TSTP Solution File: GRP684-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP684-1 : 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 00:23:58 EDT 2014
% Result : Unsatisfiable 1.20s
% Output : Refutation 1.20s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP684-1 : 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 00:56:08 CDT 2014
% % CPUTime : 1.20
% Processing problem /tmp/CiME_63769_n104.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c,b,a : constant; rd : 2; ld : 2; mult : 2;";
% let X = vars "A B C D";
% let Axioms = equations F X "
% ld(A,mult(A,A)) = A;
% rd(mult(A,A),A) = A;
% mult(A,ld(A,B)) = ld(A,mult(A,B));
% mult(rd(A,B),B) = rd(mult(A,B),B);
% ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D);
% rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D));
% ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B);
% ";
%
% let s1 = status F "
% c lr_lex;
% b lr_lex;
% a lr_lex;
% rd lr_lex;
% ld lr_lex;
% mult lr_lex;
% ";
%
% let p1 = precedence F "
% mult > ld > rd > a > b > c";
%
% let s2 = status F "
% c mul;
% b mul;
% a mul;
% rd mul;
% ld mul;
% mult mul;
% ";
%
% let p2 = precedence F "
% mult > ld > rd > 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 " rd(mult(a,mult(b,c)),mult(b,c)) = rd(mult(a,c),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 = { ld(A,mult(A,A)) = A,
% rd(mult(A,A),A) = A,
% mult(A,ld(A,B)) = ld(A,mult(A,B)),
% mult(rd(A,B),B) = rd(mult(A,B),B),
% ld(ld(A,B),mult(ld(A,B),mult(C,D))) =
% mult(ld(A,mult(A,C)),D),
% rd(mult(mult(A,B),rd(C,D)),rd(C,D)) =
% mult(A,rd(mult(B,D),D)),
% ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B) }
% (7 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 = { rd(mult(a,mult(b,c)),mult(b,c)) =
% rd(mult(a,c),c) } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] rd(mult(A,A),A) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 1
% New rule produced : [2] ld(A,mult(A,A)) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 2
% New rule produced : [3] mult(A,ld(A,B)) -> ld(A,mult(A,B))
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 3
% New rule produced : [4] mult(rd(A,B),B) -> rd(mult(A,B),B)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 4
% New rule produced : [5] rd(mult(rd(A,A),B),B) -> ld(A,mult(A,ld(B,B)))
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 5
% New rule produced :
% [6] rd(mult(mult(A,B),rd(C,D)),rd(C,D)) -> mult(A,rd(mult(B,D),D))
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 6
% New rule produced :
% [7] ld(ld(A,B),mult(ld(A,B),mult(C,D))) <-> mult(ld(A,mult(A,C)),D)
% Current number of equations to process: 1
% Current number of ordered equations: 6
% Current number of rules: 7
% Rule [7] ld(ld(A,B),mult(ld(A,B),mult(C,D))) <-> mult(ld(A,mult(A,C)),D) is composed into
% [7]
% ld(ld(A,B),mult(ld(A,B),mult(C,D))) <-> ld(ld(A,c),mult(ld(A,c),mult(C,D)))
% New rule produced :
% [8] mult(ld(A,mult(A,C)),D) <-> ld(ld(A,B),mult(ld(A,B),mult(C,D)))
% Current number of equations to process: 2
% Current number of ordered equations: 4
% Current number of rules: 8
% Rule [5] rd(mult(rd(A,A),B),B) -> ld(A,mult(A,ld(B,B))) is composed into
% [5] rd(mult(rd(A,A),B),B) -> ld(A,mult(A,rd(B,B)))
% New rule produced : [9] ld(A,A) -> rd(A,A)
% Current number of equations to process: 3
% Current number of ordered equations: 2
% Current number of rules: 9
% New rule produced : [10] ld(A,mult(A,mult(A,A))) -> mult(A,A)
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced : [11] rd(mult(mult(A,A),A),A) -> mult(A,A)
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] ld(A,mult(A,rd(rd(A,A),rd(A,A)))) -> rd(A,A)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13] rd(mult(mult(rd(A,A),B),B),B) -> ld(ld(A,B),mult(ld(A,B),B))
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] rd(mult(mult(A,B),C),C) -> mult(A,rd(mult(B,C),C))
% Rule [6] rd(mult(mult(A,B),rd(C,D)),rd(C,D)) -> mult(A,rd(mult(B,D),D))
% collapsed.
