TSTP Solution File: GRP519-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP519-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n162.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 00:23:23 EDT 2014
% Result : Unsatisfiable 1.30s
% Output : Refutation 1.30s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: CiME---2.01 format not known, defaulting to TPTP
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP519-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n162.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 15:52:48 CDT 2014
% % CPUTime : 1.30
% Processing problem /tmp/CiME_51931_n162.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c3,b3,a3 : constant; inverse : 1; multiply : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C;
% ";
%
% let s1 = status F "
% c3 lr_lex;
% b3 lr_lex;
% a3 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% ";
%
% let p1 = precedence F "
% inverse > multiply > a3 > b3 > c3";
%
% let s2 = status F "
% c3 mul;
% b3 mul;
% a3 mul;
% inverse mul;
% multiply mul;
% ";
%
% let p2 = precedence F "
% inverse > multiply > a3 = b3 = c3";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3));"
% ;
% (*
% 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 = { multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B))
% = C } (1 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(a3,b3),c3) =
% multiply(a3,multiply(b3,c3)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced :
% [1] multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) -> C
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 1
% New rule produced :
% [2]
% multiply(multiply(inverse(multiply(inverse(multiply(A,C)),V_3)),B),V_3) ->
% multiply(A,multiply(B,C))
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3] multiply(inverse(multiply(A,B)),multiply(A,multiply(C,B))) -> C
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4] multiply(inverse(multiply(inverse(multiply(A,B)),multiply(C,B))),C) -> A
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [5]
% multiply(C,multiply(B,V_3)) <->
% multiply(multiply(inverse(A),B),multiply(C,multiply(A,V_3)))
% Current number of equations to process: 25
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [6]
% multiply(multiply(inverse(A),B),multiply(C,multiply(A,V_3))) <->
% multiply(C,multiply(B,V_3))
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% multiply(inverse(multiply(A,V_3)),multiply(B,multiply(C,V_3))) <->
% multiply(multiply(inverse(A),B),C)
% Rule [3] multiply(inverse(multiply(A,B)),multiply(A,multiply(C,B))) -> C
% collapsed.
% Current number of equations to process: 70
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced : [8] multiply(multiply(inverse(A),A),C) -> C
% Current number of equations to process: 69
% Current number of ordered equations: 1
% Current number of rules: 7
% New rule produced :
% [9]
% multiply(multiply(inverse(A),B),C) <->
% multiply(inverse(multiply(A,V_3)),multiply(B,multiply(C,V_3)))
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [10]
% inverse(multiply(inverse(multiply(C,V_3)),multiply(B,V_3))) <->
% multiply(inverse(multiply(A,B)),multiply(A,C))
% Rule
% [4] multiply(inverse(multiply(inverse(multiply(A,B)),multiply(C,B))),C) -> A
% collapsed.
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [11] multiply(multiply(inverse(multiply(A,C)),multiply(A,A)),C) -> A
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [12]
% multiply(A,multiply(multiply(multiply(inverse(A),B),C),V_3)) ->
% multiply(B,multiply(C,V_3))
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [13] multiply(multiply(inverse(A),B),A) -> B
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [14] multiply(multiply(inverse(A),B),multiply(A,C)) -> multiply(B,C)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [15] multiply(multiply(inverse(multiply(inverse(A),B)),C),B) -> multiply(C,A)
% Rule
% [2]
% multiply(multiply(inverse(multiply(inverse(multiply(A,C)),V_3)),B),V_3) ->
% multiply(A,multiply(B,C)) collapsed.
% Current number of equations to process: 97
% Current number of ordered equations: 0
% Current number of rules: 12
% Rule [10]
% inverse(multiply(inverse(multiply(C,V_3)),multiply(B,V_3))) <->
% multiply(inverse(multiply(A,B)),multiply(A,C)) is composed into
% [10]
% inverse(multiply(inverse(multiply(C,V_3)),multiply(B,V_3))) <->
% multiply(A,multiply(inverse(multiply(A,B)),C))
% New rule produced :
% [16] multiply(A,multiply(B,C)) <-> multiply(B,multiply(A,C))
% Rule [11] multiply(multiply(inverse(multiply(A,C)),multiply(A,A)),C) -> A
% collapsed.
