TSTP Solution File: GRP709-1 by CiME---2.01
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP709-1 : TPTP v6.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n111.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 00:24:09 EDT 2014
% Result : Unsatisfiable 1.24s
% Output : Refutation 1.24s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP709-1 : TPTP v6.0.0. Released v4.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n111.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 01:16:53 CDT 2014
% % CPUTime : 1.24
% Processing problem /tmp/CiME_49961_n111.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a,op_c,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(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C);
% mult(op_c,A) = mult(A,op_c);
% mult(A,mult(B,op_c)) = mult(mult(A,B),op_c);
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% op_c lr_lex;
% unit lr_lex;
% rd lr_lex;
% mult lr_lex;
% ld lr_lex;
% ";
%
% let p1 = precedence F "
% ld > mult > rd > unit > op_c > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% op_c mul;
% unit mul;
% rd mul;
% mult mul;
% ld mul;
% ";
%
% let p2 = precedence F "
% ld > mult > rd > unit = op_c = 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(op_c,op_c),mult(a,b)) = mult(mult(mult(op_c,op_c),a),b);"
% ;
% (*
% 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,mult(B,mult(A,C))) =
% mult(mult(A,mult(B,A)),C),
% mult(op_c,A) = mult(A,op_c),
% mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) }
% (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(op_c,op_c),mult(a,b)) =
% mult(mult(mult(op_c,op_c),a),b) }
% (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: 9
% 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: 8
% Current number of rules: 2
% New rule produced : [3] mult(A,op_c) <-> mult(op_c,A)
% Current number of equations to process: 1
% Current number of ordered equations: 6
% Current number of rules: 3
% New rule produced : [4] mult(op_c,A) <-> mult(A,op_c)
% Current number of equations to process: 0
% Current number of ordered equations: 7
% 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: 6
% 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: 5
% 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: 4
% 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: 3
% Current number of rules: 8
% New rule produced : [9] mult(A,mult(B,op_c)) <-> mult(op_c,mult(A,B))
% Current number of equations to process: 0
% Current number of ordered equations: 15
% Current number of rules: 9
% New rule produced : [10] mult(op_c,mult(A,B)) <-> mult(A,mult(B,op_c))
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 10
% New rule produced :
% [11] mult(mult(A,mult(B,A)),C) -> mult(A,mult(B,mult(A,C)))
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 11
% New rule produced : [12] rd(A,unit) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 12
% New rule produced : [13] rd(A,A) -> unit
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 13
% New rule produced : [14] ld(unit,A) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 14
% New rule produced : [15] ld(A,A) -> unit
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 15
% New rule produced : [16] rd(mult(op_c,A),op_c) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 16
% New rule produced : [17] rd(mult(A,op_c),A) -> op_c
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 17
% New rule produced : [18] rd(A,ld(B,A)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 18
% New rule produced : [19] mult(op_c,rd(A,op_c)) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 19
% New rule produced : [20] ld(A,mult(op_c,A)) -> op_c
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 20
% New rule produced : [21] ld(op_c,mult(A,op_c)) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced : [22] ld(rd(A,B),A) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [23] mult(A,mult(op_c,B)) <-> mult(op_c,mult(A,B))
% Current number of equations to process: 8
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced : [24] mult(op_c,mult(A,B)) <-> mult(A,mult(op_c,B))
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] mult(A,mult(op_c,op_c)) <-> mult(op_c,mult(op_c,A))
% Current number of equations to process: 7
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced : [26] mult(op_c,mult(op_c,A)) <-> mult(A,mult(op_c,op_c))
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [27] ld(A,mult(op_c,mult(A,B))) -> mult(B,op_c)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [28] mult(B,mult(op_c,ld(B,A))) -> mult(op_c,A)
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [29] ld(op_c,mult(A,mult(B,op_c))) -> mult(A,B)
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [30] rd(mult(op_c,mult(A,B)),mult(B,op_c)) -> A
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [31] mult(op_c,mult(rd(A,mult(B,op_c)),B)) -> A
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [32] rd(mult(A,mult(B,op_c)),mult(A,B)) -> op_c
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [33] mult(mult(A,A),B) -> mult(A,mult(A,B))
% The conjecture has been reduced.
