TSTP Solution File: GRP002-2 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP002-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n127.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 00:22:08 EDT 2014
% Result : Unsatisfiable 1.35s
% Output : Refutation 1.35s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP002-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n127.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 : Thu Jun 5 15:36:38 CDT 2014
% % CPUTime : 1.35
% Processing problem /tmp/CiME_62771_n127.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " k,j,h,d,c,b,a,identity : constant; inverse : 1; multiply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z));
% multiply(identity,X) = X;
% multiply(inverse(X),X) = identity;
% multiply(X,identity) = X;
% multiply(X,inverse(X)) = identity;
% multiply(X,multiply(X,X)) = identity;
% multiply(a,b) = c;
% multiply(c,inverse(a)) = d;
% multiply(d,inverse(b)) = h;
% multiply(h,b) = j;
% multiply(j,inverse(h)) = k;
% ";
%
% let s1 = status F "
% k lr_lex;
% j lr_lex;
% h lr_lex;
% d lr_lex;
% c lr_lex;
% b lr_lex;
% a lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% identity lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > identity > a > b > c > d > h > j > k";
%
% let s2 = status F "
% k mul;
% j mul;
% h mul;
% d mul;
% c mul;
% b mul;
% a mul;
% inverse mul;
% multiply mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > identity = a = b = c = d = h = j = k";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(k,inverse(b)) = identity;"
% ;
% (*
% 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 = { multiply(multiply(X,Y),Z) =
% multiply(X,multiply(Y,Z)),
% multiply(identity,X) = X,
% multiply(inverse(X),X) = identity,
% multiply(X,identity) = X,
% multiply(X,inverse(X)) = identity,
% multiply(X,multiply(X,X)) = identity,
% multiply(a,b) = c,
% multiply(c,inverse(a)) = d,
% multiply(d,inverse(b)) = h,
% multiply(h,b) = j,
% multiply(j,inverse(h)) = k } (11 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { multiply(k,inverse(b)) = identity }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] multiply(X,identity) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 1
% New rule produced : [2] multiply(identity,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 2
% New rule produced : [3] multiply(a,b) -> c
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 3
% New rule produced : [4] multiply(h,b) -> j
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 4
% New rule produced : [5] multiply(X,inverse(X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 5
% New rule produced : [6] multiply(inverse(X),X) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 6
% New rule produced : [7] multiply(c,inverse(a)) -> d
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 7
% New rule produced : [8] multiply(d,inverse(b)) -> h
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 8
% New rule produced : [9] multiply(j,inverse(h)) -> k
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 9
% New rule produced : [10] multiply(X,multiply(X,X)) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [11] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] inverse(identity) -> identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] multiply(a,multiply(b,X)) -> multiply(c,X)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] multiply(c,inverse(b)) -> a
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] multiply(c,multiply(b,b)) -> a
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] multiply(h,multiply(b,X)) -> multiply(j,X)
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] multiply(Y,multiply(inverse(Y),X)) -> X
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] multiply(inverse(Y),multiply(Y,X)) -> X
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] multiply(j,inverse(b)) -> h
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] multiply(j,multiply(b,b)) -> h
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [21] inverse(inverse(X)) -> X
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] multiply(inverse(X),inverse(X)) -> X
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [23] multiply(inverse(a),c) -> b
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] multiply(inverse(h),j) -> b
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] inverse(a) -> multiply(inverse(c),d)
% Rule [7] multiply(c,inverse(a)) -> d collapsed.
% Rule [23] multiply(inverse(a),c) -> b collapsed.
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [26] inverse(b) -> multiply(inverse(d),h)
% Rule [8] multiply(d,inverse(b)) -> h collapsed.
% Rule [14] multiply(c,inverse(b)) -> a collapsed.
% Rule [19] multiply(j,inverse(b)) -> h collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% multiply(k,multiply(inverse(d),h)) = identity
%
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [27] inverse(h) -> multiply(inverse(j),k)
% Rule [9] multiply(j,inverse(h)) -> k collapsed.
