TSTP Solution File: GRP698-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP698-1 : TPTP v6.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n082.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 1.82s
% Output : Refutation 1.82s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP698-1 : TPTP v6.0.0. Released v4.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n082.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 01:09:33 CDT 2014
% % CPUTime : 1.82
% Processing problem /tmp/CiME_60165_n082.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c,b,a,unit : constant; 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(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C));
% mult(mult(A,B),mult(B,mult(C,B))) = mult(mult(A,mult(B,mult(B,C))),B);
% ";
%
% let s1 = status F "
% c lr_lex;
% b lr_lex;
% a lr_lex;
% unit lr_lex;
% rd lr_lex;
% mult lr_lex;
% ld lr_lex;
% ";
%
% let p1 = precedence F "
% ld > mult > rd > unit > a > b > c";
%
% let s2 = status F "
% c mul;
% b mul;
% a mul;
% unit mul;
% rd mul;
% mult mul;
% ld mul;
% ";
%
% let p2 = precedence F "
% ld > mult > rd > 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(a,mult(b,c)) = mult(rd(mult(a,b),a),mult(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(mult(mult(A,B),A),mult(A,C)) =
% mult(A,mult(mult(mult(B,A),A),C)),
% mult(mult(A,B),mult(B,mult(C,B))) =
% mult(mult(A,mult(B,mult(B,C))),B) }
% (8 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(a,mult(b,c)) =
% mult(rd(mult(a,b),a),mult(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: 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(A,mult(mult(mult(B,A),A),C)) <-> mult(mult(mult(A,B),A),mult(A,C))
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 7
% New rule produced :
% [8] mult(mult(mult(A,B),A),mult(A,C)) <-> mult(A,mult(mult(mult(B,A),A),C))
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 8
% New rule produced :
% [9] mult(mult(A,mult(B,mult(B,C))),B) -> mult(mult(A,B),mult(B,mult(C,B)))
% Current number of equations to process: 0
% Current number of ordered equations: 8
% 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: 6
% 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: 5
% 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: 3
% Current number of rules: 12
% New rule produced : [13] ld(A,A) -> unit
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 13
% New rule produced : [14] rd(A,ld(B,A)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 1
% 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(mult(mult(A,B),A),A) -> mult(A,mult(mult(B,A),A))
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17] mult(mult(A,A),mult(A,B)) -> mult(A,mult(mult(A,A),B))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18] mult(mult(A,mult(B,B)),B) -> mult(mult(A,B),mult(B,B))
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19] mult(mult(A,mult(A,B)),A) -> mult(A,mult(A,mult(B,A)))
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] mult(mult(A,A),A) -> mult(A,mult(A,A))
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21] mult(mult(A,B),A) <-> rd(mult(A,mult(mult(B,A),A)),A)
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [22] rd(mult(A,mult(mult(B,A),A)),A) <-> mult(mult(A,B),A)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [23] mult(B,mult(mult(ld(B,A),B),B)) -> mult(mult(A,B),B)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] mult(A,mult(mult(A,A),ld(A,B))) -> mult(mult(A,A),B)
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] rd(mult(mult(A,B),mult(B,B)),B) -> mult(A,mult(B,B))
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] rd(mult(A,mult(A,mult(B,A))),A) -> mult(A,mult(A,B))
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [27] mult(A,mult(A,mult(ld(A,B),A))) -> mult(mult(A,B),A)
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [28] rd(mult(A,mult(A,A)),A) -> mult(A,A)
% Current number of equations to process: 96
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [29] ld(mult(A,A),mult(A,mult(A,A))) -> A
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [30] mult(mult(A,rd(B,A)),A) -> rd(mult(A,mult(B,A)),A)
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31] mult(mult(A,mult(B,A)),A) -> mult(mult(A,B),mult(A,A))
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [32] ld(A,mult(mult(B,A),A)) -> mult(mult(ld(A,B),A),A)
% Current number of equations to process: 131
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [33] ld(A,mult(mult(A,A),B)) -> mult(mult(A,A),ld(A,B))
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [34] mult(rd(A,B),mult(B,B)) -> rd(mult(A,mult(B,B)),B)
% Current number of equations to process: 151
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [35] mult(A,mult(A,rd(B,A))) -> rd(mult(A,mult(A,B)),A)
% Current number of equations to process: 164
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [36] ld(A,mult(mult(A,B),A)) -> mult(A,mult(ld(A,B),A))
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [37] rd(rd(mult(A,mult(B,A)),A),A) -> mult(A,rd(B,A))
% Current number of equations to process: 197
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [38] rd(mult(mult(A,B),mult(A,A)),A) -> mult(A,mult(B,A))
% Current number of equations to process: 215
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [39] mult(mult(A,rd(B,A)),mult(A,A)) -> mult(mult(A,B),A)
% Current number of equations to process: 214
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [40] mult(mult(ld(A,unit),A),A) -> A
% Current number of equations to process: 239
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [41] ld(A,mult(B,A)) -> mult(mult(ld(A,rd(B,A)),A),A)
% Rule [29] ld(mult(A,A),mult(A,mult(A,A))) -> A collapsed.
