TSTP Solution File: GRP509-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP509-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n073.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 00:23:22 EDT 2014
% Result : Unsatisfiable 1.24s
% Output : Refutation 1.24s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP509-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n073.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 15:07:53 CDT 2014
% % CPUTime : 1.24
% Processing problem /tmp/CiME_45833_n073.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(multiply(A,B),C),inverse(multiply(A,C))) = B;
% ";
%
% let s1 = status F "
% b1 lr_lex;
% a1 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% ";
%
% let p1 = precedence F "
% inverse > multiply > a1 > b1";
%
% let s2 = status F "
% b1 mul;
% a1 mul;
% inverse mul;
% multiply mul;
% ";
%
% let p2 = precedence F "
% inverse > multiply > 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(multiply(A,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(inverse(a1),a1) =
% multiply(inverse(b1),b1) } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced :
% [1] multiply(multiply(multiply(A,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,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) -> C
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% inverse(multiply(multiply(V_3,C),inverse(multiply(V_3,A)))) <->
% multiply(multiply(A,B),inverse(multiply(C,B)))
% Rule
% [2] multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) -> C
% collapsed.
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [4] multiply(A,multiply(multiply(C,B),inverse(multiply(A,B)))) -> C
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [5]
% multiply(multiply(A,B),inverse(multiply(C,B))) <->
% multiply(multiply(A,V_3),inverse(multiply(C,V_3)))
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [6]
% multiply(multiply(B,C),inverse(multiply(B,C))) <->
% multiply(multiply(A,A),inverse(multiply(A,A)))
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [7] multiply(A,inverse(A)) <-> multiply(multiply(B,B),inverse(multiply(B,B)))
% Rule
% [6]
% multiply(multiply(B,C),inverse(multiply(B,C))) <->
% multiply(multiply(A,A),inverse(multiply(A,A))) collapsed.
% Current number of equations to process: 37
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [8] multiply(A,multiply(multiply(B,B),inverse(multiply(B,B)))) -> A
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced : [9] multiply(multiply(A,B),inverse(A)) -> B
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 7
% Rule [7]
% multiply(A,inverse(A)) <->
% multiply(multiply(B,B),inverse(multiply(B,B))) is composed into
% [7] multiply(A,inverse(A)) <-> multiply(B,inverse(B))
% Rule [3]
% inverse(multiply(multiply(V_3,C),inverse(multiply(V_3,A)))) <->
% multiply(multiply(A,B),inverse(multiply(C,B))) is composed into
% [3]
% inverse(multiply(multiply(V_3,C),inverse(multiply(V_3,A)))) ->
% multiply(A,inverse(C))
% New rule produced :
% [10] multiply(multiply(A,C),inverse(multiply(B,C))) -> multiply(A,inverse(B))
% Rule [1] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) -> B
% collapsed.
% Rule [4] multiply(A,multiply(multiply(C,B),inverse(multiply(A,B)))) -> C
% collapsed.
% Rule
% [5]
% multiply(multiply(A,B),inverse(multiply(C,B))) <->
% multiply(multiply(A,V_3),inverse(multiply(C,V_3))) collapsed.
% Rule [8] multiply(A,multiply(multiply(B,B),inverse(multiply(B,B)))) -> A
% collapsed.
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [11] multiply(A,multiply(C,inverse(A))) -> C
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [12] multiply(A,multiply(B,inverse(B))) -> A
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [13] multiply(A,inverse(multiply(B,A))) -> inverse(B)
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [14] multiply(multiply(A,inverse(A)),inverse(B)) -> inverse(B)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [15] inverse(multiply(A,inverse(B))) -> multiply(B,inverse(A))
% Rule
% [3]
% inverse(multiply(multiply(V_3,C),inverse(multiply(V_3,A)))) ->
% multiply(A,inverse(C)) collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [16]
% multiply(multiply(V_3,A),inverse(multiply(V_3,C))) -> multiply(A,inverse(C))
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [17] inverse(multiply(A,B)) -> multiply(inverse(A),inverse(B))
% Rule
% [10] multiply(multiply(A,C),inverse(multiply(B,C))) -> multiply(A,inverse(B))
% collapsed.
% Rule [13] multiply(A,inverse(multiply(B,A))) -> inverse(B) collapsed.
% Rule [15] inverse(multiply(A,inverse(B))) -> multiply(B,inverse(A))
% collapsed.
% Rule
% [16]
% multiply(multiply(V_3,A),inverse(multiply(V_3,C))) -> multiply(A,inverse(C))
% collapsed.
