TSTP Solution File: GRP696-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP696-1 : TPTP v6.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n104.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 00:24:03 EDT 2014
% Result : Unsatisfiable 1.62s
% Output : Refutation 1.62s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP696-1 : TPTP v6.0.0. Released v4.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n104.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 01:07:58 CDT 2014
% % CPUTime : 1.62
% Processing problem /tmp/CiME_4840_n104.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c,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(A,i(mult(B,A))) = i(B);
% mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C));
% mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C)));
% mult(i(A),A) = unit;
% mult(A,i(A)) = unit;
% ";
%
% let s1 = status F "
% c lr_lex;
% 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 > c";
%
% let s2 = status F "
% c mul;
% 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 = c";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " mult(mult(mult(a,b),a),mult(a,c)) = mult(a,mult(mult(mult(b,a),a),c));"
% ;
% (*
% 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(A,i(mult(B,A))) = i(B),
% mult(A,mult(B,C)) =
% mult(rd(mult(A,B),A),mult(A,C)),
% mult(mult(A,B),C) =
% mult(mult(A,C),ld(C,mult(B,C))),
% mult(i(A),A) = unit,
% mult(A,i(A)) = unit } (11 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(mult(a,b),a),mult(a,c)) =
% mult(a,mult(mult(mult(b,a),a),c)) }
% (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: 11
% 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: 10
% Current number of rules: 2
% New rule produced : [3] mult(A,i(A)) -> unit
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 3
% New rule produced : [4] mult(i(A),A) -> unit
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 4
% New rule produced : [5] rd(mult(A,B),B) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 5
% New rule produced : [6] mult(A,ld(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 6
% New rule produced : [7] mult(rd(A,B),B) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 7
% New rule produced : [8] ld(A,mult(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 8
% New rule produced : [9] mult(A,i(mult(B,A))) -> i(B)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 9
% New rule produced :
% [10] mult(mult(A,B),C) <-> mult(mult(A,C),ld(C,mult(B,C)))
% Current number of equations to process: 0
% Current number of ordered equations: 24
% Current number of rules: 10
% New rule produced : [11] mult(rd(mult(A,B),A),mult(A,C)) -> mult(A,mult(B,C))
% Current number of equations to process: 0
% Current number of ordered equations: 23
% Current number of rules: 11
% New rule produced :
% [12] mult(mult(A,C),ld(C,mult(B,C))) <-> mult(mult(A,B),C)
% Current number of equations to process: 0
% Current number of ordered equations: 22
% Current number of rules: 12
% New rule produced : [13] i(unit) -> unit
% Current number of equations to process: 1
% Current number of ordered equations: 17
% Current number of rules: 13
% New rule produced : [14] rd(A,unit) -> A
% Current number of equations to process: 1
% Current number of ordered equations: 15
% Current number of rules: 14
% New rule produced : [15] rd(A,A) -> unit
% Current number of equations to process: 1
% Current number of ordered equations: 14
% Current number of rules: 15
% New rule produced : [16] ld(unit,A) -> A
% Current number of equations to process: 1
% Current number of ordered equations: 12
% Current number of rules: 16
% New rule produced : [17] ld(A,A) -> unit
% Current number of equations to process: 1
% Current number of ordered equations: 11
% Current number of rules: 17
% New rule produced : [18] rd(unit,A) -> i(A)
% Current number of equations to process: 2
% Current number of ordered equations: 9
% Current number of rules: 18
% New rule produced : [19] ld(A,unit) -> i(A)
% Current number of equations to process: 3
% Current number of ordered equations: 7
% Current number of rules: 19
% New rule produced : [20] i(i(A)) -> A
% Current number of equations to process: 3
% Current number of ordered equations: 6
% Current number of rules: 20
% New rule produced : [21] rd(A,ld(B,A)) -> B
% Current number of equations to process: 2
% Current number of ordered equations: 5
% Current number of rules: 21
% New rule produced : [22] ld(rd(A,B),A) -> B
% Current number of equations to process: 2
% Current number of ordered equations: 4
% Current number of rules: 22
% New rule produced : [23] mult(A,i(B)) -> i(rd(B,A))
% Rule [3] mult(A,i(A)) -> unit collapsed.