% Rule [32] ld(A,mult(mult(B,A),A)) -> mult(mult(ld(A,B),A),A) collapsed.
% Rule [36] ld(A,mult(mult(A,B),A)) -> mult(A,mult(ld(A,B),A)) collapsed.
% Current number of equations to process: 242
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [42] mult(mult(A,A),ld(A,unit)) -> A
% Current number of equations to process: 242
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [43] ld(A,rd(mult(A,mult(A,B)),A)) -> mult(A,rd(B,A))
% Current number of equations to process: 270
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [44] mult(A,rd(unit,A)) -> unit
% Current number of equations to process: 286
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [45] mult(A,rd(rd(B,A),A)) -> rd(rd(mult(A,B),A),A)
% Current number of equations to process: 287
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [46] rd(mult(A,mult(mult(A,A),B)),mult(A,B)) -> mult(A,A)
% Current number of equations to process: 286
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [47] ld(mult(A,A),mult(A,mult(mult(A,A),B))) -> mult(A,B)
% Current number of equations to process: 285
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [48] mult(mult(rd(A,mult(B,B)),B),mult(B,B)) -> mult(A,B)
% Current number of equations to process: 284
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [49] mult(B,mult(ld(B,A),B)) -> rd(mult(A,mult(B,B)),B)
% Rule [27] mult(A,mult(A,mult(ld(A,B),A))) -> mult(mult(A,B),A) collapsed.
% Current number of equations to process: 304
% Current number of ordered equations: 0
% Current number of rules: 45
% Rule [39] mult(mult(A,rd(B,A)),mult(A,A)) -> mult(mult(A,B),A) is composed into
% [39] mult(mult(A,rd(B,A)),mult(A,A)) -> mult(A,rd(mult(B,mult(A,A)),A))
% Rule [22] rd(mult(A,mult(mult(B,A),A)),A) <-> mult(mult(A,B),A) is composed into
% [22] rd(mult(A,mult(mult(B,A),A)),A) -> mult(A,rd(mult(B,mult(A,A)),A))
% Rule [7]
% mult(A,mult(mult(mult(B,A),A),C)) <-> mult(mult(mult(A,B),A),mult(A,C)) is composed into
% [7]
% mult(A,mult(mult(mult(B,A),A),C)) ->
% mult(mult(A,rd(mult(B,mult(A,A)),A)),mult(A,C))
% New rule produced : [50] mult(mult(A,B),A) -> mult(A,rd(mult(B,mult(A,A)),A))
% Rule
% [8] mult(mult(mult(A,B),A),mult(A,C)) <-> mult(A,mult(mult(mult(B,A),A),C))
% collapsed.
% Rule [16] mult(mult(mult(A,B),A),A) -> mult(A,mult(mult(B,A),A)) collapsed.
% Rule [19] mult(mult(A,mult(A,B)),A) -> mult(A,mult(A,mult(B,A))) collapsed.
% Rule [20] mult(mult(A,A),A) -> mult(A,mult(A,A)) collapsed.
% Rule [21] mult(mult(A,B),A) <-> rd(mult(A,mult(mult(B,A),A)),A) collapsed.
% Rule [30] mult(mult(A,rd(B,A)),A) -> rd(mult(A,mult(B,A)),A) collapsed.
% Rule [31] mult(mult(A,mult(B,A)),A) -> mult(mult(A,B),mult(A,A)) collapsed.
% Current number of equations to process: 306
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [51] rd(mult(A,rd(mult(B,mult(A,A)),A)),A) -> mult(A,B)
% Current number of equations to process: 305
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [52] mult(mult(A,B),mult(A,A)) -> mult(A,mult(B,mult(A,A)))
% Rule [38] rd(mult(mult(A,B),mult(A,A)),A) -> mult(A,mult(B,A)) collapsed.