% Rule [24] multiply(inverse(h),j) -> b collapsed.
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [28] inverse(X) -> multiply(X,X)
% Rule [5] multiply(X,inverse(X)) -> identity collapsed.
% Rule [6] multiply(inverse(X),X) -> identity collapsed.
% Rule [12] inverse(identity) -> identity collapsed.
% Rule [17] multiply(Y,multiply(inverse(Y),X)) -> X collapsed.
% Rule [18] multiply(inverse(Y),multiply(Y,X)) -> X collapsed.
% Rule [21] inverse(inverse(X)) -> X collapsed.
% Rule [22] multiply(inverse(X),inverse(X)) -> X collapsed.
% Rule [25] inverse(a) -> multiply(inverse(c),d) collapsed.
% Rule [26] inverse(b) -> multiply(inverse(d),h) collapsed.
% Rule [27] inverse(h) -> multiply(inverse(j),k) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% multiply(k,multiply(d,multiply(d,h))) = identity
%
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [29] multiply(c,multiply(d,multiply(d,h))) -> a
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [30] multiply(j,multiply(d,multiply(d,h))) -> h
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [31] multiply(c,multiply(c,multiply(d,c))) -> b
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [32] multiply(j,multiply(j,multiply(k,j))) -> b
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [33] multiply(a,a) -> multiply(c,multiply(c,d))
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [34] multiply(b,b) -> multiply(d,multiply(d,h))
% Rule [15] multiply(c,multiply(b,b)) -> a collapsed.
% Rule [20] multiply(j,multiply(b,b)) -> h collapsed.
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [35] multiply(h,h) -> multiply(j,multiply(j,k))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [36] multiply(Y,multiply(Y,multiply(Y,X))) -> X
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [37] multiply(h,multiply(h,j)) -> b
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [38] multiply(a,multiply(a,c)) -> b
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [39] multiply(c,b) -> multiply(d,c)
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [40] multiply(j,b) -> multiply(k,j)
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [41] multiply(a,X) -> multiply(c,multiply(d,multiply(d,multiply(h,X))))
% Rule [3] multiply(a,b) -> c collapsed.
% Rule [13] multiply(a,multiply(b,X)) -> multiply(c,X) collapsed.
% Rule [33] multiply(a,a) -> multiply(c,multiply(c,d)) collapsed.
% Rule [38] multiply(a,multiply(a,c)) -> b collapsed.
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [42] multiply(c,multiply(d,multiply(d,j))) -> c
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [43] multiply(j,multiply(d,multiply(d,multiply(h,X)))) -> multiply(h,X)
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [44]
% multiply(c,multiply(d,multiply(d,multiply(h,multiply(c,multiply(c,d)))))) ->
% identity
% Current number of equations to process: 31
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [45] multiply(b,multiply(d,multiply(d,h))) -> identity
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [46] multiply(h,multiply(j,multiply(j,k))) -> identity
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [47] multiply(c,multiply(c,a)) -> multiply(d,multiply(d,h))
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 24
% Rule [47] multiply(c,multiply(c,a)) -> multiply(d,multiply(d,h)) is composed into
% [47] multiply(c,multiply(c,a)) -> multiply(j,multiply(j,h))
% Rule [34] multiply(b,b) -> multiply(d,multiply(d,h)) is composed into
% [34] multiply(b,b) -> multiply(j,multiply(j,h))
% New rule produced :
% [48] multiply(d,multiply(d,h)) -> multiply(j,multiply(j,h))
% Rule [29] multiply(c,multiply(d,multiply(d,h))) -> a collapsed.
% Rule [30] multiply(j,multiply(d,multiply(d,h))) -> h collapsed.