% Rule [9] mult(A,i(mult(B,A))) -> i(B) collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [24] mult(i(mult(A,B)),A) -> i(B)
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [25] mult(i(A),mult(A,B)) -> mult(A,mult(i(A),B))
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [26] mult(i(A),mult(B,A)) -> rd(mult(i(A),B),i(A))
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [27] mult(B,mult(ld(B,A),C)) -> mult(rd(A,B),mult(B,C))
% Current number of equations to process: 8
% Current number of ordered equations: 2
% Current number of rules: 25
% New rule produced : [28] mult(A,mult(B,ld(A,C))) <-> mult(rd(mult(A,B),A),C)
% Current number of equations to process: 8
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced : [29] mult(rd(mult(A,B),A),C) <-> mult(A,mult(B,ld(A,C)))
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 27
% Rule [10] mult(mult(A,B),C) <-> mult(mult(A,C),ld(C,mult(B,C))) is composed into
% [10] mult(mult(A,B),C) <-> mult(mult(A,C),mult(mult(i(C),B),C))
% New rule produced : [30] ld(A,mult(B,A)) -> mult(mult(i(A),B),A)
% Rule [12] mult(mult(A,C),ld(C,mult(B,C))) <-> mult(mult(A,B),C) collapsed.
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [31] ld(A,i(rd(B,A))) -> i(B)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [32] rd(i(rd(A,B)),i(A)) -> B
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [33] i(rd(B,rd(A,i(B)))) -> A
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [34] mult(A,B) -> i(rd(i(B),A))
% Rule [1] mult(A,unit) -> A collapsed.
% Rule [2] mult(unit,A) -> A collapsed.
% Rule [4] mult(i(A),A) -> unit collapsed.
% Rule [5] rd(mult(A,B),B) -> A collapsed.
% Rule [6] mult(A,ld(A,B)) -> B collapsed.
% Rule [7] mult(rd(A,B),B) -> A collapsed.
% Rule [8] ld(A,mult(A,B)) -> B collapsed.
% Rule [10] mult(mult(A,B),C) <-> mult(mult(A,C),mult(mult(i(C),B),C))
% collapsed.
% Rule [11] mult(rd(mult(A,B),A),mult(A,C)) -> mult(A,mult(B,C)) collapsed.
% Rule [23] mult(A,i(B)) -> i(rd(B,A)) collapsed.
% Rule [24] mult(i(mult(A,B)),A) -> i(B) collapsed.
% Rule [25] mult(i(A),mult(A,B)) -> mult(A,mult(i(A),B)) collapsed.
% Rule [26] mult(i(A),mult(B,A)) -> rd(mult(i(A),B),i(A)) collapsed.
% Rule [27] mult(B,mult(ld(B,A),C)) -> mult(rd(A,B),mult(B,C)) collapsed.
% Rule [28] mult(A,mult(B,ld(A,C))) <-> mult(rd(mult(A,B),A),C) collapsed.
% Rule [29] mult(rd(mult(A,B),A),C) <-> mult(A,mult(B,ld(A,C))) collapsed.