% Rule [39] mult(mult(A,rd(B,A)),mult(A,A)) -> mult(A,rd(mult(B,mult(A,A)),A))
% collapsed.
% Current number of equations to process: 320
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [53] mult(ld(A,unit),A) -> unit
% Rule [40] mult(mult(ld(A,unit),A),A) -> A collapsed.
% Current number of equations to process: 320
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [54] mult(mult(ld(A,rd(unit,A)),A),A) -> unit
% Current number of equations to process: 323
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [55] rd(mult(A,mult(B,mult(A,A))),A) -> mult(A,mult(B,A))
% Current number of equations to process: 322
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [56] rd(A,ld(A,unit)) -> mult(A,A)
% Current number of equations to process: 333
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [57] ld(mult(A,A),A) -> ld(A,unit)
% Current number of equations to process: 332
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [58] mult(mult(A,A),ld(A,ld(A,unit))) -> unit
% Current number of equations to process: 341
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [59] mult(mult(rd(unit,A),rd(unit,A)),A) -> rd(unit,A)
% Current number of equations to process: 340
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [60] ld(A,rd(mult(A,B),A)) -> mult(A,rd(ld(A,B),A))
% Rule [43] ld(A,rd(mult(A,mult(A,B)),A)) -> mult(A,rd(B,A)) collapsed.
% Current number of equations to process: 343
% Current number of ordered equations: 0
% Current number of rules: 45
% Rule [57] ld(mult(A,A),A) -> ld(A,unit) is composed into [57]
% ld(mult(A,A),A) ->
% rd(unit,A)
% New rule produced : [61] ld(A,unit) -> rd(unit,A)
% Rule [42] mult(mult(A,A),ld(A,unit)) -> A collapsed.
% Rule [53] mult(ld(A,unit),A) -> unit collapsed.
% Rule [56] rd(A,ld(A,unit)) -> mult(A,A) collapsed.
% Rule [58] mult(mult(A,A),ld(A,ld(A,unit))) -> unit collapsed.
% Current number of equations to process: 347
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [62] rd(unit,rd(unit,A)) -> A
% Current number of equations to process: 346
% Current number of ordered equations: 0
% Current number of rules: 43
% Rule [50] mult(mult(A,B),A) -> mult(A,rd(mult(B,mult(A,A)),A)) is composed into
% [50] mult(mult(A,B),A) -> mult(A,rd(mult(B,rd(A,rd(unit,A))),A))
% Rule [49] mult(B,mult(ld(B,A),B)) -> rd(mult(A,mult(B,B)),B) is composed into
% [49] mult(B,mult(ld(B,A),B)) -> rd(mult(A,rd(B,rd(unit,B))),B)
% Rule [22] rd(mult(A,mult(mult(B,A),A)),A) -> mult(A,rd(mult(B,mult(A,A)),A)) is composed into
% [22]
% rd(mult(A,mult(mult(B,A),A)),A) -> mult(A,rd(mult(B,rd(A,rd(unit,A))),A))
% Rule [7]
% mult(A,mult(mult(mult(B,A),A),C)) ->
% mult(mult(A,rd(mult(B,mult(A,A)),A)),mult(A,C)) is composed into
% [7]
% mult(A,mult(mult(mult(B,A),A),C)) ->
% mult(mult(A,rd(mult(B,rd(A,rd(unit,A))),A)),mult(A,C))
% New rule produced : [63] mult(A,A) -> rd(A,rd(unit,A))
% Rule [17] mult(mult(A,A),mult(A,B)) -> mult(A,mult(mult(A,A),B)) collapsed.
% Rule [18] mult(mult(A,mult(B,B)),B) -> mult(mult(A,B),mult(B,B)) collapsed.
% Rule [24] mult(A,mult(mult(A,A),ld(A,B))) -> mult(mult(A,A),B) collapsed.
% Rule [25] rd(mult(mult(A,B),mult(B,B)),B) -> mult(A,mult(B,B)) collapsed.
% Rule [28] rd(mult(A,mult(A,A)),A) -> mult(A,A) collapsed.
% Rule [33] ld(A,mult(mult(A,A),B)) -> mult(mult(A,A),ld(A,B)) collapsed.
% Rule [34] mult(rd(A,B),mult(B,B)) -> rd(mult(A,mult(B,B)),B) collapsed.