% Rule [45] multiply(b,multiply(d,multiply(d,h))) -> identity collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% multiply(k,multiply(j,multiply(j,h))) = identity
%
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [49] multiply(c,multiply(j,multiply(j,h))) -> a
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [50] multiply(b,multiply(j,multiply(j,h))) -> identity
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [51] multiply(c,multiply(b,X)) -> multiply(d,multiply(c,X))
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [52] multiply(j,multiply(b,X)) -> multiply(k,multiply(j,X))
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [53]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Y))))) -> identity
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 27
% Rule [41] multiply(a,X) -> multiply(c,multiply(d,multiply(d,multiply(h,X)))) is composed into
% [41] multiply(a,X) -> multiply(d,multiply(d,multiply(c,X)))
% New rule produced :
% [54]
% multiply(c,multiply(d,multiply(d,multiply(h,X)))) ->
% multiply(d,multiply(d,multiply(c,X)))
% Rule
% [44]
% multiply(c,multiply(d,multiply(d,multiply(h,multiply(c,multiply(c,d)))))) ->
% identity collapsed.
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [55] multiply(h,X) -> multiply(k,multiply(k,multiply(j,X)))
% Rule [4] multiply(h,b) -> j collapsed.
% Rule [16] multiply(h,multiply(b,X)) -> multiply(j,X) collapsed.
% Rule [35] multiply(h,h) -> multiply(j,multiply(j,k)) collapsed.
% Rule [37] multiply(h,multiply(h,j)) -> b collapsed.
% Rule [43] multiply(j,multiply(d,multiply(d,multiply(h,X)))) -> multiply(h,X)
% collapsed.
% Rule [46] multiply(h,multiply(j,multiply(j,k))) -> identity collapsed.
% Rule
% [54]
% multiply(c,multiply(d,multiply(d,multiply(h,X)))) ->
% multiply(d,multiply(d,multiply(c,X))) collapsed.
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [56] multiply(d,multiply(d,a)) -> multiply(d,c)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [57] multiply(k,multiply(k,h)) -> multiply(k,j)
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [58]
% multiply(b,X) ->
% multiply(d,multiply(d,multiply(c,multiply(d,multiply(d,multiply(c,multiply(c,X)))))))
% Rule [34] multiply(b,b) -> multiply(j,multiply(j,h)) collapsed.
% Rule [50] multiply(b,multiply(j,multiply(j,h))) -> identity collapsed.
% Rule [51] multiply(c,multiply(b,X)) -> multiply(d,multiply(c,X)) collapsed.
% Rule [52] multiply(j,multiply(b,X)) -> multiply(k,multiply(j,X)) collapsed.
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [59]
% multiply(j,multiply(d,multiply(d,multiply(c,multiply(d,multiply(d,multiply(c,
% multiply(c,
% multiply(d,
% multiply(d,
% multiply(c,
% multiply(d,
% multiply(d,
% multiply(c,
% multiply(c,X)))))))))))))))
% -> multiply(k,multiply(k,multiply(j,X)))
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 21
% Rule [58]
% multiply(b,X) ->
% multiply(d,multiply(d,multiply(c,multiply(d,multiply(d,multiply(c,
% multiply(c,X))))))) is composed into
% [58]
% multiply(b,X) ->
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,multiply(j,X)))))))
% New rule produced :
% [60]
% multiply(d,multiply(d,multiply(c,multiply(d,multiply(d,multiply(c,multiply(c,X)))))))
% ->
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,multiply(j,X)))))))
% Rule
% [59]
% multiply(j,multiply(d,multiply(d,multiply(c,multiply(d,multiply(d,multiply(c,
% multiply(c,
% multiply(d,
% multiply(d,
% multiply(c,
% multiply(d,
% multiply(d,
% multiply(c,
% multiply(c,X)))))))))))))))
% -> multiply(k,multiply(k,multiply(j,X))) collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [61] multiply(d,multiply(d,j)) -> identity
% Rule [42] multiply(c,multiply(d,multiply(d,j))) -> c collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [62] multiply(d,multiply(j,multiply(j,h))) -> h
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [63] multiply(k,multiply(k,j)) -> h
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [64] multiply(d,multiply(d,c)) -> a
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 24
% Rule [41] multiply(a,X) -> multiply(d,multiply(d,multiply(c,X))) is composed into
% [41] multiply(a,X) -> multiply(j,multiply(j,multiply(c,X)))
% Rule [39] multiply(c,b) -> multiply(d,c) is composed into [39]
% multiply(c,b) ->
% multiply(j,c)
% New rule produced : [65] d -> j
% Rule [31] multiply(c,multiply(c,multiply(d,c))) -> b collapsed.