% Rule [30] ld(A,mult(B,A)) -> mult(mult(i(A),B),A) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% i(rd(rd(i(c),a),i(rd(i(a),i(rd(i(b),a)))))) = i(rd(rd(i(c),i(rd(i(a),
% i(rd(i(a),b))))),a))
%
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [35] i(rd(i(B),rd(A,B))) -> A
% Current number of equations to process: 30
% Current number of ordered equations: 5
% Current number of rules: 15
% New rule produced : [36] i(rd(i(ld(A,B)),A)) -> B
% Current number of equations to process: 30
% Current number of ordered equations: 4
% Current number of rules: 16
% New rule produced : [37] rd(i(rd(i(B),A)),B) -> A
% Current number of equations to process: 30
% Current number of ordered equations: 3
% Current number of rules: 17
% New rule produced :
% [38] i(rd(rd(i(C),A),rd(i(rd(i(B),A)),A))) <-> i(rd(rd(i(C),B),A))
% Current number of equations to process: 4
% Current number of ordered equations: 57
% Current number of rules: 18
% New rule produced :
% [39] i(rd(rd(i(C),B),A)) <-> i(rd(rd(i(C),A),rd(i(rd(i(B),A)),A)))
% Current number of equations to process: 4
% Current number of ordered equations: 56
% Current number of rules: 19
% New rule produced :
% [40]
% i(rd(rd(i(C),i(rd(i(B),i(C)))),i(rd(i(C),A)))) -> i(rd(i(C),i(rd(i(B),A))))
% Current number of equations to process: 4
% Current number of ordered equations: 55
% Current number of rules: 20
% New rule produced : [41] ld(A,i(B)) -> rd(i(A),B)
% Rule [31] ld(A,i(rd(B,A))) -> i(B) collapsed.
% Current number of equations to process: 19
% Current number of ordered equations: 37
% Current number of rules: 20
% New rule produced : [42] ld(A,B) -> rd(i(A),i(B))
% Rule [16] ld(unit,A) -> A collapsed.
% Rule [17] ld(A,A) -> unit collapsed.
% Rule [19] ld(A,unit) -> i(A) collapsed.
% Rule [21] rd(A,ld(B,A)) -> B collapsed.
% Rule [22] ld(rd(A,B),A) -> B collapsed.
% Rule [36] i(rd(i(ld(A,B)),A)) -> B collapsed.
% Rule [41] ld(A,i(B)) -> rd(i(A),B) collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 26
% Current number of rules: 14
% New rule produced : [43] rd(i(A),rd(B,A)) -> i(B)
% Rule [35] i(rd(i(B),rd(A,B))) -> A collapsed.
% Current number of equations to process: 24
% Current number of ordered equations: 18
% Current number of rules: 14
% New rule produced : [44] rd(B,rd(A,i(B))) -> i(A)
% Rule [33] i(rd(B,rd(A,i(B)))) -> A collapsed.
% Current number of equations to process: 24
% Current number of ordered equations: 14
% Current number of rules: 14
% New rule produced : [45] i(rd(i(A),i(rd(A,B)))) -> i(rd(A,i(rd(i(A),B))))
% Current number of equations to process: 23
% Current number of ordered equations: 13
% Current number of rules: 15
% New rule produced :
% [46] i(rd(i(B),i(rd(i(C),rd(A,B))))) <-> i(rd(i(rd(i(B),rd(i(B),C))),A))
% Current number of equations to process: 20
% Current number of ordered equations: 16
% Current number of rules: 16
% New rule produced :
% [47]
% i(rd(i(B),i(rd(i(rd(C,B)),A)))) <-> i(rd(i(rd(i(B),i(C))),i(rd(i(B),A))))
% Current number of equations to process: 20
% Current number of ordered equations: 15
% Current number of rules: 17
% New rule produced :
% [48] i(rd(i(rd(i(B),rd(i(B),C))),A)) <-> i(rd(i(B),i(rd(i(C),rd(A,B)))))
% Current number of equations to process: 20
% Current number of ordered equations: 14
% Current number of rules: 18
% New rule produced :
% [49]
% i(rd(i(rd(i(B),i(C))),i(rd(i(B),A)))) <-> i(rd(i(B),i(rd(i(rd(C,B)),A))))
% Current number of equations to process: 20
% Current number of ordered equations: 13
% Current number of rules: 19
% New rule produced :