% Rule [14] multiply(multiply(inverse(A),B),multiply(A,C)) -> multiply(B,C)
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% multiply(multiply(a3,b3),c3) = multiply(b3,multiply(a3,c3))
%
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [17] multiply(A,multiply(multiply(inverse(A),B),C)) -> multiply(B,C)
% Current number of equations to process: 97
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [18] multiply(multiply(A,multiply(inverse(multiply(A,C)),A)),C) -> A
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [19] multiply(B,multiply(inverse(multiply(B,C)),multiply(A,C))) -> A
% Current number of equations to process: 108
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [20] multiply(inverse(A),multiply(B,A)) -> B
% Current number of equations to process: 166
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [21] multiply(multiply(inverse(A),B),multiply(multiply(inverse(B),C),A)) -> C
% Current number of equations to process: 170
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [22] multiply(A,B) <-> multiply(multiply(inverse(C),B),multiply(A,C))
% Current number of equations to process: 191
% Current number of ordered equations: 2
% Current number of rules: 17
% New rule produced :
% [23] multiply(multiply(inverse(C),B),multiply(A,C)) <-> multiply(A,B)
% Current number of equations to process: 191
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [24] multiply(multiply(A,multiply(inverse(B),C)),B) -> multiply(A,C)
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [25]
% multiply(C,multiply(A,multiply(B,V_3))) <->
% multiply(A,multiply(B,multiply(C,V_3)))
% Current number of equations to process: 216
% Current number of ordered equations: 1
% Current number of rules: 20
% Rule [5]
% multiply(C,multiply(B,V_3)) <->
% multiply(multiply(inverse(A),B),multiply(C,multiply(A,V_3))) is composed into
% [5]
% multiply(C,multiply(B,V_3)) <->
% multiply(A,multiply(multiply(inverse(A),B),multiply(C,V_3)))
% New rule produced :
% [26]
% multiply(A,multiply(B,multiply(C,V_3))) <->
% multiply(C,multiply(A,multiply(B,V_3)))
% Rule
% [6]
% multiply(multiply(inverse(A),B),multiply(C,multiply(A,V_3))) <->
% multiply(C,multiply(B,V_3)) collapsed.
% Current number of equations to process: 216
% Current number of ordered equations: 0
% Current number of rules: 20
% multiply(A,B) = multiply(B,A) (birth = 135, lhs_size = 3, rhs_size = 3,trace = Cp of 17 and 13)
% Initializing completion ...
% New rule produced : [1] B <-> inverse(A) multiply (A multiply B)
% Current number of equations to process: 217
% Current number of ordered equations: 35
% Current number of rules: 1
% New rule produced : [2] B <-> (inverse(A) multiply B) multiply A
% Current number of equations to process: 217
% Current number of ordered equations: 34
% Current number of rules: 2
% New rule produced : [3] C <-> (inverse(A) multiply A) multiply C
% Current number of equations to process: 217
% Current number of ordered equations: 33
% Current number of rules: 3
% New rule produced : [4] inverse(A) multiply (A multiply B) <-> B
% Current number of equations to process: 217
% Current number of ordered equations: 32
% Current number of rules: 4
% New rule produced : [5] (inverse(A) multiply B) multiply A <-> B
% Current number of equations to process: 217
% Current number of ordered equations: 31
% Current number of rules: 5
% New rule produced : [6] (inverse(A) multiply A) multiply C <-> C
% Current number of equations to process: 217
% Current number of ordered equations: 30
% Current number of rules: 6
% (A multiply C) multiply B = (B multiply C) multiply A (birth = 0, lhs_size = 5, rhs_size = 5,trace = in the starting set)
% Initializing completion ...
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
% See solution above
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.180000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------