% Rule [11] rd(mult(mult(A,A),A),A) -> mult(A,A) collapsed.
% Rule [13] rd(mult(mult(rd(A,A),B),B),B) -> ld(ld(A,B),mult(ld(A,B),B))
% collapsed.
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [15] mult(A,rd(mult(B,rd(C,D)),rd(C,D))) -> mult(A,rd(mult(B,D),D))
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [16] ld(ld(A,B),mult(ld(A,B),B)) -> mult(rd(A,A),B)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [17] ld(ld(A,C),mult(ld(A,C),mult(A,B))) -> mult(A,B)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [18] mult(A,rd(A,A)) -> A
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [19] ld(A,mult(A,mult(A,mult(A,A)))) -> mult(A,mult(A,A))
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [20] mult(mult(A,rd(mult(B,C),C)),C) -> mult(mult(A,B),C)
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [21] mult(A,rd(mult(B,mult(A,B)),mult(A,B))) -> mult(A,B)
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [22] ld(A,mult(A,mult(A,rd(rd(A,A),rd(A,A))))) -> A
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [23] rd(mult(rd(mult(A,B),B),C),C) -> mult(rd(A,B),rd(mult(B,C),C))
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [24] mult(A,rd(rd(mult(B,C),C),C)) -> mult(A,rd(B,C))
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [25] mult(rd(A,A),mult(A,A)) -> mult(A,A)
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [26] ld(rd(A,A),A) -> A
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [27] ld(A,mult(A,mult(A,B))) -> mult(A,B)
% Rule [10] ld(A,mult(A,mult(A,A))) -> mult(A,A) collapsed.
% Rule [19] ld(A,mult(A,mult(A,mult(A,A)))) -> mult(A,mult(A,A)) collapsed.
% Rule [22] ld(A,mult(A,mult(A,rd(rd(A,A),rd(A,A))))) -> A collapsed.
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [28] mult(A,rd(rd(A,A),rd(A,A))) -> A
% Rule [12] ld(A,mult(A,rd(rd(A,A),rd(A,A)))) -> rd(A,A) collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [29] ld(mult(A,A),mult(mult(A,A),mult(A,B))) -> mult(A,B)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [30] ld(rd(A,A),mult(rd(A,A),mult(A,B))) -> mult(A,B)
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 23
% Rule [5] rd(mult(rd(A,A),B),B) -> ld(A,mult(A,rd(B,B))) is composed into
% [5] rd(mult(rd(A,A),B),B) -> ld(A,rd(mult(A,B),B))
% New rule produced : [31] mult(A,rd(B,B)) -> rd(mult(A,B),B)
% Rule [18] mult(A,rd(A,A)) -> A collapsed.
% Rule [28] mult(A,rd(rd(A,A),rd(A,A))) -> A collapsed.
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [32] rd(A,rd(A,A)) -> A
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [33] mult(rd(A,A),rd(mult(A,B),B)) -> rd(mult(A,B),B)
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [34] ld(ld(A,B),mult(ld(A,B),C)) <-> ld(ld(A,c),mult(ld(A,c),C))
% Rule
% [7]
% ld(ld(A,B),mult(ld(A,B),mult(C,D))) <-> ld(ld(A,c),mult(ld(A,c),mult(C,D)))
% collapsed.
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [35] mult(rd(rd(A,A),rd(A,A)),A) -> A
% Current number of equations to process: 127
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [36] ld(rd(A,A),mult(A,A)) -> mult(A,A)
% Current number of equations to process: 131
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [37] ld(A,mult(A,mult(rd(A,A),B))) -> mult(rd(A,A),B)
% Current number of equations to process: 130
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [38] rd(rd(A,A),rd(A,A)) -> rd(A,A)
% Rule [35] mult(rd(rd(A,A),rd(A,A)),A) -> A collapsed.
% Current number of equations to process: 149
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [39] ld(A,mult(A,rd(mult(A,B),B))) -> rd(mult(A,B),B)
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [40] ld(rd(A,A),rd(mult(A,B),B)) -> rd(mult(A,B),B)
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [41] rd(rd(mult(A,B),B),B) -> rd(A,B)
% Rule [24] mult(A,rd(rd(mult(B,C),C),C)) -> mult(A,rd(B,C)) collapsed.