% Conjecture is now:
% mult(a,mult(b,mult(op_c,op_c))) = mult(mult(a,mult(op_c,op_c)),b)
%
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [34] ld(op_c,A) -> rd(A,op_c)
% Rule [21] ld(op_c,mult(A,op_c)) -> A collapsed.
% Rule [29] ld(op_c,mult(A,mult(B,op_c))) -> mult(A,B) collapsed.
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [35] rd(A,rd(A,op_c)) -> op_c
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [36] rd(mult(A,mult(B,op_c)),op_c) -> mult(A,B)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [37] mult(op_c,mult(A,rd(B,op_c))) -> mult(A,B)
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [38] rd(mult(A,mult(op_c,B)),op_c) -> mult(A,B)
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [39] ld(A,mult(op_c,mult(op_c,A))) -> mult(op_c,op_c)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [40] ld(A,mult(op_c,B)) -> mult(op_c,ld(A,B))
% Rule [20] ld(A,mult(op_c,A)) -> op_c collapsed.
% Rule [27] ld(A,mult(op_c,mult(A,B))) -> mult(B,op_c) collapsed.
% Rule [39] ld(A,mult(op_c,mult(op_c,A))) -> mult(op_c,op_c) collapsed.
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [41] rd(mult(op_c,A),mult(A,op_c)) -> unit
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [42] rd(mult(op_c,A),mult(B,op_c)) -> rd(A,B)
% Rule [30] rd(mult(op_c,mult(A,B)),mult(B,op_c)) -> A collapsed.
% Rule [41] rd(mult(op_c,A),mult(A,op_c)) -> unit collapsed.
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [43] mult(rd(A,mult(B,op_c)),B) -> rd(A,op_c)
% Rule [31] mult(op_c,mult(rd(A,mult(B,op_c)),B)) -> A collapsed.
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [44] mult(op_c,mult(op_c,ld(mult(A,op_c),A))) -> op_c
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [45] ld(mult(A,B),mult(A,mult(B,op_c))) -> op_c
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [46] rd(mult(op_c,mult(A,B)),mult(op_c,B)) -> A
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [47] mult(op_c,mult(rd(A,mult(op_c,B)),B)) -> A
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [48] rd(mult(A,mult(op_c,B)),mult(A,B)) -> op_c
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [49] ld(mult(A,B),mult(A,mult(op_c,B))) -> op_c
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [50] mult(op_c,mult(op_c,rd(A,mult(op_c,op_c)))) -> A
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [51] rd(mult(A,mult(op_c,op_c)),mult(op_c,A)) -> op_c
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [52] ld(mult(op_c,A),mult(A,mult(op_c,op_c))) -> op_c
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [53] rd(mult(op_c,A),mult(op_c,ld(B,A))) -> B
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [54] rd(mult(A,mult(A,B)),B) -> mult(A,A)
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [55] mult(A,rd(B,op_c)) -> rd(mult(A,B),op_c)
% Rule [19] mult(op_c,rd(A,op_c)) -> A collapsed.
% Rule [37] mult(op_c,mult(A,rd(B,op_c))) -> mult(A,B) collapsed.
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [56] mult(rd(A,rd(B,op_c)),B) -> mult(op_c,A)
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [57] mult(rd(A,mult(op_c,B)),B) -> rd(A,op_c)
% Rule [47] mult(op_c,mult(rd(A,mult(op_c,B)),B)) -> A collapsed.
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [58] mult(op_c,ld(A,unit)) -> ld(A,op_c)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [59] ld(A,mult(B,op_c)) -> mult(op_c,ld(A,B))
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced : [60] mult(op_c,ld(mult(op_c,A),A)) -> unit
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced : [61] rd(op_c,mult(A,op_c)) -> rd(unit,A)
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced : [62] rd(mult(op_c,A),mult(op_c,B)) -> rd(A,B)
% Rule [46] rd(mult(op_c,mult(A,B)),mult(op_c,B)) -> A collapsed.
% Rule [53] rd(mult(op_c,A),mult(op_c,ld(B,A))) -> B collapsed.