% Rule [48] multiply(d,multiply(d,h)) -> multiply(j,multiply(j,h)) collapsed.
% Rule [56] multiply(d,multiply(d,a)) -> multiply(d,c) collapsed.
% Rule
% [60]
% multiply(d,multiply(d,multiply(c,multiply(d,multiply(d,multiply(c,multiply(c,X)))))))
% ->
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,multiply(j,X)))))))
% collapsed.
% Rule [61] multiply(d,multiply(d,j)) -> identity collapsed.
% Rule [62] multiply(d,multiply(j,multiply(j,h))) -> h collapsed.
% Rule [64] multiply(d,multiply(d,c)) -> a collapsed.
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [66] multiply(j,multiply(j,c)) -> a
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [67] multiply(j,multiply(j,a)) -> multiply(j,c)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [68] multiply(k,h) -> j
% Rule [57] multiply(k,multiply(k,h)) -> multiply(k,j) collapsed.
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [69] multiply(j,a) -> c
% Rule [67] multiply(j,multiply(j,a)) -> multiply(j,c) collapsed.
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [70] multiply(c,multiply(c,multiply(j,c))) -> b
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [71] multiply(j,multiply(j,k)) -> multiply(k,multiply(k,multiply(j,h)))
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [72]
% multiply(c,multiply(c,multiply(j,X))) ->
% multiply(j,multiply(j,multiply(c,multiply(j,multiply(j,multiply(c,X))))))
% Rule [70] multiply(c,multiply(c,multiply(j,c))) -> b collapsed.
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [73]
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,multiply(j,
% multiply(k,
% multiply(k,
% multiply(j,
% multiply(k,
% multiply(k,
% multiply(j,
% multiply(j,X))))))))))))))
% -> multiply(j,multiply(j,multiply(k,multiply(k,multiply(j,X)))))
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [74]
% multiply(j,multiply(j,multiply(k,X))) ->
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,X))))))
% Rule [32] multiply(j,multiply(j,multiply(k,j))) -> b collapsed.
% Rule
% [73]
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,multiply(j,
% multiply(k,
% multiply(k,
% multiply(j,
% multiply(k,
% multiply(k,
% multiply(j,
% multiply(j,X))))))))))))))
% -> multiply(j,multiply(j,multiply(k,multiply(k,multiply(j,X))))) collapsed.
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [75] multiply(j,multiply(k,multiply(k,multiply(j,h)))) -> k
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [76] multiply(c,multiply(c,j)) -> multiply(j,multiply(j,multiply(c,a)))
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [77] multiply(c,multiply(j,multiply(j,multiply(c,a)))) -> j
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [78]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))))) ->
% Z
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [79] multiply(c,multiply(j,multiply(c,c))) -> multiply(j,h)
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [80]
% multiply(c,multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,
% multiply(k,
% multiply(j,X)))))))))
% -> multiply(j,multiply(j,multiply(c,X)))
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [81]
% multiply(j,multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,
% multiply(k,
% multiply(j,X)))))))))
% -> multiply(k,multiply(k,multiply(j,X)))
% Current number of equations to process: 142
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [82]
% multiply(j,multiply(j,multiply(c,multiply(j,multiply(j,multiply(c,multiply(c,X)))))))
% ->
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,multiply(j,X)))))))
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [83] multiply(Y,multiply(X,multiply(Y,multiply(X,Y)))) -> multiply(X,X)
% Rule
% [53]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Y))))) -> identity
% collapsed.