% Current number of equations to process: 163
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [42] rd(mult(A,rd(C,B)),rd(C,B)) -> rd(mult(A,B),B)
% Rule [15] mult(A,rd(mult(B,rd(C,D)),rd(C,D))) -> mult(A,rd(mult(B,D),D))
% collapsed.
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 29
% Rule [34] ld(ld(A,B),mult(ld(A,B),C)) <-> ld(ld(A,c),mult(ld(A,c),C)) is composed into
% [34] ld(ld(A,B),mult(ld(A,B),C)) -> ld(A,mult(A,C))
% New rule produced : [43] ld(ld(A,c),mult(ld(A,c),B)) -> ld(A,mult(A,B))
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [44] ld(A,ld(A,mult(A,B))) -> ld(A,B)
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [45] rd(mult(rd(A,rd(B,B)),B),B) -> rd(rd(mult(A,B),B),rd(B,B))
% Current number of equations to process: 175
% Current number of ordered equations: 0
% Current number of rules: 32
% Rule [23] rd(mult(rd(mult(A,B),B),C),C) -> mult(rd(A,B),rd(mult(B,C),C)) is composed into
% [23] rd(mult(rd(mult(A,B),B),C),C) -> mult(A,ld(B,rd(mult(B,C),C)))
% New rule produced :
% [46] mult(rd(A,B),rd(mult(B,C),C)) -> mult(A,ld(B,rd(mult(B,C),C)))
% Rule [33] mult(rd(A,A),rd(mult(A,B),B)) -> rd(mult(A,B),B) collapsed.
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [47] ld(rd(A,A),mult(rd(A,A),B)) -> ld(A,mult(A,B))
% Rule [30] ld(rd(A,A),mult(rd(A,A),mult(A,B))) -> mult(A,B) collapsed.
% Current number of equations to process: 173
% Current number of ordered equations: 0
% Current number of rules: 32
% Rule [16] ld(ld(A,B),mult(ld(A,B),B)) -> mult(rd(A,A),B) is composed into
% [16] ld(ld(A,B),mult(ld(A,B),B)) -> ld(A,mult(A,B))
% New rule produced : [48] mult(rd(A,A),B) -> ld(A,mult(A,B))
% Rule [5] rd(mult(rd(A,A),B),B) -> ld(A,rd(mult(A,B),B)) collapsed.
% Rule [25] mult(rd(A,A),mult(A,A)) -> mult(A,A) collapsed.
% Rule [37] ld(A,mult(A,mult(rd(A,A),B))) -> mult(rd(A,A),B) collapsed.
% Rule [47] ld(rd(A,A),mult(rd(A,A),B)) -> ld(A,mult(A,B)) collapsed.
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 29
% Rule [46] mult(rd(A,B),rd(mult(B,C),C)) -> mult(A,ld(B,rd(mult(B,C),C))) is composed into
% [46] mult(rd(A,B),rd(mult(B,C),C)) -> mult(A,rd(ld(B,mult(B,C)),C))
% Rule [23] rd(mult(rd(mult(A,B),B),C),C) -> mult(A,ld(B,rd(mult(B,C),C))) is composed into
% [23] rd(mult(rd(mult(A,B),B),C),C) -> mult(A,rd(ld(B,mult(B,C)),C))
% New rule produced : [49] ld(A,rd(mult(A,B),B)) -> rd(ld(A,mult(A,B)),B)
% Current number of equations to process: 175
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [50] ld(rd(A,A),ld(A,mult(A,B))) -> ld(A,mult(A,B))
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [51] ld(A,mult(A,mult(ld(A,B),C))) -> mult(ld(A,B),C)
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [52] ld(mult(A,A),mult(mult(A,A),B)) -> ld(A,mult(A,B))
% Rule [29] ld(mult(A,A),mult(mult(A,A),mult(A,B))) -> mult(A,B) collapsed.