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced : [63] rd(mult(A,op_c),mult(B,op_c)) -> rd(A,B)
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced : [64] rd(A,mult(B,op_c)) <-> rd(rd(A,op_c),B)
% Rule [61] rd(op_c,mult(A,op_c)) -> rd(unit,A) collapsed.
% Current number of equations to process: 63
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced : [65] rd(rd(A,op_c),B) <-> rd(A,mult(B,op_c))
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced : [66] mult(op_c,rd(A,mult(op_c,op_c))) -> rd(A,op_c)
% Rule [50] mult(op_c,mult(op_c,rd(A,mult(op_c,op_c)))) -> A collapsed.
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced : [67] mult(op_c,ld(mult(A,op_c),A)) -> unit
% Rule [44] mult(op_c,mult(op_c,ld(mult(A,op_c),A))) -> op_c collapsed.
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced : [68] mult(B,mult(B,ld(mult(B,B),A))) -> A
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced : [69] ld(mult(A,A),mult(A,mult(A,B))) -> B
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced : [70] mult(op_c,ld(rd(mult(op_c,B),A),B)) -> A
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced : [71] ld(rd(A,mult(B,op_c)),rd(A,op_c)) -> B
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced : [72] rd(mult(A,mult(op_c,op_c)),A) -> mult(op_c,op_c)
% Current number of equations to process: 95
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced : [73] rd(mult(op_c,mult(A,op_c)),A) -> mult(op_c,op_c)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced : [74] rd(mult(A,B),ld(A,B)) -> mult(A,A)
% Current number of equations to process: 93
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced : [75] mult(op_c,ld(A,rd(B,op_c))) -> ld(A,B)
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced : [76] ld(A,rd(mult(A,B),op_c)) -> rd(B,op_c)
% Current number of equations to process: 102
% Current number of ordered equations: 0
% Current number of rules: 60
% Rule [59] ld(A,mult(B,op_c)) -> mult(op_c,ld(A,B)) is composed into [59]
% ld(A,
% mult(B,op_c))
% ->
% rd(
% ld(A,B),
% rd(unit,op_c))
% Rule [56] mult(rd(A,rd(B,op_c)),B) -> mult(op_c,A) is composed into [56]
% mult(
% rd(A,
% rd(B,op_c)),B)
% ->
% rd(A,
% rd(unit,op_c))
% Rule [9] mult(A,mult(B,op_c)) <-> mult(op_c,mult(A,B)) is composed into
% [9] mult(A,mult(B,op_c)) -> rd(mult(A,B),rd(unit,op_c))
% Rule [3] mult(A,op_c) <-> mult(op_c,A) is composed into [3]
% mult(A,op_c) ->
% rd(A,rd(unit,op_c))
% New rule produced : [77] mult(op_c,A) -> rd(A,rd(unit,op_c))
% Rule [4] mult(op_c,A) <-> mult(A,op_c) collapsed.
% Rule [10] mult(op_c,mult(A,B)) <-> mult(A,mult(B,op_c)) collapsed.
% Rule [16] rd(mult(op_c,A),op_c) -> A collapsed.
% Rule [23] mult(A,mult(op_c,B)) <-> mult(op_c,mult(A,B)) collapsed.
% Rule [24] mult(op_c,mult(A,B)) <-> mult(A,mult(op_c,B)) collapsed.
% Rule [25] mult(A,mult(op_c,op_c)) <-> mult(op_c,mult(op_c,A)) collapsed.
% Rule [26] mult(op_c,mult(op_c,A)) <-> mult(A,mult(op_c,op_c)) collapsed.
% Rule [28] mult(B,mult(op_c,ld(B,A))) -> mult(op_c,A) collapsed.
% Rule [38] rd(mult(A,mult(op_c,B)),op_c) -> mult(A,B) collapsed.
% Rule [40] ld(A,mult(op_c,B)) -> mult(op_c,ld(A,B)) collapsed.
% Rule [42] rd(mult(op_c,A),mult(B,op_c)) -> rd(A,B) collapsed.
% Rule [48] rd(mult(A,mult(op_c,B)),mult(A,B)) -> op_c collapsed.
% Rule [49] ld(mult(A,B),mult(A,mult(op_c,B))) -> op_c collapsed.