% [50] rd(i(rd(rd(i(C),B),A)),i(rd(i(C),A))) -> rd(i(rd(i(B),A)),A)
% Current number of equations to process: 22
% Current number of ordered equations: 12
% Current number of rules: 20
% New rule produced :
% [51] rd(rd(i(B),A),rd(i(B),i(rd(i(C),A)))) -> rd(i(B),rd(i(B),C))
% Current number of equations to process: 21
% Current number of ordered equations: 12
% Current number of rules: 21
% New rule produced : [52] i(rd(rd(i(A),i(B)),B)) -> i(rd(rd(i(A),B),i(B)))
% Current number of equations to process: 23
% Current number of ordered equations: 11
% Current number of rules: 22
% New rule produced :
% [53] rd(i(rd(i(rd(i(B),rd(i(B),C))),i(rd(i(B),A)))),B) -> i(rd(i(C),A))
% Current number of equations to process: 22
% Current number of ordered equations: 11
% Current number of rules: 23
% New rule produced :
% [54] i(rd(i(rd(i(B),rd(i(B),C))),i(rd(i(B),rd(A,C))))) -> i(rd(i(B),A))
% Current number of equations to process: 21
% Current number of ordered equations: 11
% Current number of rules: 24
% New rule produced :
% [55] rd(i(rd(i(rd(i(B),A)),A)),rd(rd(i(C),B),A)) -> i(rd(i(C),A))
% Current number of equations to process: 20
% Current number of ordered equations: 11
% Current number of rules: 25
% New rule produced :
% [56] rd(i(rd(i(C),i(rd(i(B),A)))),rd(i(C),rd(i(C),B))) -> i(rd(i(C),A))
% Current number of equations to process: 19
% Current number of ordered equations: 11
% Current number of rules: 26
% New rule produced :
% [57] i(rd(rd(A,C),B)) <-> i(rd(rd(A,B),rd(i(rd(i(C),B)),B)))
% Rule [39] i(rd(rd(i(C),B),A)) <-> i(rd(rd(i(C),A),rd(i(rd(i(B),A)),A)))
% collapsed.
% Current number of equations to process: 19
% Current number of ordered equations: 10
% Current number of rules: 26
% New rule produced :
% [58] i(rd(rd(A,B),rd(i(rd(i(C),B)),B))) <-> i(rd(rd(A,C),B))
% Rule [38] i(rd(rd(i(C),A),rd(i(rd(i(B),A)),A))) <-> i(rd(rd(i(C),B),A))
% collapsed.
% Current number of equations to process: 19
% Current number of ordered equations: 9
% Current number of rules: 26
% New rule produced :
% [59] i(rd(rd(i(C),B),rd(i(rd(A,B)),B))) <-> i(rd(rd(i(C),i(A)),B))
% Current number of equations to process: 20
% Current number of ordered equations: 8
% Current number of rules: 27
% New rule produced :
% [60] i(rd(rd(i(C),i(A)),B)) <-> i(rd(rd(i(C),B),rd(i(rd(A,B)),B)))
% Current number of equations to process: 20
% Current number of ordered equations: 7
% Current number of rules: 28
% New rule produced : [61] i(rd(rd(i(B),A),i(B))) <-> rd(i(rd(i(A),i(B))),i(B))
% Current number of equations to process: 19
% Current number of ordered equations: 7
% Current number of rules: 29
% New rule produced : [62] rd(i(rd(i(A),i(B))),i(B)) <-> i(rd(rd(i(B),A),i(B)))
% Current number of equations to process: 19
% Current number of ordered equations: 5
% Current number of rules: 30
% New rule produced :
% [63] rd(rd(i(B),A),rd(i(rd(i(C),rd(i(C),B))),i(rd(i(C),A)))) -> C
% Current number of equations to process: 21
% Current number of ordered equations: 5
% Current number of rules: 31
% New rule produced : [64] i(rd(i(A),i(rd(i(B),i(A))))) <-> rd(i(A),rd(i(A),B))
% Current number of equations to process: 20
% Current number of ordered equations: 6
% Current number of rules: 32
% New rule produced : [65] rd(i(A),rd(i(A),B)) <-> i(rd(i(A),i(rd(i(B),i(A)))))
% Current number of equations to process: 20
% Current number of ordered equations: 5
% Current number of rules: 33
% New rule produced :
% [66] i(rd(rd(A,i(rd(i(B),A))),i(rd(A,C)))) -> i(rd(A,i(rd(i(B),C))))
% Rule
% [40]
% i(rd(rd(i(C),i(rd(i(B),i(C)))),i(rd(i(C),A)))) -> i(rd(i(C),i(rd(i(B),A))))
% collapsed.