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 32
% Rule [45] rd(mult(rd(A,rd(B,B)),B),B) -> rd(rd(mult(A,B),B),rd(B,B)) is composed into
% [45] rd(mult(rd(A,rd(B,B)),B),B) -> rd(mult(A,B),B)
% New rule produced : [53] rd(rd(mult(A,B),B),rd(B,B)) -> rd(mult(A,B),B)
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [54] rd(mult(A,mult(A,A)),mult(A,A)) -> A
% Current number of equations to process: 178
% Current number of ordered equations: 0
% Current number of rules: 34
% Rule [31] mult(A,rd(B,B)) -> rd(mult(A,B),B) is composed into [31]
% mult(A,rd(B,B))
% ->
% rd(A,rd(B,B))
% Rule [4] mult(rd(A,B),B) -> rd(mult(A,B),B) is composed into [4]
% mult(rd(A,B),B)
% -> rd(A,rd(B,B))
% New rule produced : [55] rd(mult(A,B),B) -> rd(A,rd(B,B))
% Rule [1] rd(mult(A,A),A) -> A collapsed.
% Rule [14] rd(mult(mult(A,B),C),C) -> mult(A,rd(mult(B,C),C)) collapsed.
% Rule [20] mult(mult(A,rd(mult(B,C),C)),C) -> mult(mult(A,B),C) collapsed.
% Rule [21] mult(A,rd(mult(B,mult(A,B)),mult(A,B))) -> mult(A,B) collapsed.
% Rule [23] rd(mult(rd(mult(A,B),B),C),C) -> mult(A,rd(ld(B,mult(B,C)),C))
% collapsed.
% Rule [39] ld(A,mult(A,rd(mult(A,B),B))) -> rd(mult(A,B),B) collapsed.
% Rule [40] ld(rd(A,A),rd(mult(A,B),B)) -> rd(mult(A,B),B) collapsed.
% Rule [41] rd(rd(mult(A,B),B),B) -> rd(A,B) collapsed.
% Rule [42] rd(mult(A,rd(C,B)),rd(C,B)) -> rd(mult(A,B),B) collapsed.
% Rule [45] rd(mult(rd(A,rd(B,B)),B),B) -> rd(mult(A,B),B) collapsed.
% Rule [46] mult(rd(A,B),rd(mult(B,C),C)) -> mult(A,rd(ld(B,mult(B,C)),C))
% collapsed.
% Rule [49] ld(A,rd(mult(A,B),B)) -> rd(ld(A,mult(A,B)),B) collapsed.
% Rule [53] rd(rd(mult(A,B),B),rd(B,B)) -> rd(mult(A,B),B) collapsed.
% Rule [54] rd(mult(A,mult(A,A)),mult(A,A)) -> A collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% rd(a,rd(mult(b,c),mult(b,c))) = rd(a,rd(c,c))
%
% Current number of equations to process: 208
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [56] rd(ld(A,mult(A,B)),B) -> ld(A,rd(A,rd(B,B)))
% Current number of equations to process: 207
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [57] rd(rd(A,rd(B,B)),B) -> rd(A,B)
% Current number of equations to process: 206
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [58] rd(A,rd(mult(A,A),mult(A,A))) -> A
% Current number of equations to process: 205
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [59] mult(A,rd(B,rd(C,C))) -> rd(mult(A,B),rd(C,C))
% Current number of equations to process: 204
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [60] mult(rd(mult(A,B),rd(C,C)),C) -> mult(mult(A,B),C)
% Current number of equations to process: 203
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [61] ld(A,rd(mult(A,A),rd(B,B))) -> rd(A,rd(B,B))
% Current number of equations to process: 202
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [62] ld(rd(A,A),rd(A,rd(B,B))) -> rd(A,rd(B,B))
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [63] rd(A,rd(rd(C,B),rd(C,B))) -> rd(A,rd(B,B))
% Current number of equations to process: 200
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [64] rd(rd(A,rd(B,B)),rd(B,B)) -> rd(A,rd(B,B))
% Current number of equations to process: 199
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [65] mult(A,ld(B,rd(B,rd(C,C)))) -> rd(rd(A,rd(B,B)),rd(C,C))
% Current number of equations to process: 199
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [66] ld(ld(A,B),ld(A,mult(A,B))) -> ld(ld(A,B),B)
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [67] ld(A,ld(A,rd(A,rd(B,B)))) -> ld(A,rd(B,B))
% Current number of equations to process: 200
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [68] ld(ld(A,B),ld(A,mult(A,C))) -> ld(ld(A,B),C)
% Rule [66] ld(ld(A,B),ld(A,mult(A,B))) -> ld(ld(A,B),B) collapsed.
