TSTP Solution File: GRP564-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP564-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n112.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 1.20s
% Output : Refutation 1.20s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP564-1 : TPTP v6.0.0. Bugfixed v2.7.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n112.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 20:05:23 CDT 2014
% % CPUTime : 1.20
% Processing problem /tmp/CiME_46249_n112.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a : 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 "
% b lr_lex;
% a lr_lex;
% multiply lr_lex;
% divide lr_lex;
% inverse lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > divide > inverse > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% multiply mul;
% divide mul;
% inverse mul;
% ";
%
% let p2 = precedence F "
% multiply > divide > inverse > a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(a,b) = multiply(b,a);"
% ;
% (*
% 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(a,b) = multiply(b,a) }
% (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(a,inverse(b)) = divide(b,inverse(a))
%
% 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.
% 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)
% 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.
% 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)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [26] inverse(inverse(A)) -> A
% Rule [19] divide(inverse(inverse(A)),inverse(B)) -> divide(A,inverse(B))
% collapsed.
% Rule [20] divide(A,inverse(inverse(B))) -> divide(A,B) collapsed.
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [27] divide(divide(A,A),inverse(B)) -> B
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [28]
% divide(A,divide(divide(inverse(B),inverse(A)),C)) -> divide(B,inverse(C))
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [29]
% divide(inverse(A),inverse(divide(divide(B,inverse(A)),C))) -> divide(B,C)
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [30] divide(A,divide(divide(A,B),divide(inverse(B),inverse(C)))) -> C
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [31] divide(divide(A,B),divide(divide(A,C),B)) -> C
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [32] divide(inverse(A),divide(B,A)) -> inverse(B)
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 23
% Rule [8] divide(A,B) <-> divide(inverse(B),inverse(A)) is composed into
% [8] divide(A,B) <-> inverse(divide(B,inverse(inverse(A))))
% New rule produced :
% [33] divide(inverse(A),B) -> inverse(divide(A,inverse(B)))
% Rule [6] divide(A,divide(inverse(B),inverse(A))) -> B collapsed.
% Rule
% [9] divide(inverse(divide(A,C)),inverse(divide(divide(A,inverse(B)),C))) -> B
% collapsed.
% Rule [10] divide(inverse(B),inverse(A)) <-> divide(A,B) collapsed.
% Rule [11] divide(inverse(A),inverse(divide(A,inverse(B)))) -> B collapsed.
% Rule [12] divide(inverse(divide(B,B)),inverse(A)) -> A collapsed.
% Rule
% [14]
% divide(inverse(B),inverse(divide(inverse(A),inverse(divide(divide(A,inverse(B)),
% inverse(C)))))) -> C
% collapsed.
% Rule [15] divide(divide(A,B),divide(divide(inverse(C),inverse(A)),B)) -> C
% collapsed.
% Rule
% [28]
% divide(A,divide(divide(inverse(B),inverse(A)),C)) -> divide(B,inverse(C))
% collapsed.
% Rule
% [29]
% divide(inverse(A),inverse(divide(divide(B,inverse(A)),C))) -> divide(B,C)
% collapsed.
% Rule [30] divide(A,divide(divide(A,B),divide(inverse(B),inverse(C)))) -> C
% collapsed.
% Rule [32] divide(inverse(A),divide(B,A)) -> inverse(B) collapsed.
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [34] inverse(divide(B,A)) <-> divide(A,B)
% Current number of equations to process: 77
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced : [35] divide(A,B) <-> inverse(divide(B,A))
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [36] inverse(divide(divide(B,B),A)) -> A
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [37] divide(A,divide(divide(B,inverse(A)),C)) <-> divide(C,B)
% Current number of equations to process: 80
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [38] divide(C,B) <-> divide(A,divide(divide(B,inverse(A)),C))
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [39] divide(divide(A,inverse(B)),C) <-> divide(divide(B,C),inverse(A))
% Current number of equations to process: 88
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [40] divide(divide(B,C),inverse(A)) <-> divide(divide(A,inverse(B)),C)
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [41] divide(A,B) <-> divide(divide(C,B),inverse(divide(A,C)))
% Current number of equations to process: 87
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [42] divide(divide(C,B),inverse(divide(A,C))) <-> divide(A,B)
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 22
% Rule [41] divide(A,B) <-> divide(divide(C,B),inverse(divide(A,C))) is composed into
% [41] divide(A,B) <-> inverse(divide(B,divide(C,inverse(divide(A,C)))))
% Rule [39] divide(divide(A,inverse(B)),C) <-> divide(divide(B,C),inverse(A)) is composed into
% [39]
% divide(divide(A,inverse(B)),C) <-> inverse(divide(C,divide(B,inverse(A))))
% Rule [23] divide(divide(A,inverse(C)),B) <-> divide(divide(A,B),inverse(C)) is composed into
% [23]
% divide(divide(A,inverse(C)),B) <-> inverse(divide(B,divide(A,inverse(C))))
% New rule produced :
% [43]
% divide(divide(B,A),inverse(C)) -> inverse(divide(A,divide(B,inverse(C))))
% Rule [24] divide(divide(A,B),inverse(C)) <-> divide(divide(A,inverse(C)),B)
% collapsed.
% Rule [27] divide(divide(A,A),inverse(B)) -> B collapsed.
% Rule [40] divide(divide(B,C),inverse(A)) <-> divide(divide(A,inverse(B)),C)
% collapsed.
% Rule [42] divide(divide(C,B),inverse(divide(A,C))) <-> divide(A,B) collapsed.
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [44] divide(divide(A,A),B) -> inverse(B)
% Rule [36] inverse(divide(divide(B,B),A)) -> A collapsed.
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [45] divide(A,inverse(B)) <-> divide(divide(C,inverse(B)),divide(C,A))
% Current number of equations to process: 87
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [46] divide(divide(C,inverse(B)),divide(C,A)) <-> divide(A,inverse(B))
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [47] divide(divide(A,C),B) <-> divide(divide(A,B),C)
% Current number of equations to process: 93
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [48] divide(divide(A,B),divide(C,B)) -> divide(A,C)
% Rule [31] divide(divide(A,B),divide(divide(A,C),B)) -> C collapsed.
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [49] divide(A,divide(B,inverse(A))) -> inverse(B)
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [50] inverse(divide(A,inverse(B))) <-> inverse(divide(B,inverse(A)))
% Current number of equations to process: 97
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [51] divide(B,inverse(A)) <-> divide(A,inverse(B))
% Rule [50] inverse(divide(A,inverse(B))) <-> inverse(divide(B,inverse(A)))
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 101
% Current number of ordered equations: 0
% Current number of rules: 24
% 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
% [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
% [17] divide(A,divide(A,B)) -> B; trace = Cp of 10 and 6
% [22] divide(A,inverse(divide(B,A))) -> B; trace = Cp of 11 and 10
% [33] divide(inverse(A),B) -> inverse(divide(A,inverse(B))); trace = Cp of 17 and 11
% [34] inverse(divide(B,A)) <-> divide(A,B); trace = Cp of 22 and 17
% [51] divide(B,inverse(A)) <-> divide(A,inverse(B)); trace = Cp of 34 and 33
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.080000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------