TSTP Solution File: GRP409-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP409-1 : 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 00:22:54 EDT 2014
% Result : Unsatisfiable 1.34s
% Output : Refutation 1.34s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP409-1 : 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 12:43:38 CDT 2014
% % CPUTime : 1.34
% Processing problem /tmp/CiME_41816_n109.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b1,a1 : constant; inverse : 1; multiply : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B;
% ";
%
% let s1 = status F "
% b1 lr_lex;
% a1 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > a1 > b1";
%
% let s2 = status F "
% b1 mul;
% a1 mul;
% inverse mul;
% multiply mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > a1 = b1";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(inverse(a1),a1) = multiply(inverse(b1),b1);"
% ;
% (*
% 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(multiply(inverse(multiply(A,inverse(
% multiply(B,C)))),
% multiply(A,inverse(C))),inverse(
% multiply(
% inverse(C),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(inverse(a1),a1) =
% multiply(inverse(b1),b1) } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced :
% [1]
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(C),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(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(
% multiply(A,C)))),
% multiply(B,inverse(C))),inverse(C))),
% inverse(multiply(inverse(C),C))) -> inverse(C)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(
% multiply(
% inverse(
% multiply(C,
% inverse(
% multiply(B,A)))),
% multiply(C,
% inverse(A))),
% inverse(A))),
% inverse(A))),inverse(multiply(inverse(A),A)))
% -> inverse(A)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(
% inverse(C),C)))))
% Current number of equations to process: 20
% Current number of ordered equations: 1
% Current number of rules: 4
% Rule [4]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,
% inverse(C))) <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(
% multiply(
% inverse(C),C))))) is composed into
% [4]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% <->
% multiply(inverse(multiply(b1,inverse(multiply(B,C)))),multiply(b1,inverse(C)))
% New rule produced :
% [5]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(b1,inverse(B))),multiply(b1,inverse(inverse(
% multiply(
% inverse(C),C)))))
% Current number of equations to process: 24
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced :
% [7]
% multiply(inverse(multiply(b1,inverse(B))),multiply(b1,inverse(inverse(
% multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),inverse(C))) ->
% multiply(inverse(multiply(b1,inverse(multiply(inverse(C),C)))),multiply(b1,
% inverse(C)))
% Rule
% [2]
% multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(
% multiply(A,C)))),
% multiply(B,inverse(C))),inverse(C))),
% inverse(multiply(inverse(C),C))) -> inverse(C) collapsed.
% Rule
% [3]
% multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(
% multiply(
% inverse(
% multiply(C,
% inverse(
% multiply(B,A)))),
% multiply(C,
% inverse(A))),
% inverse(A))),
% inverse(A))),inverse(multiply(inverse(A),A)))
% -> inverse(A) collapsed.
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [9]
% multiply(inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(B,inverse(C))) -> A
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [10]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(
% inverse(A),A)))))
% Current number of equations to process: 24
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [11]
% multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(A),A)))))
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [12]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),
% multiply(A,inverse(C))),inverse(multiply(V_3,
% multiply(inverse(C),C))))),B)
% ->
% multiply(inverse(multiply(b1,inverse(multiply(V_3,multiply(inverse(C),C))))),
% multiply(b1,inverse(multiply(inverse(C),C))))
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [13]
% multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))
% <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% Rule
% [4]
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,inverse(C)))
% <->
% multiply(inverse(multiply(b1,inverse(multiply(B,C)))),multiply(b1,inverse(C)))
% collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [14]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(V_3,inverse(B))),multiply(V_3,inverse(inverse(
% multiply(
% inverse(C),C)))))
% Rule
% [6]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(b1,inverse(B))),multiply(b1,inverse(inverse(
% multiply(
% inverse(C),C)))))
% collapsed.
% Rule
% [7]
% multiply(inverse(multiply(b1,inverse(B))),multiply(b1,inverse(inverse(
% multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(C),C)))))
% collapsed.
% Rule
% [10]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(
% inverse(A),A)))))
% collapsed.
% Rule
% [11]
% multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(
% inverse(A),A)))))
% <->
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(
% inverse(A),A)))))
% collapsed.