% Rule [46] rd(mult(A,mult(mult(A,A),B)),mult(A,B)) -> mult(A,A) collapsed.
% Rule [47] ld(mult(A,A),mult(A,mult(mult(A,A),B))) -> mult(A,B) collapsed.
% Rule [48] mult(mult(rd(A,mult(B,B)),B),mult(B,B)) -> mult(A,B) collapsed.
% Rule [51] rd(mult(A,rd(mult(B,mult(A,A)),A)),A) -> mult(A,B) collapsed.
% Rule [52] mult(mult(A,B),mult(A,A)) -> mult(A,mult(B,mult(A,A))) collapsed.
% Rule [55] rd(mult(A,mult(B,mult(A,A))),A) -> mult(A,mult(B,A)) collapsed.
% Rule [57] ld(mult(A,A),A) -> rd(unit,A) collapsed.
% Rule [59] mult(mult(rd(unit,A),rd(unit,A)),A) -> rd(unit,A) collapsed.
% Current number of equations to process: 358
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [64] mult(rd(A,rd(unit,A)),ld(A,rd(unit,A))) -> unit
% Current number of equations to process: 362
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [65] mult(rd(unit,A),rd(A,rd(unit,A))) -> A
% Current number of equations to process: 361
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [66] rd(rd(rd(unit,A),A),rd(unit,A)) -> rd(unit,A)
% Current number of equations to process: 360
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [67] rd(mult(A,rd(A,rd(unit,A))),A) -> rd(A,rd(unit,A))
% Current number of equations to process: 359
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [68] ld(A,rd(rd(mult(A,B),A),A)) -> rd(rd(B,A),A)
% Current number of equations to process: 357
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [69] rd(rd(rd(A,rd(unit,A)),A),A) -> unit
% Current number of equations to process: 360
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [70] mult(A,rd(rd(A,rd(unit,A)),A)) -> rd(A,rd(unit,A))
% Current number of equations to process: 387
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [71] mult(ld(A,rd(unit,A)),A) -> rd(unit,A)
% Rule [54] mult(mult(ld(A,rd(unit,A)),A),A) -> unit collapsed.
% Current number of equations to process: 403
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [72] mult(A,rd(ld(A,ld(A,B)),A)) -> ld(A,rd(B,A))
% Current number of equations to process: 404
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [73] rd(rd(A,rd(unit,A)),A) -> A
% Rule [69] rd(rd(rd(A,rd(unit,A)),A),A) -> unit collapsed.
% Rule [70] mult(A,rd(rd(A,rd(unit,A)),A)) -> rd(A,rd(unit,A)) collapsed.
% Current number of equations to process: 412
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [74] ld(A,rd(A,rd(unit,A))) -> A
% Current number of equations to process: 413
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [75] mult(rd(A,rd(unit,A)),A) -> mult(A,rd(A,rd(unit,A)))
% Current number of equations to process: 420
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [76] rd(unit,ld(A,rd(unit,A))) -> rd(A,rd(unit,A))
% Current number of equations to process: 422
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [77] ld(A,rd(unit,A)) -> rd(unit,rd(A,rd(unit,A)))
% Rule [64] mult(rd(A,rd(unit,A)),ld(A,rd(unit,A))) -> unit collapsed.
% Rule [71] mult(ld(A,rd(unit,A)),A) -> rd(unit,A) collapsed.
% Rule [76] rd(unit,ld(A,rd(unit,A))) -> rd(A,rd(unit,A)) collapsed.
% Current number of equations to process: 422
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [78] mult(rd(unit,rd(A,rd(unit,A))),A) -> rd(unit,A)
% Current number of equations to process: 425
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [79] ld(rd(unit,A),A) -> rd(A,rd(unit,A))
% Current number of equations to process: 427
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [80] rd(A,rd(A,rd(unit,A))) -> rd(unit,A)
% Current number of equations to process: 426
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [81] mult(A,rd(rd(unit,rd(A,rd(unit,A))),A)) -> rd(unit,rd(A,rd(unit,A)))
% Current number of equations to process: 428
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [82] ld(rd(unit,A),rd(rd(unit,A),A)) -> rd(unit,A)
% Current number of equations to process: 428
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [83] rd(rd(unit,A),A) -> rd(unit,rd(A,rd(unit,A)))
% Rule [66] rd(rd(rd(unit,A),A),rd(unit,A)) -> rd(unit,A) collapsed.