% Current number of equations to process: 20
% Current number of ordered equations: 4
% Current number of rules: 33
% New rule produced : [67] i(rd(A,i(rd(i(A),A)))) -> A
% Current number of equations to process: 28
% Current number of ordered equations: 4
% Current number of rules: 34
% New rule produced : [68] rd(i(A),i(rd(A,B))) -> rd(A,i(rd(i(A),B)))
% Rule [45] i(rd(i(A),i(rd(A,B)))) -> i(rd(A,i(rd(i(A),B)))) collapsed.
% Current number of equations to process: 117
% Current number of ordered equations: 4
% Current number of rules: 34
% Rule [61] i(rd(rd(i(B),A),i(B))) <-> rd(i(rd(i(A),i(B))),i(B)) is composed into
% [61] i(rd(rd(i(B),A),i(B))) -> rd(i(B),i(rd(i(i(A)),i(B))))
% Rule [60] i(rd(rd(i(C),i(A)),B)) <-> i(rd(rd(i(C),B),rd(i(rd(A,B)),B))) is composed into
% [60] i(rd(rd(i(C),i(A)),B)) <-> i(rd(rd(i(C),B),rd(B,i(rd(i(A),B)))))
% Rule [57] i(rd(rd(A,C),B)) <-> i(rd(rd(A,B),rd(i(rd(i(C),B)),B))) is composed into
% [57] i(rd(rd(A,C),B)) <-> i(rd(rd(A,B),rd(B,i(rd(i(i(C)),B)))))
% Rule [50] rd(i(rd(rd(i(C),B),A)),i(rd(i(C),A))) -> rd(i(rd(i(B),A)),A) is composed into
% [50] rd(i(rd(rd(i(C),B),A)),i(rd(i(C),A))) -> rd(A,i(rd(i(i(B)),A)))
% New rule produced : [69] rd(i(rd(B,A)),A) -> rd(A,i(rd(i(B),A)))
% Rule [55] rd(i(rd(i(rd(i(B),A)),A)),rd(rd(i(C),B),A)) -> i(rd(i(C),A))
% collapsed.
% Rule [58] i(rd(rd(A,B),rd(i(rd(i(C),B)),B))) <-> i(rd(rd(A,C),B)) collapsed.
% Rule [59] i(rd(rd(i(C),B),rd(i(rd(A,B)),B))) <-> i(rd(rd(i(C),i(A)),B))
% collapsed.
% Rule [62] rd(i(rd(i(A),i(B))),i(B)) <-> i(rd(rd(i(B),A),i(B))) collapsed.
% Current number of equations to process: 131
% Current number of ordered equations: 2
% Current number of rules: 31
% New rule produced : [70] rd(rd(i(A),i(B)),B) -> rd(rd(i(A),B),i(B))
% Rule [52] i(rd(rd(i(A),i(B)),B)) -> i(rd(rd(i(A),B),i(B))) collapsed.