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [15]
% multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),
% multiply(B,inverse(C))),inverse(inverse(
% multiply(
% inverse(V_3),V_3)))))
% ->
% multiply(inverse(multiply(b1,inverse(multiply(inverse(C),C)))),multiply(b1,
% inverse(
% inverse(
% multiply(
% inverse(V_3),V_3)))))
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [16]
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(V_3),V_3))),V_3))))
% <->
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,inverse(V_3)))))
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [17]
% multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,inverse(V_3)))))
% <->
% inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(V_3),V_3))),V_3))))
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [18]
% multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,
% inverse(C))))),
% multiply(A,inverse(inverse(C)))),inverse(V_3))),B)
% ->
% multiply(inverse(multiply(b1,inverse(V_3))),multiply(b1,inverse(multiply(
% inverse(
% inverse(C)),
% inverse(C)))))
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [19]
% multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,
% inverse(V_3)))))
% <->
% multiply(inverse(multiply(V_4,inverse(B))),multiply(V_4,inverse(multiply(C,
% inverse(V_3)))))
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [20]
% multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,
% inverse(V_3))))),
% multiply(C,inverse(V_3))) -> B
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [21]
% multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(C),C))),C) -> B
% Rule
% [20]
% multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,
% inverse(multiply(C,
% inverse(V_3))))),
% inverse(multiply(inverse(multiply(C,inverse(V_3))),multiply(C,
% inverse(V_3))))),
% multiply(C,inverse(V_3))) -> B collapsed.
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [22]
% inverse(multiply(B,inverse(multiply(multiply(multiply(A,multiply(B,inverse(C))),
% inverse(multiply(inverse(C),C))),C)))) ->
% A
% Current number of equations to process: 145
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [23]
% multiply(inverse(A),A) <->
% multiply(inverse(multiply(b1,inverse(multiply(inverse(inverse(B)),inverse(B))))),
% multiply(b1,inverse(multiply(inverse(inverse(B)),inverse(B)))))
% Current number of equations to process: 174
% Current number of ordered equations: 1
% Current number of rules: 15
% Rule [23]
% multiply(inverse(A),A) <->
% multiply(inverse(multiply(b1,inverse(multiply(inverse(inverse(B)),
% inverse(B))))),multiply(b1,
% inverse(multiply(
% inverse(
% inverse(B)),
% inverse(B))))) is composed into
% [23] multiply(inverse(A),A) <-> multiply(inverse(b1),b1)
% New rule produced :
% [24]
% multiply(inverse(multiply(b1,inverse(multiply(inverse(inverse(B)),inverse(B))))),
% multiply(b1,inverse(multiply(inverse(inverse(B)),inverse(B))))) <->
% multiply(inverse(A),A)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 16
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [1]
% multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,
% inverse(C))),
% inverse(multiply(inverse(C),C))) -> B; trace = in the starting set
% [4] multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,
% inverse(C))) <->
% multiply(inverse(multiply(b1,inverse(multiply(B,C)))),multiply(b1,
% inverse(C))); trace = Self cp of 1
% [5] multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(
% inverse(
% multiply(
% inverse(C),C))))),
% inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(
% multiply(
% inverse(C),C)))))
% <->
% multiply(inverse(multiply(V_3,inverse(multiply(B,C)))),multiply(V_3,
% inverse(C))); trace = Self cp of 1
% [9] multiply(inverse(multiply(B,inverse(multiply(multiply(A,inverse(multiply(
% inverse(C),C))),C)))),
% multiply(B,inverse(C))) -> A; trace = Cp of 5 and 1
% [12] multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),
% multiply(A,inverse(C))),inverse(multiply(V_3,
% multiply(
% inverse(C),C))))),B)
% ->
% multiply(inverse(multiply(b1,inverse(multiply(V_3,multiply(inverse(C),C))))),
% multiply(b1,inverse(multiply(inverse(C),C)))); trace = Cp of 4 and 1
% [18] multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,
% inverse(C))))),
% multiply(A,inverse(inverse(C)))),inverse(V_3))),B)
% ->
% multiply(inverse(multiply(b1,inverse(V_3))),multiply(b1,inverse(
% multiply(
% inverse(
% inverse(C)),
% inverse(C))))); trace = Cp of 12 and 9
% [24] multiply(inverse(multiply(b1,inverse(multiply(inverse(inverse(B)),
% inverse(B))))),multiply(b1,
% inverse(multiply(
% inverse(
% inverse(B)),
% inverse(B)))))
% <-> multiply(inverse(A),A); trace = Cp of 18 and 1
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.230000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------