TSTP Solution File: GRP671-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP671-1 : TPTP v6.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n092.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 00:23:56 EDT 2014
% Result : Unsatisfiable 1.13s
% Output : Refutation 1.13s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP671-1 : TPTP v6.0.0. Released v4.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n092.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 : Sat Jun 7 00:45:58 CDT 2014
% % CPUTime : 1.13
% Processing problem /tmp/CiME_3338_n092.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a,unit : constant; i : 1; rd : 2; mult : 2; ld : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% mult(A,ld(A,B)) = B;
% ld(A,mult(A,B)) = B;
% mult(rd(A,B),B) = A;
% rd(mult(A,B),B) = A;
% mult(A,unit) = A;
% mult(unit,A) = A;
% mult(i(A),mult(A,B)) = B;
% mult(mult(A,B),i(B)) = A;
% mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B);
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% i lr_lex;
% unit lr_lex;
% rd lr_lex;
% mult lr_lex;
% ld lr_lex;
% ";
%
% let p1 = precedence F "
% ld > mult > rd > i > unit > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% i mul;
% unit mul;
% rd mul;
% mult mul;
% ld mul;
% ";
%
% let p2 = precedence F "
% ld > mult > rd > i > unit = a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " mult(mult(a,b),a) = mult(a,mult(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 = { mult(A,ld(A,B)) = B,
% ld(A,mult(A,B)) = B,
% mult(rd(A,B),B) = A,
% rd(mult(A,B),B) = A,
% mult(A,unit) = A,
% mult(unit,A) = A,
% mult(i(A),mult(A,B)) = B,
% mult(mult(A,B),i(B)) = A,
% mult(mult(A,B),mult(C,mult(A,B))) =
% mult(mult(mult(A,mult(B,C)),A),B) }
% (9 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 = { mult(mult(a,b),a) = mult(a,mult(b,a)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] mult(A,unit) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 1
% New rule produced : [2] mult(unit,A) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 2
% New rule produced : [3] rd(mult(A,B),B) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 3
% New rule produced : [4] mult(A,ld(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 4
% New rule produced : [5] mult(rd(A,B),B) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 5
% New rule produced : [6] ld(A,mult(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 6
% New rule produced : [7] mult(mult(A,B),i(B)) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced : [8] mult(i(A),mult(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [9] mult(mult(mult(A,mult(B,C)),A),B) -> mult(mult(A,B),mult(C,mult(A,B)))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] rd(A,unit) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] rd(A,A) -> unit
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] ld(unit,A) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] ld(A,A) -> unit
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] rd(A,ld(B,A)) -> B
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] ld(rd(A,B),A) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] mult(A,i(unit)) -> A
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] mult(A,i(A)) -> unit
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] mult(A,B) -> rd(A,i(B))
% Rule [1] mult(A,unit) -> A collapsed.
% Rule [2] mult(unit,A) -> A collapsed.
% Rule [3] rd(mult(A,B),B) -> A collapsed.
% Rule [4] mult(A,ld(A,B)) -> B collapsed.
% Rule [5] mult(rd(A,B),B) -> A collapsed.
% Rule [6] ld(A,mult(A,B)) -> B collapsed.
% Rule [7] mult(mult(A,B),i(B)) -> A collapsed.
% Rule [8] mult(i(A),mult(A,B)) -> B collapsed.
% Rule
% [9] mult(mult(mult(A,mult(B,C)),A),B) -> mult(mult(A,B),mult(C,mult(A,B)))
% collapsed.
% Rule [16] mult(A,i(unit)) -> A collapsed.