% Rule [51] rd(mult(A,mult(op_c,op_c)),mult(op_c,A)) -> op_c collapsed.
% Rule [52] ld(mult(op_c,A),mult(A,mult(op_c,op_c))) -> op_c collapsed.
% Rule [57] mult(rd(A,mult(op_c,B)),B) -> rd(A,op_c) collapsed.
% Rule [58] mult(op_c,ld(A,unit)) -> ld(A,op_c) collapsed.
% Rule [60] mult(op_c,ld(mult(op_c,A),A)) -> unit collapsed.
% Rule [62] rd(mult(op_c,A),mult(op_c,B)) -> rd(A,B) collapsed.
% Rule [66] mult(op_c,rd(A,mult(op_c,op_c))) -> rd(A,op_c) collapsed.
% Rule [67] mult(op_c,ld(mult(A,op_c),A)) -> unit collapsed.
% Rule [70] mult(op_c,ld(rd(mult(op_c,B),A),B)) -> A collapsed.
% Rule [72] rd(mult(A,mult(op_c,op_c)),A) -> mult(op_c,op_c) collapsed.
% Rule [73] rd(mult(op_c,mult(A,op_c)),A) -> mult(op_c,op_c) collapsed.
% Rule [75] mult(op_c,ld(A,rd(B,op_c))) -> ld(A,B) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% mult(a,mult(b,rd(op_c,rd(unit,op_c)))) = mult(mult(a,rd(op_c,rd(unit,op_c))),b)
%
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [78] rd(rd(A,rd(unit,op_c)),op_c) -> A
% Current number of equations to process: 127
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [79] rd(ld(A,unit),rd(unit,op_c)) -> ld(A,op_c)
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [80] rd(rd(A,op_c),rd(unit,op_c)) -> A
% Current number of equations to process: 127
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [81] rd(unit,A) <-> rd(op_c,rd(A,rd(unit,op_c)))
% Current number of equations to process: 131
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced : [82] rd(op_c,rd(A,rd(unit,op_c))) <-> rd(unit,A)
% Current number of equations to process: 131
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [83] mult(A,ld(mult(A,A),B)) -> ld(A,B)
% Rule [68] mult(B,mult(B,ld(mult(B,B),A))) -> A collapsed.
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [84] ld(mult(A,A),mult(A,B)) -> ld(A,B)
% Rule [69] ld(mult(A,A),mult(A,mult(A,B))) -> B collapsed.
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [85] rd(rd(mult(A,B),op_c),rd(B,op_c)) -> A
% Current number of equations to process: 144
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [86] rd(A,rd(B,op_c)) <-> rd(rd(A,rd(unit,op_c)),B)
% Current number of equations to process: 143
% Current number of ordered equations: 1
% Current number of rules: 43
% New rule produced : [87] rd(rd(A,rd(unit,op_c)),B) <-> rd(A,rd(B,op_c))
% Rule [78] rd(rd(A,rd(unit,op_c)),op_c) -> A collapsed.
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [88] rd(A,rd(B,rd(unit,op_c))) <-> rd(rd(A,op_c),B)
% Current number of equations to process: 142
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced : [89] rd(rd(A,op_c),B) <-> rd(A,rd(B,rd(unit,op_c)))
% Rule [85] rd(rd(mult(A,B),op_c),rd(B,op_c)) -> A collapsed.
% Current number of equations to process: 142
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [90] rd(A,ld(A,unit)) -> mult(A,A)
% Current number of equations to process: 142
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [91] rd(A,ld(B,ld(B,A))) -> mult(B,B)
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [92] ld(A,rd(A,op_c)) -> rd(unit,op_c)
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [93] ld(A,rd(B,op_c)) -> rd(ld(A,B),op_c)
% Rule [71] ld(rd(A,mult(B,op_c)),rd(A,op_c)) -> B collapsed.
% Rule [76] ld(A,rd(mult(A,B),op_c)) -> rd(B,op_c) collapsed.
% Rule [92] ld(A,rd(A,op_c)) -> rd(unit,op_c) collapsed.