% Rule [82] ld(rd(unit,A),rd(rd(unit,A),A)) -> rd(unit,A) collapsed.
% Current number of equations to process: 441
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [84] ld(A,rd(rd(B,A),A)) -> rd(rd(ld(A,B),A),A)
% Rule [68] ld(A,rd(rd(mult(A,B),A),A)) -> rd(rd(B,A),A) collapsed.
% Current number of equations to process: 440
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [85] ld(A,ld(A,rd(B,A))) -> rd(ld(A,ld(A,B)),A)
% Current number of equations to process: 449
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [86] mult(A,rd(unit,rd(A,rd(unit,A)))) -> rd(unit,A)
% Current number of equations to process: 449
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [87] rd(rd(unit,A),rd(unit,rd(A,rd(unit,A)))) -> A
% Current number of equations to process: 469
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [88] ld(rd(unit,rd(A,rd(unit,A))),rd(unit,A)) -> A
% Current number of equations to process: 469
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [89] mult(rd(A,rd(unit,A)),ld(A,ld(rd(A,rd(unit,A)),B))) -> ld(A,B)
% Current number of equations to process: 508
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [90] rd(rd(mult(A,rd(B,rd(unit,B))),B),rd(B,rd(unit,B))) -> rd(A,B)
% Current number of equations to process: 507
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [91] ld(rd(A,B),rd(mult(A,rd(B,rd(unit,B))),B)) -> rd(B,rd(unit,B))
% Current number of equations to process: 506
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [92] rd(rd(unit,rd(A,rd(unit,A))),rd(unit,A)) -> rd(unit,A)
% Current number of equations to process: 512
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [93] ld(rd(unit,A),rd(unit,rd(A,rd(unit,A)))) -> rd(unit,A)
% Current number of equations to process: 511
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [94] mult(rd(A,rd(unit,A)),mult(A,B)) -> mult(A,mult(rd(A,rd(unit,A)),B))
% Current number of equations to process: 556
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [95] mult(mult(A,rd(B,rd(unit,B))),B) -> mult(mult(A,B),rd(B,rd(unit,B)))
% Current number of equations to process: 584
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [96]
% ld(mult(A,rd(mult(B,rd(A,rd(unit,A))),A)),mult(A,mult(mult(B,A),A))) -> A
% Current number of equations to process: 607
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [97] ld(mult(A,rd(B,rd(unit,B))),mult(mult(A,B),rd(B,rd(unit,B)))) -> B
% Current number of equations to process: 636
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [98]
% mult(mult(A,rd(A,rd(unit,A))),rd(A,rd(unit,A))) ->
% mult(A,mult(A,mult(A,rd(A,rd(unit,A)))))
% Current number of equations to process: 663
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced : [99] ld(mult(A,mult(A,B)),mult(A,mult(A,mult(B,A)))) -> A
% Current number of equations to process: 678
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [100]
% mult(A,rd(mult(A,mult(A,mult(B,rd(A,rd(unit,A))))),A)) <->
% mult(A,mult(rd(A,rd(unit,A)),mult(B,A)))
% Current number of equations to process: 707
% Current number of ordered equations: 1
% Current number of rules: 57
% New rule produced :
% [101]
% mult(A,mult(rd(A,rd(unit,A)),mult(B,A))) <->
% mult(A,rd(mult(A,mult(A,mult(B,rd(A,rd(unit,A))))),A))
% Current number of equations to process: 707
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [102]
% mult(mult(A,rd(A,rd(unit,A))),mult(A,B)) ->
% mult(A,mult(mult(A,rd(A,rd(unit,A))),B))
% Current number of equations to process: 763
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [103] ld(mult(A,B),mult(A,rd(mult(B,rd(A,rd(unit,A))),A))) -> A
% Current number of equations to process: 806
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced : [104] rd(mult(mult(A,B),B),mult(mult(ld(B,A),B),B)) -> B
% Current number of equations to process: 836
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [105]
% mult(mult(mult(mult(A,B),B),B),B) ->
% mult(mult(A,rd(B,rd(unit,B))),rd(B,rd(unit,B)))
% Current number of equations to process: 871
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [106]
% mult(mult(A,mult(B,A)),rd(A,rd(unit,A))) ->
% mult(A,mult(mult(B,A),rd(A,rd(unit,A))))
% Current number of equations to process: 912
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [107] rd(mult(rd(A,rd(unit,A)),B),mult(rd(A,rd(unit,A)),ld(A,B))) -> A
% Current number of equations to process: 962
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [108] ld(A,mult(rd(A,rd(unit,A)),B)) -> mult(rd(A,rd(unit,A)),ld(A,B))
% Current number of equations to process: 992
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [109] mult(rd(A,B),rd(B,rd(unit,B))) -> rd(mult(A,rd(B,rd(unit,B))),B)
% Rule [65] mult(rd(unit,A),rd(A,rd(unit,A))) -> A collapsed.