% Rule [17] mult(A,i(A)) -> unit collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% rd(rd(a,i(b)),i(a)) = rd(a,i(rd(b,i(a))))
%
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [19] rd(A,i(unit)) -> A
% Current number of equations to process: 3
% Current number of ordered equations: 8
% Current number of rules: 8
% New rule produced : [20] rd(unit,i(A)) -> A
% Current number of equations to process: 3
% Current number of ordered equations: 7
% Current number of rules: 9
% New rule produced : [21] rd(A,i(ld(A,B))) -> B
% Current number of equations to process: 3
% Current number of ordered equations: 6
% Current number of rules: 10
% New rule produced : [22] rd(rd(A,B),i(B)) -> A
% Current number of equations to process: 3
% Current number of ordered equations: 4
% Current number of rules: 11
% New rule produced : [23] rd(rd(A,i(B)),B) -> A
% Current number of equations to process: 3
% Current number of ordered equations: 3
% Current number of rules: 12
% New rule produced : [24] ld(A,rd(A,i(B))) -> B
% Current number of equations to process: 3
% Current number of ordered equations: 2
% Current number of rules: 13
% New rule produced : [25] rd(i(A),i(rd(A,i(B)))) -> B
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [26]
% rd(rd(rd(A,i(rd(B,i(C)))),i(A)),i(B)) ->
% rd(rd(A,i(B)),i(rd(C,i(rd(A,i(B))))))
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [27] rd(A,i(i(unit))) -> A
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [28] rd(A,i(i(A))) -> unit
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [29] i(unit) -> unit
% Rule [19] rd(A,i(unit)) -> A collapsed.
% Rule [27] rd(A,i(i(unit))) -> A collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [30] ld(A,unit) -> i(A)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [31] i(ld(B,A)) <-> ld(A,B)
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced : [32] ld(A,B) <-> i(ld(B,A))
% Rule [15] ld(rd(A,B),A) -> B collapsed.
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [33] rd(unit,A) -> i(A)
% Rule [20] rd(unit,i(A)) -> A collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [34] i(i(A)) -> A
% Rule [28] rd(A,i(i(A))) -> unit collapsed.
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [35] i(ld(A,rd(A,B))) -> B
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [36] ld(A,B) -> rd(i(A),i(B))
% Rule [12] ld(unit,A) -> A collapsed.
% Rule [13] ld(A,A) -> unit collapsed.
% Rule [14] rd(A,ld(B,A)) -> B collapsed.
% Rule [21] rd(A,i(ld(A,B))) -> B collapsed.
% Rule [24] ld(A,rd(A,i(B))) -> B collapsed.
% Rule [30] ld(A,unit) -> i(A) collapsed.
% Rule [31] i(ld(B,A)) <-> ld(A,B) collapsed.
% Rule [32] ld(A,B) <-> i(ld(B,A)) collapsed.
% Rule [35] i(ld(A,rd(A,B))) -> B collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [37] rd(A,i(rd(i(A),i(B)))) -> B
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [38] rd(A,rd(B,i(A))) -> i(B)
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [39] rd(i(rd(A,B)),i(A)) -> B
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [40] i(rd(i(B),i(A))) <-> rd(i(A),i(B))
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 15
% New rule produced : [41] rd(i(A),i(B)) <-> i(rd(i(B),i(A)))
% Rule [39] rd(i(rd(A,B)),i(A)) -> B collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [42] i(rd(i(A),i(rd(A,B)))) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [43] rd(rd(A,B),i(rd(B,i(rd(A,B))))) <-> rd(rd(A,i(A)),B)
% Current number of equations to process: 5
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced : [44] rd(rd(A,i(A)),B) <-> rd(rd(A,B),i(rd(B,i(rd(A,B)))))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [45] rd(rd(A,C),i(rd(rd(C,i(B)),i(rd(A,C))))) <-> rd(rd(rd(A,i(B)),i(A)),C)
% Current number of equations to process: 4
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [46] rd(rd(rd(A,i(B)),i(A)),C) <-> rd(rd(A,C),i(rd(rd(C,i(B)),i(rd(A,C)))))
% Rule
% [26]
% rd(rd(rd(A,i(rd(B,i(C)))),i(A)),i(B)) ->
% rd(rd(A,i(B)),i(rd(C,i(rd(A,i(B)))))) collapsed.