% Current number of equations to process: 183
% Current number of ordered equations: 2
% Current number of rules: 31
% New rule produced : [71] rd(rd(i(A),i(B)),i(A)) -> rd(i(A),rd(i(A),B))
% Current number of equations to process: 210
% Current number of ordered equations: 2
% Current number of rules: 32
% New rule produced : [72] rd(i(rd(A,i(rd(i(A),B)))),A) -> i(rd(A,B))
% Current number of equations to process: 214
% Current number of ordered equations: 2
% Current number of rules: 33
% New rule produced : [73] i(rd(rd(i(rd(B,A)),B),i(B))) -> i(rd(A,B))
% Current number of equations to process: 213
% Current number of ordered equations: 2
% Current number of rules: 34
% New rule produced : [74] rd(rd(i(A),rd(i(A),B)),A) -> i(rd(i(B),i(A)))
% Current number of equations to process: 211
% Current number of ordered equations: 2
% Current number of rules: 35
% New rule produced : [75] rd(A,rd(i(A),rd(i(A),B))) -> i(rd(i(A),i(B)))
% Current number of equations to process: 295
% Current number of ordered equations: 2
% Current number of rules: 36
% New rule produced : [76] i(rd(i(A),B)) <-> i(rd(i(B),rd(B,i(rd(A,B)))))
% The conjecture has been reduced.
% Conjecture is now:
% i(rd(rd(i(c),a),i(rd(i(a),i(rd(i(b),a)))))) = i(rd(rd(i(c),a),rd(a,rd(
% i(b),
% rd(b,
% i(
% rd(a,b)))))))
%
% Current number of equations to process: 332
% Current number of ordered equations: 3
% Current number of rules: 37
% New rule produced : [77] i(rd(i(B),rd(B,i(rd(A,B))))) <-> i(rd(i(A),B))
% Current number of equations to process: 332
% Current number of ordered equations: 2
% Current number of rules: 38
% New rule produced : [78] rd(rd(A,B),rd(B,i(rd(C,B)))) <-> rd(rd(A,C),B)
% Current number of equations to process: 331
% Current number of ordered equations: 3
% Current number of rules: 39
% New rule produced : [79] rd(rd(A,C),B) <-> rd(rd(A,B),rd(B,i(rd(C,B))))
% Rule [60] i(rd(rd(i(C),i(A)),B)) <-> i(rd(rd(i(C),B),rd(B,i(rd(i(A),B)))))
% collapsed.
% Rule [70] rd(rd(i(A),i(B)),B) -> rd(rd(i(A),B),i(B)) collapsed.
% Rule [74] rd(rd(i(A),rd(i(A),B)),A) -> i(rd(i(B),i(A))) collapsed.
% Current number of equations to process: 333
% Current number of ordered equations: 2
% Current number of rules: 37
% New rule produced : [80] i(rd(rd(A,B),A)) -> rd(A,i(rd(B,A)))
% Rule [61] i(rd(rd(i(B),A),i(B))) -> rd(i(B),i(rd(i(i(A)),i(B)))) collapsed.
% Current number of equations to process: 351
% Current number of ordered equations: 2
% Current number of rules: 37
% New rule produced : [81] rd(rd(A,B),rd(A,i(rd(i(A),B)))) -> A
% Current number of equations to process: 364
% Current number of ordered equations: 2
% Current number of rules: 38
% New rule produced : [82] rd(rd(i(A),B),i(A)) -> i(rd(i(A),i(rd(B,i(A)))))
% Rule [71] rd(rd(i(A),i(B)),i(A)) -> rd(i(A),rd(i(A),B)) collapsed.
% Current number of equations to process: 387
% Current number of ordered equations: 2
% Current number of rules: 38
% New rule produced : [83] i(rd(A,i(rd(i(B),A)))) <-> rd(A,rd(A,B))
% Rule [64] i(rd(i(A),i(rd(i(B),i(A))))) <-> rd(i(A),rd(i(A),B)) collapsed.
% Rule [67] i(rd(A,i(rd(i(A),A)))) -> A collapsed.