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [84]
% multiply(c,multiply(c,multiply(k,j))) ->
% multiply(j,multiply(j,multiply(c,c)))
% Current number of equations to process: 199
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [85]
% multiply(X,multiply(X,multiply(Y,Y))) <->
% multiply(Y,multiply(X,multiply(Y,X)))
% Current number of equations to process: 201
% Current number of ordered equations: 1
% Current number of rules: 32
% New rule produced :
% [86]
% multiply(Y,multiply(X,multiply(Y,X))) <->
% multiply(X,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [87] multiply(c,multiply(j,multiply(j,multiply(c,c)))) -> multiply(k,j)
% Current number of equations to process: 241
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [88] multiply(c,multiply(k,j)) -> multiply(j,multiply(j,multiply(c,h)))
% Rule
% [84]
% multiply(c,multiply(c,multiply(k,j))) ->
% multiply(j,multiply(j,multiply(c,c))) collapsed.
% Current number of equations to process: 243
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [89]
% multiply(c,multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,
% multiply(k,c))))))))
% -> multiply(j,multiply(j,multiply(c,a)))
% Current number of equations to process: 248
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [90] multiply(X,multiply(j,multiply(X,multiply(j,multiply(X,c))))) -> a
% Current number of equations to process: 252
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [91] multiply(X,multiply(k,multiply(X,multiply(k,multiply(X,j))))) -> h
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [92]
% multiply(j,multiply(k,multiply(j,multiply(k,k)))) ->
% multiply(k,multiply(j,h))
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [93]
% multiply(c,multiply(j,multiply(c,multiply(j,j)))) ->
% multiply(j,multiply(c,a))
% Current number of equations to process: 271
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [94]
% multiply(c,multiply(j,h)) ->
% multiply(j,multiply(j,multiply(c,multiply(j,j))))
% Current number of equations to process: 273
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [95]
% multiply(X,multiply(X,a)) <->
% multiply(j,multiply(X,multiply(j,multiply(X,c))))
% Rule [47] multiply(c,multiply(c,a)) -> multiply(j,multiply(j,h)) collapsed.
% Current number of equations to process: 275
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced :
% [96]
% multiply(j,multiply(X,multiply(j,multiply(X,c)))) <->
% multiply(X,multiply(X,a))
% Current number of equations to process: 275
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [97]
% multiply(X,multiply(X,h)) <->
% multiply(k,multiply(X,multiply(k,multiply(X,j))))
% Rule [49] multiply(c,multiply(j,multiply(j,h))) -> a collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(j,j))))) = identity
%
% Current number of equations to process: 288
% Current number of ordered equations: 1
% Current number of rules: 41
% New rule produced :
% [98] multiply(c,multiply(k,multiply(j,multiply(k,multiply(j,j))))) -> a
% Current number of equations to process: 287
% Current number of ordered equations: 1
% Current number of rules: 42
% New rule produced :
% [99]
% multiply(k,multiply(X,multiply(k,multiply(X,j)))) <->
% multiply(X,multiply(X,h))
% Current number of equations to process: 287
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [100]
% multiply(c,multiply(k,multiply(j,j))) ->
% multiply(j,multiply(c,multiply(j,j)))
% Current number of equations to process: 292
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [101] multiply(c,multiply(j,multiply(c,a))) -> multiply(k,multiply(j,j))
% Current number of equations to process: 301
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [102] multiply(j,multiply(c,multiply(j,multiply(k,multiply(j,j))))) -> a
% Current number of equations to process: 305
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [103] multiply(c,multiply(j,multiply(k,multiply(j,j)))) -> multiply(j,c)
% Rule [102] multiply(j,multiply(c,multiply(j,multiply(k,multiply(j,j))))) -> a
% collapsed.