% Current number of equations to process: 200
% Current number of ordered equations: 0
% Current number of rules: 33
% Rule [48] mult(rd(A,A),B) -> ld(A,mult(A,B)) is composed into [48]
% mult(rd(A,A),B)
% ->
% ld(rd(A,A),B)
% Rule [3] mult(A,ld(A,B)) -> ld(A,mult(A,B)) is composed into [3]
% mult(A,ld(A,B))
% -> ld(rd(A,A),B)
% New rule produced : [69] ld(A,mult(A,B)) -> ld(rd(A,A),B)
% Rule [2] ld(A,mult(A,A)) -> A collapsed.
% Rule [8] mult(ld(A,mult(A,C)),D) <-> ld(ld(A,B),mult(ld(A,B),mult(C,D)))
% collapsed.
% Rule [16] ld(ld(A,B),mult(ld(A,B),B)) -> ld(A,mult(A,B)) collapsed.
% Rule [17] ld(ld(A,C),mult(ld(A,C),mult(A,B))) -> mult(A,B) collapsed.
% Rule [27] ld(A,mult(A,mult(A,B))) -> mult(A,B) collapsed.
% Rule [34] ld(ld(A,B),mult(ld(A,B),C)) -> ld(A,mult(A,C)) collapsed.
% Rule [43] ld(ld(A,c),mult(ld(A,c),B)) -> ld(A,mult(A,B)) collapsed.
% Rule [44] ld(A,ld(A,mult(A,B))) -> ld(A,B) collapsed.
% Rule [50] ld(rd(A,A),ld(A,mult(A,B))) -> ld(A,mult(A,B)) collapsed.
% Rule [51] ld(A,mult(A,mult(ld(A,B),C))) -> mult(ld(A,B),C) collapsed.
% Rule [52] ld(mult(A,A),mult(mult(A,A),B)) -> ld(A,mult(A,B)) collapsed.
% Rule [56] rd(ld(A,mult(A,B)),B) -> ld(A,rd(A,rd(B,B))) collapsed.
% Rule [68] ld(ld(A,B),ld(A,mult(A,C))) -> ld(ld(A,B),C) collapsed.
% Current number of equations to process: 214
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [70] rd(ld(rd(A,A),B),B) -> ld(A,rd(A,rd(B,B)))
% Current number of equations to process: 212
% Current number of ordered equations: 2
% Current number of rules: 22
% New rule produced :
% [71] ld(rd(ld(A,B),ld(A,B)),mult(C,D)) <-> mult(ld(rd(A,A),C),D)
% Current number of equations to process: 234
% Current number of ordered equations: 35
% Current number of rules: 23
% Rule [71] ld(rd(ld(A,B),ld(A,B)),mult(C,D)) <-> mult(ld(rd(A,A),C),D) is composed into
% [71] ld(rd(ld(A,B),ld(A,B)),mult(C,D)) <-> ld(rd(ld(A,c),ld(A,c)),mult(C,D))
% New rule produced :
% [72] mult(ld(rd(A,A),C),D) <-> ld(rd(ld(A,B),ld(A,B)),mult(C,D))
% Current number of equations to process: 234
% Current number of ordered equations: 34
% Current number of rules: 24
% New rule produced : [73] ld(rd(A,A),mult(A,B)) -> mult(A,B)
% Rule [36] ld(rd(A,A),mult(A,A)) -> mult(A,A) collapsed.
% Current number of equations to process: 235
% Current number of ordered equations: 30
% Current number of rules: 24
% New rule produced : [74] ld(A,ld(rd(A,A),B)) -> ld(A,B)
% Current number of equations to process: 236
% Current number of ordered equations: 28
% Current number of rules: 25
% New rule produced : [75] rd(rd(A,B),rd(B,B)) -> rd(A,B)
% Rule [38] rd(rd(A,A),rd(A,A)) -> rd(A,A) collapsed.
% Current number of equations to process: 236
% Current number of ordered equations: 26
% Current number of rules: 25
% New rule produced : [76] rd(mult(A,B),rd(B,B)) -> mult(A,B)
% Current number of equations to process: 237
% Current number of ordered equations: 24
% Current number of rules: 26
% Rule [70] rd(ld(rd(A,A),B),B) -> ld(A,rd(A,rd(B,B))) is composed into
% [70] rd(ld(rd(A,A),B),B) -> rd(rd(A,A),rd(B,B))
% New rule produced : [77] ld(A,rd(A,rd(B,B))) -> rd(rd(A,A),rd(B,B))
% Rule [65] mult(A,ld(B,rd(B,rd(C,C)))) -> rd(rd(A,rd(B,B)),rd(C,C)) collapsed.
