TSTP Solution File: GRP562-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP562-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n083.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 00:23:28 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 : GRP562-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n083.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 19:55:38 CDT 2014
% % CPUTime : 1.12
% Processing problem /tmp/CiME_42149_n083.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; multiply : 2; divide : 2; inverse : 1;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(divide(divide(A,inverse(B)),C),divide(A,C)) = B;
% multiply(A,B) = divide(A,inverse(B));
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% multiply lr_lex;
% divide lr_lex;
% inverse lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > divide > inverse > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% multiply mul;
% divide mul;
% inverse mul;
% ";
%
% let p2 = precedence F "
% multiply > 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 = { divide(divide(divide(A,inverse(B)),C),divide(A,C))
% = B,
% multiply(A,B) = divide(A,inverse(B)) }
% (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) -> divide(A,inverse(B))
% The conjecture has been reduced.
% Conjecture is now:
% divide(divide(inverse(b2),inverse(b2)),inverse(a2)) = a2
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced :
% [2] divide(divide(divide(A,inverse(B)),C),divide(A,C)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3] divide(A,divide(divide(B,inverse(A)),divide(B,inverse(C)))) -> C
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4]
% divide(divide(divide(divide(divide(A,inverse(B)),C),inverse(V_3)),divide(A,C)),B)
% -> V_3
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] divide(divide(A,inverse(B)),A) -> B
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] divide(A,divide(inverse(B),inverse(A))) -> B
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] divide(A,divide(B,B)) -> A
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] divide(A,B) <-> divide(inverse(B),inverse(A))
% Rule [2] divide(divide(divide(A,inverse(B)),C),divide(A,C)) -> B collapsed.
% Rule
% [4]
% divide(divide(divide(divide(divide(A,inverse(B)),C),inverse(V_3)),divide(A,C)),B)
% -> V_3 collapsed.
% Rule [5] divide(divide(A,inverse(B)),A) -> B collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% divide(inverse(inverse(a2)),inverse(divide(inverse(b2),inverse(b2)))) = a2
%
% Current number of equations to process: 22
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [9] divide(inverse(divide(A,C)),inverse(divide(divide(A,inverse(B)),C))) -> B
% Current number of equations to process: 21
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced : [10] divide(inverse(B),inverse(A)) <-> divide(A,B)
% The conjecture has been reduced.
% Conjecture is now:
% divide(inverse(inverse(a2)),inverse(divide(b2,b2))) = a2
%
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [11] divide(inverse(A),inverse(divide(A,inverse(B)))) -> B
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [12] divide(inverse(divide(B,B)),inverse(A)) -> A
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [13] divide(A,divide(inverse(inverse(A)),inverse(inverse(B)))) -> B
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [14]
% divide(inverse(B),inverse(divide(inverse(A),inverse(divide(divide(A,inverse(B)),
% inverse(C)))))) -> C
% Current number of equations to process: 23
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced :
% [15] divide(divide(A,B),divide(divide(inverse(C),inverse(A)),B)) -> C
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [16]
% divide(inverse(inverse(B)),inverse(inverse(divide(inverse(A),inverse(B)))))
% -> A
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [17] divide(A,divide(A,B)) -> B
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [18] divide(inverse(inverse(A)),inverse(inverse(B))) -> divide(A,B)
% Rule [13] divide(A,divide(inverse(inverse(A)),inverse(inverse(B)))) -> B
% collapsed.
% Rule
% [16]
% divide(inverse(inverse(B)),inverse(inverse(divide(inverse(A),inverse(B)))))
% -> A collapsed.
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [19] divide(inverse(inverse(A)),inverse(B)) -> divide(A,inverse(B))
% Rule [18] divide(inverse(inverse(A)),inverse(inverse(B))) -> divide(A,B)
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% divide(a2,inverse(divide(b2,b2))) = a2
%
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [20] divide(A,inverse(inverse(B))) -> divide(A,B)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [21] divide(inverse(A),inverse(divide(B,inverse(A)))) -> B
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [22] divide(A,inverse(divide(B,A))) -> B
% Rule [21] divide(inverse(A),inverse(divide(B,inverse(A)))) -> B collapsed.
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [23] divide(divide(A,inverse(C)),B) <-> divide(divide(A,B),inverse(C))
% Current number of equations to process: 44
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [24] divide(divide(A,B),inverse(C)) <-> divide(divide(A,inverse(C)),B)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [25] divide(B,B) <-> divide(A,A)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 18
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 13 rules have been used:
% [1]
% multiply(A,B) -> divide(A,inverse(B)); trace = in the starting set
% [2] divide(divide(divide(A,inverse(B)),C),divide(A,C)) -> B; trace = in the starting set
% [3] divide(A,divide(divide(B,inverse(A)),divide(B,inverse(C)))) -> C; trace = Self cp of 2
% [4] divide(divide(divide(divide(divide(A,inverse(B)),C),inverse(V_3)),
% divide(A,C)),B) -> V_3; trace = Self cp of 2
% [5] divide(divide(A,inverse(B)),A) -> B; trace = Self cp of 4
% [6] divide(A,divide(inverse(B),inverse(A))) -> B; trace = Self cp of 5
% [7] divide(A,divide(B,B)) -> A; trace = Cp of 5 and 2
% [8] divide(A,B) <-> divide(inverse(B),inverse(A)); trace = Cp of 6 and 3
% [10] divide(inverse(B),inverse(A)) <-> divide(A,B); trace = Cp of 6 and 3
% [11] divide(inverse(A),inverse(divide(A,inverse(B)))) -> B; trace = Self cp of 4
% [12] divide(inverse(divide(B,B)),inverse(A)) -> A; trace = Cp of 8 and 7
% [19] divide(inverse(inverse(A)),inverse(B)) -> divide(A,inverse(B)); trace = Self cp of 11
% [25] divide(B,B) <-> divide(A,A); trace = Cp of 12 and 6
% % 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
%------------------------------------------------------------------------------