% Current number of equations to process: 409
% Current number of ordered equations: 2
% Current number of rules: 37
% New rule produced : [84] rd(i(A),rd(i(A),rd(A,B))) -> i(rd(i(A),i(B)))
% Current number of equations to process: 428
% Current number of ordered equations: 2
% Current number of rules: 38
% New rule produced : [85] i(rd(i(A),rd(i(A),B))) <-> rd(i(A),i(rd(i(B),i(A))))
% Current number of equations to process: 440
% Current number of ordered equations: 5
% Current number of rules: 39
% New rule produced : [86] i(rd(i(A),i(rd(B,i(A))))) <-> rd(i(A),rd(i(A),i(B)))
% Current number of equations to process: 440
% Current number of ordered equations: 4
% Current number of rules: 40
% New rule produced : [87] rd(i(A),i(rd(i(B),i(A)))) <-> i(rd(i(A),rd(i(A),B)))
% Current number of equations to process: 440
% Current number of ordered equations: 3
% Current number of rules: 41
% New rule produced : [88] rd(i(A),rd(i(A),i(B))) <-> i(rd(i(A),i(rd(B,i(A)))))
% Current number of equations to process: 440
% Current number of ordered equations: 2
% Current number of rules: 42
% New rule produced : [89] i(rd(A,i(rd(i(A),rd(B,i(A)))))) -> i(rd(i(A),B))
% Current number of equations to process: 489
% Current number of ordered equations: 2
% Current number of rules: 43
% New rule produced : [90] rd(rd(A,B),rd(A,i(rd(i(C),B)))) -> rd(A,rd(A,C))
% Rule [51] rd(rd(i(B),A),rd(i(B),i(rd(i(C),A)))) -> rd(i(B),rd(i(B),C))
% collapsed.
% Rule [81] rd(rd(A,B),rd(A,i(rd(i(A),B)))) -> A collapsed.
% Current number of equations to process: 488
% Current number of ordered equations: 2
% Current number of rules: 42
% New rule produced :
% [91] i(rd(rd(i(C),i(rd(A,i(C)))),i(rd(i(C),B)))) -> i(rd(i(C),i(rd(A,B))))
% Current number of equations to process: 491
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced : [92] rd(A,i(rd(i(A),A))) -> i(A)
% Current number of equations to process: 493
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced : [93] rd(A,i(rd(i(A),rd(B,i(A))))) -> rd(i(A),B)
% Rule [89] i(rd(A,i(rd(i(A),rd(B,i(A)))))) -> i(rd(i(A),B)) collapsed.
% Current number of equations to process: 514
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced : [94] rd(B,i(rd(rd(i(B),A),B))) -> rd(i(A),B)
% Current number of equations to process: 540
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced : [95] rd(i(A),rd(A,i(rd(i(B),A)))) -> rd(B,A)
% Current number of equations to process: 544
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced : [96] rd(i(A),A) -> i(rd(A,i(A)))
% Rule [92] rd(A,i(rd(i(A),A))) -> i(A) collapsed.
% Current number of equations to process: 558
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced : [97] rd(i(rd(A,B)),A) -> i(rd(A,rd(B,A)))
% Rule [72] rd(i(rd(A,i(rd(i(A),B)))),A) -> i(rd(A,B)) collapsed.
% Rule [73] i(rd(rd(i(rd(B,A)),B),i(B))) -> i(rd(A,B)) collapsed.
% Current number of equations to process: 561
% Current number of ordered equations: 1
% Current number of rules: 45
% New rule produced : [98] rd(i(A),rd(A,rd(A,B))) -> i(rd(A,i(B)))
% Current number of equations to process: 566
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced : [99] i(rd(i(A),i(rd(B,A)))) -> rd(A,rd(i(A),i(B)))
% The conjecture has been reduced.