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [94] ld(rd(unit,A),op_c) -> rd(A,rd(unit,op_c))
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [95] ld(ld(A,op_c),ld(A,unit)) -> rd(unit,op_c)
% Current number of equations to process: 151
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [96] ld(A,unit) -> rd(ld(A,op_c),op_c)
% Rule [79] rd(ld(A,unit),rd(unit,op_c)) -> ld(A,op_c) collapsed.
% Rule [90] rd(A,ld(A,unit)) -> mult(A,A) collapsed.
% Rule [95] ld(ld(A,op_c),ld(A,unit)) -> rd(unit,op_c) collapsed.
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [97] rd(rd(A,rd(unit,op_c)),ld(A,op_c)) -> mult(A,A)
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [98] rd(unit,rd(A,op_c)) -> rd(op_c,A)
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [99] ld(mult(A,A),B) -> ld(A,ld(A,B))
% Rule [83] mult(A,ld(mult(A,A),B)) -> ld(A,B) collapsed.
% Rule [84] ld(mult(A,A),mult(A,B)) -> ld(A,B) collapsed.
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [100] mult(rd(op_c,rd(A,rd(unit,op_c))),A) -> unit
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [101] mult(rd(unit,A),rd(A,rd(unit,op_c))) -> op_c
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced : [102] rd(rd(A,op_c),rd(B,op_c)) -> rd(A,B)
% Rule [80] rd(rd(A,op_c),rd(unit,op_c)) -> A collapsed.
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced : [103] ld(rd(rd(A,op_c),B),A) -> rd(B,rd(unit,op_c))
% Current number of equations to process: 166
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced : [104] mult(rd(unit,A),rd(unit,A)) -> rd(rd(unit,A),A)
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [105] mult(A,rd(B,rd(unit,op_c))) -> rd(mult(A,B),rd(unit,op_c))
% Rule [101] mult(rd(unit,A),rd(A,rd(unit,op_c))) -> op_c collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% rd(mult(a,b),rd(unit,rd(op_c,rd(unit,op_c)))) = mult(rd(a,rd(unit,rd(op_c,
% rd(unit,op_c)))),b)
%
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [106]
% mult(A,rd(B,rd(unit,rd(op_c,rd(unit,op_c))))) ->
% rd(mult(A,B),rd(unit,rd(op_c,rd(unit,op_c))))
% Current number of equations to process: 226
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [107]
% mult(rd(A,rd(unit,rd(op_c,rd(unit,op_c)))),B) ->
% rd(mult(A,B),rd(unit,rd(op_c,rd(unit,op_c))))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 239
% Current number of ordered equations: 0
% Current number of rules: 52
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 14 rules have been used:
% [1]
% mult(A,unit) -> A; trace = in the starting set
% [2] mult(unit,A) -> A; trace = in the starting set
% [3] mult(A,op_c) <-> mult(op_c,A); trace = in the starting set
% [7] mult(rd(A,B),B) -> A; trace = in the starting set
% [9] mult(A,mult(B,op_c)) <-> mult(op_c,mult(A,B)); trace = in the starting set
% [11] mult(mult(A,mult(B,A)),C) -> mult(A,mult(B,mult(A,C))); trace = in the starting set
% [19] mult(op_c,rd(A,op_c)) -> A; trace = Cp of 7 and 3
% [23] mult(A,mult(op_c,B)) <-> mult(op_c,mult(A,B)); trace = Cp of 9 and 3
% [33] mult(mult(A,A),B) -> mult(A,mult(A,B)); trace = Cp of 11 and 2
% [37] mult(op_c,mult(A,rd(B,op_c))) -> mult(A,B); trace = Cp of 23 and 19
% [56] mult(rd(A,rd(B,op_c)),B) -> mult(op_c,A); trace = Cp of 37 and 7
% [77] mult(op_c,A) -> rd(A,rd(unit,op_c)); trace = Cp of 56 and 1
% [105] mult(A,rd(B,rd(unit,op_c))) -> rd(mult(A,B),rd(unit,op_c)); trace = Cp of 9 and 3
% [107] mult(rd(A,rd(unit,rd(op_c,rd(unit,op_c)))),B) ->
% rd(mult(A,B),rd(unit,rd(op_c,rd(unit,op_c)))); trace = Cp of 11 and 3
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.130000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------