% Current number of equations to process: 1010
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [110]
% mult(mult(A,mult(B,rd(mult(C,rd(B,rd(unit,B))),B))),B) ->
% mult(mult(A,B),mult(mult(C,B),B))
% Current number of equations to process: 1041
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [111]
% mult(mult(A,mult(A,B)),rd(A,rd(unit,A))) ->
% mult(A,mult(A,mult(B,rd(A,rd(unit,A)))))
% Current number of equations to process: 1097
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced : [112] ld(mult(A,rd(B,A)),rd(mult(A,mult(B,A)),A)) -> A
% Current number of equations to process: 1141
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [113] rd(mult(A,mult(B,rd(A,rd(unit,A)))),A) -> mult(A,mult(B,A))
% Current number of equations to process: 1178
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [114] ld(mult(A,mult(B,A)),mult(mult(A,B),rd(A,rd(unit,A)))) -> A
% Current number of equations to process: 1200
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [115]
% mult(A,mult(mult(A,B),rd(A,rd(unit,A)))) ->
% mult(A,mult(A,mult(B,rd(A,rd(unit,A)))))
% Current number of equations to process: 1241
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced : [116] rd(rd(mult(A,mult(A,B)),A),mult(A,rd(B,A))) -> A
% Current number of equations to process: 1291
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [117] mult(mult(A,B),rd(A,rd(unit,A))) -> mult(A,mult(B,rd(A,rd(unit,A))))
% Rule
% [98]
% mult(mult(A,rd(A,rd(unit,A))),rd(A,rd(unit,A))) ->
% mult(A,mult(A,mult(A,rd(A,rd(unit,A))))) collapsed.
% Rule
% [106]
% mult(mult(A,mult(B,A)),rd(A,rd(unit,A))) ->
% mult(A,mult(mult(B,A),rd(A,rd(unit,A)))) collapsed.
% Rule
% [111]
% mult(mult(A,mult(A,B)),rd(A,rd(unit,A))) ->
% mult(A,mult(A,mult(B,rd(A,rd(unit,A))))) collapsed.
% Rule [114] ld(mult(A,mult(B,A)),mult(mult(A,B),rd(A,rd(unit,A)))) -> A
% collapsed.
% Rule
% [115]
% mult(A,mult(mult(A,B),rd(A,rd(unit,A)))) ->
% mult(A,mult(A,mult(B,rd(A,rd(unit,A))))) collapsed.
% Current number of equations to process: 1332
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced : [118] rd(mult(A,B),mult(mult(ld(B,rd(A,B)),B),B)) -> B
% Current number of equations to process: 1381
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced : [119] rd(rd(rd(mult(A,B),A),A),rd(rd(B,A),A)) -> A
% Current number of equations to process: 1419
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [120] ld(A,rd(mult(B,rd(A,rd(unit,A))),A)) -> mult(ld(A,B),A)
% Current number of equations to process: 1462
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced : [121] rd(rd(mult(A,B),A),mult(A,rd(ld(A,B),A))) -> A
% Current number of equations to process: 1478
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced : [122] rd(ld(A,rd(B,A)),rd(ld(A,ld(A,B)),A)) -> A
% Current number of equations to process: 1521
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [123] ld(A,rd(unit,rd(A,rd(unit,A)))) -> rd(rd(unit,rd(A,rd(unit,A))),A)
% Current number of equations to process: 1557
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced : [124] rd(rd(rd(A,B),B),rd(rd(ld(B,A),B),B)) -> B
% Current number of equations to process: 1561
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [125] ld(rd(unit,A),rd(A,rd(unit,A))) -> rd(rd(A,rd(unit,A)),rd(unit,A))
% Current number of equations to process: 1599
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [126] ld(rd(A,rd(unit,A)),ld(A,B)) -> ld(A,ld(rd(A,rd(unit,A)),B))
% Current number of equations to process: 1594
% Current number of ordered equations: 0
% Current number of rules: 77
% Rule [123] ld(A,rd(unit,rd(A,rd(unit,A)))) -> rd(rd(unit,rd(A,rd(unit,A))),A) is composed into
% [123] ld(A,rd(unit,rd(A,rd(unit,A)))) -> rd(rd(unit,A),rd(A,rd(unit,A)))
% New rule produced :
% [127] rd(rd(A,rd(B,rd(unit,B))),B) -> rd(rd(A,B),rd(B,rd(unit,B)))
% Rule
% [81] mult(A,rd(rd(unit,rd(A,rd(unit,A))),A)) -> rd(unit,rd(A,rd(unit,A)))
% collapsed.
