TSTP Solution File: GRP514-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP514-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n166.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 1.18s
% Output : Refutation 1.18s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP514-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n166.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 15:21:28 CDT 2014
% % CPUTime : 1.18
% Processing problem /tmp/CiME_23530_n166.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; inverse : 1; multiply : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B;
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% ";
%
% let p1 = precedence F "
% inverse > multiply > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% inverse mul;
% multiply mul;
% ";
%
% let p2 = precedence F "
% inverse > multiply > 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 = { multiply(A,multiply(multiply(B,C),inverse(
% multiply(A,C))))
% = B } (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(inverse(b2),b2),a2) = a2 }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced :
% [1] multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 1
% New rule produced :
% [2]
% multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(
% multiply(V_3,C)))))))
% -> V_3
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 2
% New rule produced :
% [3]
% multiply(A,multiply(multiply(B,multiply(multiply(C,V_3),inverse(multiply(A,V_3)))),
% inverse(C))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced : [4] multiply(A,multiply(B,inverse(B))) -> A
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] multiply(A,multiply(B,inverse(A))) -> B
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) -> A
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7] multiply(A,multiply(multiply(B,C),inverse(B))) -> multiply(A,C)
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8] multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),C) -> A
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9] multiply(A,multiply(B,inverse(multiply(A,multiply(B,inverse(C)))))) -> C
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10] multiply(A,multiply(multiply(B,multiply(C,inverse(A))),inverse(C))) -> B
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] multiply(C,B) <-> multiply(multiply(A,B),multiply(C,inverse(A)))
% Current number of equations to process: 25
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced :
% [12] multiply(multiply(A,B),multiply(C,inverse(A))) <-> multiply(C,B)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13] multiply(A,multiply(B,inverse(multiply(B,multiply(A,inverse(C)))))) -> C
% Current number of equations to process: 30
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced :
% [14] multiply(multiply(A,multiply(B,inverse(C))),multiply(C,inverse(B))) -> A
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15]
% multiply(A,multiply(B,inverse(multiply(B,C)))) <->
% multiply(A,multiply(V_3,inverse(multiply(V_3,C))))
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% multiply(B,multiply(V_3,inverse(multiply(V_3,C)))) <->
% multiply(A,multiply(B,inverse(multiply(A,C))))
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [17]
% multiply(A,multiply(B,inverse(multiply(A,C)))) <->
% multiply(B,multiply(V_3,inverse(multiply(V_3,C))))
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% multiply(B,multiply(C,inverse(multiply(C,inverse(A))))) <-> multiply(A,B)
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [19]
% multiply(A,B) <-> multiply(B,multiply(C,inverse(multiply(C,inverse(A)))))
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 19
% Rule [19]
% multiply(A,B) <->
% multiply(B,multiply(C,inverse(multiply(C,inverse(A))))) is composed into
% [19] multiply(A,B) <-> multiply(B,A)
% New rule produced :
% [20] multiply(A,multiply(C,inverse(multiply(C,inverse(B))))) -> multiply(A,B)
% Rule
% [18]
% multiply(B,multiply(C,inverse(multiply(C,inverse(A))))) <-> multiply(A,B)
% collapsed.
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [21]
% multiply(A,multiply(multiply(B,V_3),inverse(multiply(C,V_3)))) ->
% multiply(A,multiply(B,inverse(C)))
% Rule [1] multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) -> B
% collapsed.
% Rule
% [2]
% multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(
% multiply(V_3,C)))))))
% -> V_3 collapsed.
% Rule
% [3]
% multiply(A,multiply(multiply(B,multiply(multiply(C,V_3),inverse(multiply(A,V_3)))),
% inverse(C))) -> B collapsed.
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [22]
% multiply(B,multiply(A,inverse(C))) <-> multiply(A,multiply(B,inverse(C)))
% Rule
% [14] multiply(multiply(A,multiply(B,inverse(C))),multiply(C,inverse(B))) -> A
% collapsed.
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [23] multiply(multiply(A,C),B) <-> multiply(multiply(A,B),C)
% Rule [8] multiply(multiply(A,multiply(B,inverse(multiply(B,C)))),C) -> A
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 69
% 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 9 rules have been used:
% [1]
% multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) -> B; trace = in the starting set
% [2] multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(
% multiply(V_3,C)))))))
% -> V_3; trace = Self cp of 1
% [3] multiply(A,multiply(multiply(B,multiply(multiply(C,V_3),inverse(multiply(A,V_3)))),
% inverse(C))) -> B; trace = Self cp of 1
% [4] multiply(A,multiply(B,inverse(B))) -> A; trace = Cp of 2 and 1
% [5] multiply(A,multiply(B,inverse(A))) -> B; trace = Cp of 4 and 1
% [6] multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) -> A; trace = Cp of 5 and 2
% [7] multiply(A,multiply(multiply(B,C),inverse(B))) -> multiply(A,C); trace = Cp of 5 and 3
% [12] multiply(multiply(A,B),multiply(C,inverse(A))) <-> multiply(C,B); trace = Cp of 6 and 2
% [23] multiply(multiply(A,C),B) <-> multiply(multiply(A,B),C); trace = Cp of 12 and 7
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.070000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------