% Rule [67] ld(A,ld(A,rd(A,rd(B,B)))) -> ld(A,rd(B,B)) collapsed.
% Current number of equations to process: 241
% Current number of ordered equations: 18
% Current number of rules: 25
% New rule produced : [78] mult(rd(A,rd(B,B)),B) -> mult(A,B)
% Rule [60] mult(rd(mult(A,B),rd(C,C)),C) -> mult(mult(A,B),C) collapsed.
% Current number of equations to process: 240
% Current number of ordered equations: 18
% Current number of rules: 25
% New rule produced : [79] ld(rd(A,A),ld(A,B)) -> ld(A,B)
% Current number of equations to process: 238
% Current number of ordered equations: 19
% Current number of rules: 26
% New rule produced : [80] mult(A,ld(rd(A,A),B)) -> mult(A,B)
% Current number of equations to process: 238
% Current number of ordered equations: 18
% Current number of rules: 27
% New rule produced : [81] ld(rd(A,A),rd(B,B)) -> rd(rd(A,A),rd(B,B))
% Current number of equations to process: 237
% Current number of ordered equations: 18
% Current number of rules: 28
% New rule produced : [82] ld(rd(ld(A,B),ld(A,B)),B) -> ld(rd(A,A),B)
% Current number of equations to process: 237
% Current number of ordered equations: 17
% Current number of rules: 29
% Rule [72] mult(ld(rd(A,A),C),D) <-> ld(rd(ld(A,B),ld(A,B)),mult(C,D)) is composed into
% [72] mult(ld(rd(A,A),C),D) -> ld(rd(A,A),mult(C,D))
% New rule produced : [83] ld(rd(ld(A,B),ld(A,B)),C) -> ld(rd(A,A),C)
% Rule
% [71] ld(rd(ld(A,B),ld(A,B)),mult(C,D)) <-> ld(rd(ld(A,c),ld(A,c)),mult(C,D))
% collapsed.
% Rule [82] ld(rd(ld(A,B),ld(A,B)),B) -> ld(rd(A,A),B) collapsed.
% Current number of equations to process: 237
% Current number of ordered equations: 14
% Current number of rules: 28
% New rule produced : [84] ld(rd(A,A),ld(rd(A,A),B)) -> ld(rd(A,A),B)
% Current number of equations to process: 237
% Current number of ordered equations: 11
% Current number of rules: 29
% New rule produced : [85] ld(rd(A,A),mult(ld(A,B),C)) -> mult(ld(A,B),C)
% Current number of equations to process: 237
% Current number of ordered equations: 10
% Current number of rules: 30
% New rule produced : [86] ld(A,rd(rd(A,A),rd(B,B))) -> ld(A,rd(B,B))
% Current number of equations to process: 236
% Current number of ordered equations: 10
% Current number of rules: 31
% New rule produced : [87] ld(ld(A,B),ld(rd(A,A),C)) -> ld(ld(A,B),C)
% Current number of equations to process: 237
% Current number of ordered equations: 8
% Current number of rules: 32
% New rule produced : [88] rd(rd(A,rd(B,B)),rd(C,B)) -> rd(A,rd(C,B))
% Rule [64] rd(rd(A,rd(B,B)),rd(B,B)) -> rd(A,rd(B,B)) collapsed.
% Current number of equations to process: 237
% Current number of ordered equations: 7
% Current number of rules: 32
% New rule produced : [89] rd(A,rd(mult(B,B),mult(B,B))) -> rd(A,rd(B,B))
% Rule [58] rd(A,rd(mult(A,A),mult(A,A))) -> A collapsed.
% Current number of equations to process: 237
% Current number of ordered equations: 5
% Current number of rules: 32
% New rule produced : [90] ld(rd(A,A),ld(ld(A,c),B)) -> ld(ld(A,c),B)
% Current number of equations to process: 244
% Current number of ordered equations: 5
% Current number of rules: 33
% New rule produced :
% [91] rd(ld(rd(A,A),B),ld(A,B)) -> rd(A,rd(ld(A,B),ld(A,B)))
% Current number of equations to process: 244
% Current number of ordered equations: 4
% Current number of rules: 34
% New rule produced :
% [92] ld(rd(A,A),rd(B,rd(C,C))) -> rd(ld(rd(A,A),B),rd(C,C))
% Rule [62] ld(rd(A,A),rd(A,rd(B,B))) -> rd(A,rd(B,B)) collapsed.