% Current number of equations to process: 1622
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [128] mult(A,mult(rd(B,rd(A,rd(unit,A))),A)) -> rd(mult(A,B),A)
% Current number of equations to process: 1639
% Current number of ordered equations: 0
% Current number of rules: 78
% Rule [60] ld(A,rd(mult(A,B),A)) -> mult(A,rd(ld(A,B),A)) is composed into
% [60] ld(A,rd(mult(A,B),A)) -> mult(rd(B,rd(A,rd(unit,A))),A)
% New rule produced :
% [129] mult(A,rd(ld(A,B),A)) -> mult(rd(B,rd(A,rd(unit,A))),A)
% Rule [72] mult(A,rd(ld(A,ld(A,B)),A)) -> ld(A,rd(B,A)) collapsed.
% Rule [121] rd(rd(mult(A,B),A),mult(A,rd(ld(A,B),A))) -> A collapsed.
% Current number of equations to process: 1655
% Current number of ordered equations: 0
% Current number of rules: 77
% Rule [41] ld(A,mult(B,A)) -> mult(mult(ld(A,rd(B,A)),A),A) is composed into
% [41] ld(A,mult(B,A)) -> mult(mult(mult(rd(ld(A,B),rd(A,rd(unit,A))),A),A),A)
% New rule produced :
% [130] ld(A,rd(B,A)) -> mult(rd(ld(A,B),rd(A,rd(unit,A))),A)
% Rule [60] ld(A,rd(mult(A,B),A)) -> mult(rd(B,rd(A,rd(unit,A))),A) collapsed.
% Rule [77] ld(A,rd(unit,A)) -> rd(unit,rd(A,rd(unit,A))) collapsed.
% Rule [84] ld(A,rd(rd(B,A),A)) -> rd(rd(ld(A,B),A),A) collapsed.
% Rule [85] ld(A,ld(A,rd(B,A))) -> rd(ld(A,ld(A,B)),A) collapsed.
% Rule [118] rd(mult(A,B),mult(mult(ld(B,rd(A,B)),B),B)) -> B collapsed.
% Rule [120] ld(A,rd(mult(B,rd(A,rd(unit,A))),A)) -> mult(ld(A,B),A) collapsed.
% Rule [122] rd(ld(A,rd(B,A)),rd(ld(A,ld(A,B)),A)) -> A collapsed.
% Rule [125] ld(rd(unit,A),rd(A,rd(unit,A))) -> rd(rd(A,rd(unit,A)),rd(unit,A))
% collapsed.
% Current number of equations to process: 1661
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [131] rd(rd(mult(A,B),A),mult(rd(B,rd(A,rd(unit,A))),A)) -> A
% Current number of equations to process: 1738
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [132] rd(mult(A,mult(B,A)),rd(A,rd(unit,A))) -> rd(mult(A,B),A)
% Current number of equations to process: 1781
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [133] rd(mult(A,rd(B,A)),A) -> rd(mult(A,B),rd(A,rd(unit,A)))
% Current number of equations to process: 1797
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [134] ld(rd(mult(A,B),A),mult(A,mult(B,A))) -> rd(A,rd(unit,A))
% Current number of equations to process: 1841
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [135]
% mult(ld(A,rd(B,rd(A,rd(unit,A)))),A) -> mult(rd(ld(A,B),rd(A,rd(unit,A))),A)
% Current number of equations to process: 1880
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [136]
% mult(rd(rd(A,rd(unit,A)),rd(unit,rd(A,rd(unit,A)))),rd(unit,A)) ->
% rd(rd(A,rd(unit,A)),rd(unit,A))
% Current number of equations to process: 1921
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [137] ld(rd(A,rd(unit,A)),rd(unit,A)) -> rd(rd(unit,A),rd(A,rd(unit,A)))
% Current number of equations to process: 1944
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [138] mult(rd(mult(A,B),rd(A,rd(unit,A))),A) -> mult(A,rd(B,A))
% Current number of equations to process: 1951
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [139] ld(A,rd(B,rd(A,rd(unit,A)))) -> rd(ld(A,B),rd(A,rd(unit,A)))
% Rule [123] ld(A,rd(unit,rd(A,rd(unit,A)))) -> rd(rd(unit,A),rd(A,rd(unit,A)))
% collapsed.