% Conjecture is now:
% i(rd(rd(i(c),a),rd(a,rd(i(a),b)))) = i(rd(rd(i(c),a),rd(a,rd(i(b),rd(b,
% i(rd(a,b)))))))
%
% Current number of equations to process: 577
% Current number of ordered equations: 1
% Current number of rules: 47
% New rule produced : [100] rd(i(rd(A,i(rd(i(B),A)))),rd(B,A)) -> A
% Current number of equations to process: 580
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced : [101] rd(i(B),i(rd(rd(B,A),i(B)))) -> rd(i(A),i(B))
% Current number of equations to process: 579
% Current number of ordered equations: 1
% Current number of rules: 49
% New rule produced : [102] rd(rd(A,B),i(rd(B,rd(A,B)))) -> rd(A,rd(A,B))
% Current number of equations to process: 578
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced : [103] rd(i(B),A) <-> rd(i(A),rd(A,i(rd(B,A))))
% Rule [32] rd(i(rd(A,B)),i(A)) -> B collapsed.
% Rule [37] rd(i(rd(i(B),A)),B) -> A collapsed.
% Rule [50] rd(i(rd(rd(i(C),B),A)),i(rd(i(C),A))) -> rd(A,i(rd(i(i(B)),A)))
% collapsed.
% Rule [53] rd(i(rd(i(rd(i(B),rd(i(B),C))),i(rd(i(B),A)))),B) -> i(rd(i(C),A))
% collapsed.
% Rule [69] rd(i(rd(B,A)),A) -> rd(A,i(rd(i(B),A))) collapsed.
% Rule [76] i(rd(i(A),B)) <-> i(rd(i(B),rd(B,i(rd(A,B))))) collapsed.
% Rule [97] rd(i(rd(A,B)),A) -> i(rd(A,rd(B,A))) collapsed.
% Rule [100] rd(i(rd(A,i(rd(i(B),A)))),rd(B,A)) -> A collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 594
% Current number of ordered equations: 1
% Current number of rules: 43
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 21 rules have been used:
% [2]
% mult(unit,A) -> A; trace = in the starting set
% [3] mult(A,i(A)) -> unit; trace = in the starting set
% [4] mult(i(A),A) -> unit; trace = in the starting set
% [5] rd(mult(A,B),B) -> A; trace = in the starting set
% [7] mult(rd(A,B),B) -> A; trace = in the starting set
% [8] ld(A,mult(A,B)) -> B; trace = in the starting set
% [9] mult(A,i(mult(B,A))) -> i(B); trace = in the starting set
% [11] mult(rd(mult(A,B),A),mult(A,C)) -> mult(A,mult(B,C)); trace = in the starting set
% [12] mult(mult(A,C),ld(C,mult(B,C))) <-> mult(mult(A,B),C); trace = in the starting set
% [15] rd(A,A) -> unit; trace = Cp of 5 and 2
% [18] rd(unit,A) -> i(A); trace = Cp of 5 and 4
% [20] i(i(A)) -> A; trace = Cp of 5 and 3
% [23] mult(A,i(B)) -> i(rd(B,A)); trace = Cp of 9 and 7
% [34] mult(A,B) -> i(rd(i(B),A)); trace = Cp of 23 and 20
% [43] rd(i(A),rd(B,A)) -> i(B); trace = Cp of 23 and 8
% [56] rd(i(rd(i(C),i(rd(i(B),A)))),rd(i(C),rd(i(C),B))) -> i(rd(i(C),A)); trace = Cp of 12 and 5
% [57] i(rd(rd(A,C),B)) <-> i(rd(rd(A,B),rd(B,i(rd(i(i(C)),B))))); trace = Cp of 23 and 11
% [75] rd(A,rd(i(A),rd(i(A),B))) -> i(rd(i(A),i(B))); trace = Cp of 56 and 15
% [76] i(rd(i(A),B)) <-> i(rd(i(B),rd(B,i(rd(A,B))))); trace = Cp of 57 and 18
% [99] i(rd(i(A),i(rd(B,A)))) -> rd(A,rd(i(A),i(B))); trace = Cp of 75 and 43
% [103] rd(i(B),A) <-> rd(i(A),rd(A,i(rd(B,A)))); trace = Cp of 76 and 20
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.510000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------