% Current number of equations to process: 246
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [93] ld(rd(rd(A,B),rd(A,B)),B) -> ld(rd(A,B),rd(A,rd(B,B)))
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [94] ld(A,rd(mult(A,B),rd(C,C))) -> rd(ld(rd(A,A),B),rd(C,C))
% Rule [61] ld(A,rd(mult(A,A),rd(B,B))) -> rd(A,rd(B,B)) collapsed.
% Current number of equations to process: 244
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced : [95] rd(ld(rd(A,A),B),rd(B,B)) -> ld(rd(A,A),B)
% Current number of equations to process: 243
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [96] rd(ld(rd(A,A),mult(B,C)),C) -> rd(ld(rd(A,A),B),rd(C,C))
% Current number of equations to process: 241
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [97] ld(rd(A,A),mult(mult(A,B),C)) -> mult(mult(A,B),C)
% Current number of equations to process: 253
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [98] rd(mult(A,rd(B,C)),rd(C,C)) -> mult(A,rd(B,C))
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [99] rd(rd(A,rd(B,C)),rd(C,C)) -> rd(A,rd(B,C))
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [100] rd(mult(A,mult(B,C)),rd(C,C)) -> mult(A,mult(B,C))
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [101] rd(A,rd(mult(B,C),mult(B,C))) -> rd(A,rd(C,C))
% Rule [89] rd(A,rd(mult(B,B),mult(B,B))) -> rd(A,rd(B,B)) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 248
% Current number of ordered equations: 0
% Current number of rules: 41
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 20 rules have been used:
% [1]
% rd(mult(A,A),A) -> A; trace = in the starting set
% [3] mult(A,ld(A,B)) -> ld(A,mult(A,B)); trace = in the starting set
% [4] mult(rd(A,B),B) -> rd(mult(A,B),B); trace = in the starting set
% [5] rd(mult(rd(A,A),B),B) -> ld(A,mult(A,ld(B,B))); trace = in the starting set
% [6] rd(mult(mult(A,B),rd(C,D)),rd(C,D)) -> mult(A,rd(mult(B,D),D)); trace = in the starting set
% [9] ld(A,A) -> rd(A,A); trace = Cp of 5 and 4
% [12] ld(A,mult(A,rd(rd(A,A),rd(A,A)))) -> rd(A,A); trace = Cp of 5 and 1
% [14] rd(mult(mult(A,B),C),C) -> mult(A,rd(mult(B,C),C)); trace = Cp of 6 and 1
% [15] mult(A,rd(mult(B,rd(C,D)),rd(C,D))) -> mult(A,rd(mult(B,D),D)); trace = in the starting set
% [18] mult(A,rd(A,A)) -> A; trace = Cp of 9 and 3
% [23] rd(mult(rd(mult(A,B),B),C),C) -> mult(rd(A,B),rd(mult(B,C),C)); trace = Cp of 14 and 4
% [31] mult(A,rd(B,B)) -> rd(mult(A,B),B); trace = Cp of 18 and 14
% [32] rd(A,rd(A,A)) -> A; trace = Cp of 12 and 3
% [33] mult(rd(A,A),rd(mult(A,B),B)) -> rd(mult(A,B),B); trace = Cp of 23 and 1
% [41] rd(rd(mult(A,B),B),B) -> rd(A,B); trace = Cp of 33 and 4
% [55] rd(mult(A,B),B) -> rd(A,rd(B,B)); trace = Cp of 41 and 31
% [59] mult(A,rd(B,rd(C,C))) -> rd(mult(A,B),rd(C,C)); trace = Cp of 6 and 1
% [63] rd(A,rd(rd(C,B),rd(C,B))) -> rd(A,rd(B,B)); trace = Cp of 33 and 15
% [76] rd(mult(A,B),rd(B,B)) -> mult(A,B); trace = Cp of 59 and 32
% [101] rd(A,rd(mult(B,C),mult(B,C))) -> rd(A,rd(C,C)); trace = Cp of 76 and 63
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.100000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------