% Rule
% [135]
% mult(ld(A,rd(B,rd(A,rd(unit,A)))),A) -> mult(rd(ld(A,B),rd(A,rd(unit,A))),A)
% collapsed.
% Current number of equations to process: 2000
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [140] ld(rd(unit,rd(A,rd(unit,A))),A) -> rd(A,rd(unit,rd(A,rd(unit,A))))
% Current number of equations to process: 2020
% Current number of ordered equations: 0
% Current number of rules: 78
% Rule [130] ld(A,rd(B,A)) -> mult(rd(ld(A,B),rd(A,rd(unit,A))),A) is composed into
% [130] ld(A,rd(B,A)) -> rd(mult(ld(A,B),A),rd(A,rd(unit,A)))
% Rule [129] mult(A,rd(ld(A,B),A)) -> mult(rd(B,rd(A,rd(unit,A))),A) is composed into
% [129] mult(A,rd(ld(A,B),A)) -> rd(mult(B,A),rd(A,rd(unit,A)))
% Rule [41]
% ld(A,mult(B,A)) -> mult(mult(mult(rd(ld(A,B),rd(A,rd(unit,A))),A),A),A) is composed into
% [41] ld(A,mult(B,A)) -> rd(mult(mult(mult(ld(A,B),A),A),A),rd(A,rd(unit,A)))
% New rule produced :
% [141] mult(rd(A,rd(B,rd(unit,B))),B) -> rd(mult(A,B),rd(B,rd(unit,B)))
% Rule [78] mult(rd(unit,rd(A,rd(unit,A))),A) -> rd(unit,A) collapsed.
% Rule [128] mult(A,mult(rd(B,rd(A,rd(unit,A))),A)) -> rd(mult(A,B),A)
% collapsed.
% Rule [131] rd(rd(mult(A,B),A),mult(rd(B,rd(A,rd(unit,A))),A)) -> A collapsed.
% Rule [138] mult(rd(mult(A,B),rd(A,rd(unit,A))),A) -> mult(A,rd(B,A))
% collapsed.
% Current number of equations to process: 2028
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [142] mult(A,rd(mult(B,A),rd(A,rd(unit,A)))) -> rd(mult(A,B),A)
% Current number of equations to process: 2027
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [143]
% rd(mult(A,rd(mult(B,rd(A,rd(unit,A))),A)),rd(A,rd(unit,A))) ->
% mult(A,rd(B,A))
% Current number of equations to process: 2026
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [144] mult(A,rd(B,rd(A,rd(unit,A)))) -> rd(mult(A,B),rd(A,rd(unit,A)))
% Rule [86] mult(A,rd(unit,rd(A,rd(unit,A)))) -> rd(unit,A) collapsed.
% Rule [142] mult(A,rd(mult(B,A),rd(A,rd(unit,A)))) -> rd(mult(A,B),A)
% collapsed.
% Current number of equations to process: 2125
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [145] mult(rd(mult(A,mult(B,A)),A),mult(A,C)) -> mult(A,mult(mult(B,A),C))
% Current number of equations to process: 2156
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [146] mult(rd(mult(A,B),A),mult(A,C)) -> mult(A,mult(B,C))
% Rule
% [145] mult(rd(mult(A,mult(B,A)),A),mult(A,C)) -> mult(A,mult(mult(B,A),C))
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 2200
% Current number of ordered equations: 0
% Current number of rules: 77
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 4 rules have been used:
% [5]
% mult(rd(A,B),B) -> A; trace = in the starting set
% [7] mult(A,mult(mult(mult(B,A),A),C)) <-> mult(mult(mult(A,B),A),mult(A,C)); trace = in the starting set
% [145] mult(rd(mult(A,mult(B,A)),A),mult(A,C)) -> mult(A,mult(mult(B,A),C)); trace = Cp of 7 and 5
% [146] mult(rd(mult(A,B),A),mult(A,C)) -> mult(A,mult(B,C)); trace = Cp of 145 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.710000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------