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [47] rd(i(A),i(rd(A,B))) -> i(B)
% Rule [25] rd(i(A),i(rd(A,i(B)))) -> B collapsed.
% Rule [42] i(rd(i(A),i(rd(A,B)))) -> B collapsed.
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [48] i(rd(B,A)) <-> rd(A,B)
% Rule [40] i(rd(i(B),i(A))) <-> rd(i(A),i(B)) collapsed.
% Current number of equations to process: 6
% Current number of ordered equations: 1
% Current number of rules: 18
% Rule [45]
% rd(rd(A,C),i(rd(rd(C,i(B)),i(rd(A,C))))) <-> rd(rd(rd(A,i(B)),i(A)),C) is composed into
% [45]
% rd(rd(A,C),i(rd(rd(C,i(B)),i(rd(A,C))))) <-> rd(i(rd(i(A),rd(A,i(B)))),C)
% New rule produced : [49] rd(A,B) <-> i(rd(B,A))
% Rule [22] rd(rd(A,B),i(B)) -> A collapsed.
% Rule [23] rd(rd(A,i(B)),B) -> A collapsed.
% Rule [41] rd(i(A),i(B)) <-> i(rd(i(B),i(A))) collapsed.
% Rule
% [46] rd(rd(rd(A,i(B)),i(A)),C) <-> rd(rd(A,C),i(rd(rd(C,i(B)),i(rd(A,C)))))
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% i(rd(i(a),rd(a,i(b)))) = rd(a,i(rd(b,i(a))))
%
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [50] i(rd(i(B),rd(A,B))) -> A
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [51] rd(i(A),rd(B,A)) -> i(B)
% Rule [50] i(rd(i(B),rd(A,B))) -> A collapsed.
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [52] rd(A,i(rd(i(A),B))) -> i(B)
% Rule [37] rd(A,i(rd(i(A),i(B)))) -> B collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [53] rd(i(A),rd(A,rd(A,i(B)))) <-> rd(rd(B,i(B)),rd(A,i(B)))
% Current number of equations to process: 6
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [54] rd(rd(B,i(B)),rd(A,i(B))) <-> rd(i(A),rd(A,rd(A,i(B))))
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [55] rd(B,A) <-> rd(i(A),rd(A,rd(A,i(B))))
% Current number of equations to process: 15
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced : [56] rd(i(A),rd(A,rd(A,i(B)))) <-> rd(B,A)
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [57] i(rd(i(A),rd(A,i(B)))) <-> rd(A,i(rd(B,i(A))))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 14
% Current number of ordered equations: 1
% Current number of rules: 21
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 12 rules have been used:
% [1]
% mult(A,unit) -> A; trace = in the starting set
% [3] rd(mult(A,B),B) -> A; trace = in the starting set
% [7] mult(mult(A,B),i(B)) -> A; trace = in the starting set
% [10] rd(A,unit) -> A; trace = Cp of 3 and 1
% [18] mult(A,B) -> rd(A,i(B)); trace = Cp of 7 and 3
% [22] rd(rd(A,B),i(B)) -> A; trace = in the starting set
% [25] rd(i(A),i(rd(A,i(B)))) -> B; trace = in the starting set
% [26] rd(rd(rd(A,i(rd(B,i(C)))),i(A)),i(B)) ->
% rd(rd(A,i(B)),i(rd(C,i(rd(A,i(B)))))); trace = in the starting set
% [38] rd(A,rd(B,i(A))) -> i(B); trace = Cp of 25 and 22
% [45] rd(rd(A,C),i(rd(rd(C,i(B)),i(rd(A,C))))) <->
% rd(i(rd(i(A),rd(A,i(B)))),C); trace = Cp of 26 and 25
% [49] rd(A,B) <-> i(rd(B,A)); trace = Cp of 38 and 22
% [57] i(rd(i(A),rd(A,i(B)))) <-> rd(A,i(rd(B,i(A)))); trace = Cp of 45 and 10
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.020000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------