> C; trace = in the starting set
% [3] double_divide(inverse(double_divide(A,inverse(double_divide(inverse(
% double_divide(
% double_divide(B,C),
% inverse(
% double_divide(B,
% inverse(A))))),
% inverse(V_3))))),C) -> V_3; trace = Self cp of 2
% [5] double_divide(inverse(double_divide(A,inverse(A))),inverse(B)) -> B; trace = Cp of 3 and 2
% [7] double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) -> B; trace = Cp of 5 and 2
% [30] inverse(double_divide(A,inverse(double_divide(B,inverse(B))))) -> A; trace = Cp of 7 and 5
% % 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
%------------------------------------------------------------------------------