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [18] multiply(B,inverse(A)) <-> multiply(inverse(A),inverse(inverse(B)))
% Current number of equations to process: 58
% Current number of ordered equations: 1
% Current number of rules: 7
% New rule produced :
% [19] multiply(inverse(A),inverse(inverse(B))) <-> multiply(B,inverse(A))
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [20] multiply(A,multiply(inverse(A),inverse(inverse(B)))) -> B
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [21] multiply(inverse(A),multiply(A,inverse(B))) -> inverse(B)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [22] multiply(multiply(B,A),inverse(C)) -> multiply(A,multiply(B,inverse(C)))
% Rule [9] multiply(multiply(A,B),inverse(A)) -> B collapsed.
% Rule [14] multiply(multiply(A,inverse(A)),inverse(B)) -> inverse(B)
% collapsed.
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 9
% Rule [18] multiply(B,inverse(A)) <-> multiply(inverse(A),inverse(inverse(B))) is composed into
% [18] multiply(B,inverse(A)) <-> multiply(inverse(A),B)
% New rule produced : [23] inverse(inverse(A)) -> A
% Rule [19] multiply(inverse(A),inverse(inverse(B))) <-> multiply(B,inverse(A))
% collapsed.
% Rule [20] multiply(A,multiply(inverse(A),inverse(inverse(B)))) -> B
% collapsed.
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [24] multiply(A,multiply(inverse(A),B)) -> B
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [25] multiply(inverse(A),multiply(inverse(B),A)) -> inverse(B)
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 10
% multiply(B,A) = multiply(A,B) (birth = 134, lhs_size = 3, rhs_size = 3,trace = Cp of 23 and 18)
% Initializing completion ...
% New rule produced : [1] A <-> inverse(inverse(A))
% Current number of equations to process: 83
% Current number of ordered equations: 15
% Current number of rules: 1
% New rule produced : [2] inverse(inverse(A)) <-> A
% Current number of equations to process: 83
% Current number of ordered equations: 14
% Current number of rules: 2
% New rule produced : [3] A <-> (inverse(B) multiply B) multiply A
% Current number of equations to process: 82
% Current number of ordered equations: 17
% Current number of rules: 3
% New rule produced : [4] B <-> (inverse(A) multiply B) multiply A
% Current number of equations to process: 82
% Current number of ordered equations: 15
% Current number of rules: 4
% New rule produced : [5] (inverse(A) multiply B) multiply A <-> B
% Current number of equations to process: 82
% Current number of ordered equations: 13
% Current number of rules: 5
% New rule produced : [6] (inverse(B) multiply B) multiply A <-> A
% Current number of equations to process: 82
% Current number of ordered equations: 12
% Current number of rules: 6
% New rule produced :
% [7] inverse(A multiply B) <-> inverse(A) multiply inverse(B)
% Current number of equations to process: 110
% Current number of ordered equations: 17
% Current number of rules: 7
% New rule produced :
% [8] inverse(A) multiply inverse(B) <-> inverse(A multiply B)
% Current number of equations to process: 110
% Current number of ordered equations: 16
% Current number of rules: 8
% New rule produced :
% [9] inverse(B) <-> inverse(A) multiply (inverse(B) multiply A)
% Current number of equations to process: 123
% Current number of ordered equations: 31
% Current number of rules: 9
% New rule produced :
% [10] inverse(A) multiply (inverse(B) multiply A) <-> inverse(B)
% Current number of equations to process: 123
% Current number of ordered equations: 30
% Current number of rules: 10
% New rule produced :
% [11]
% inverse(C) multiply (A multiply B) <-> (inverse(C) multiply B) multiply A
% Current number of equations to process: 141
% Current number of ordered equations: 57
% Current number of rules: 11
% New rule produced :
% [12]
% (inverse(C) multiply B) multiply A <-> inverse(C) multiply (A multiply B)
% Current number of equations to process: 141
% Current number of ordered equations: 56
% Current number of rules: 12
% New rule produced :
% [13] B <-> inverse(A multiply C) multiply ((A multiply B) multiply C)
% Current number of equations to process: 164
% Current number of ordered equations: 117
% Current number of rules: 13
% New rule produced :
% [14] inverse(A multiply C) multiply ((A multiply B) multiply C) <-> B
% Current number of equations to process: 164
% Current number of ordered equations: 116
% Current number of rules: 14
% New rule produced : [15] A <-> inverse(inverse(inverse(inverse(A))))
% Current number of equations to process: 164
% Current number of ordered equations: 115
% Current number of rules: 15
% New rule produced : [16] inverse(inverse(inverse(inverse(A)))) <-> A
% Current number of equations to process: 164
% Current number of ordered equations: 114
% Current number of rules: 16
% New rule produced : [17] inverse(B) multiply B <-> inverse(A) multiply A
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 164
% Current number of ordered equations: 106
% Current number of rules: 17
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 1 rules have been used:
% [17]
% inverse(B) multiply B <-> inverse(A) multiply A; trace = in the starting set
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.110000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------