% Current number of equations to process: 306
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [104]
% multiply(c,multiply(j,multiply(j,multiply(c,h)))) ->
% multiply(j,multiply(j,multiply(c,c)))
% Current number of equations to process: 307
% Current number of ordered equations: 0
% Current number of rules: 47
% Rule [88] multiply(c,multiply(k,j)) -> multiply(j,multiply(j,multiply(c,h))) is composed into
% [88] multiply(c,multiply(k,j)) -> multiply(j,multiply(c,j))
% New rule produced : [105] multiply(j,multiply(c,h)) -> multiply(c,j)
% Rule
% [104]
% multiply(c,multiply(j,multiply(j,multiply(c,h)))) ->
% multiply(j,multiply(j,multiply(c,c))) collapsed.
% Current number of equations to process: 310
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [106] multiply(c,h) -> multiply(j,multiply(j,multiply(c,j)))
% Rule [105] multiply(j,multiply(c,h)) -> multiply(c,j) collapsed.
% Current number of equations to process: 315
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [107]
% multiply(X,multiply(k,multiply(X,multiply(k,multiply(X,h))))) ->
% multiply(k,j)
% Current number of equations to process: 317
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [108]
% multiply(X,multiply(j,multiply(X,multiply(j,multiply(X,a))))) ->
% multiply(j,c)
% Current number of equations to process: 324
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [109]
% multiply(X,multiply(j,multiply(X,c))) <->
% multiply(j,multiply(j,multiply(X,multiply(X,a))))
% Current number of equations to process: 329
% Current number of ordered equations: 1
% Current number of rules: 50
% New rule produced :
% [110]
% multiply(j,multiply(j,multiply(X,multiply(X,a)))) <->
% multiply(X,multiply(j,multiply(X,c)))
% Current number of equations to process: 329
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [111]
% multiply(c,multiply(k,multiply(c,multiply(k,a)))) ->
% multiply(j,multiply(k,multiply(j,j)))
% Current number of equations to process: 340
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [112] multiply(c,multiply(j,c)) -> multiply(k,multiply(c,multiply(k,a)))
% Current number of equations to process: 341
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [113]
% multiply(X,multiply(k,multiply(X,j))) <->
% multiply(k,multiply(k,multiply(X,multiply(X,h))))
% Current number of equations to process: 347
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [114]
% multiply(k,multiply(k,multiply(X,multiply(X,h)))) <->
% multiply(X,multiply(k,multiply(X,j)))
% Current number of equations to process: 347
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [115]
% multiply(X,multiply(X,multiply(k,j))) <->
% multiply(k,multiply(X,multiply(k,multiply(X,h))))
% Current number of equations to process: 357
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [116]
% multiply(k,multiply(X,multiply(k,multiply(X,h)))) <->
% multiply(X,multiply(X,multiply(k,j)))
% Current number of equations to process: 357
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [117]
% multiply(X,multiply(X,multiply(j,c))) <->
% multiply(j,multiply(X,multiply(j,multiply(X,a))))
% Current number of equations to process: 373
% Current number of ordered equations: 1
% Current number of rules: 58
% New rule produced :
% [118]
% multiply(j,multiply(X,multiply(j,multiply(X,a)))) <->
% multiply(X,multiply(X,multiply(j,c)))
% Current number of equations to process: 373
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [119]
% multiply(c,multiply(j,multiply(k,multiply(c,multiply(k,a))))) ->
% multiply(j,j)
% Current number of equations to process: 384
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [120]
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,j)))))) ->
% b
% Current number of equations to process: 386
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [121] multiply(j,multiply(k,multiply(k,multiply(j,j)))) -> multiply(k,b)
% Rule
% [120]
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,j)))))) ->
% b collapsed.
% Current number of equations to process: 386
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [122]
% multiply(X,multiply(c,multiply(X,multiply(c,multiply(X,a))))) ->
% multiply(k,multiply(j,multiply(k,multiply(j,j))))
% Current number of equations to process: 384
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [123]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Z))))) ->
% multiply(Y,multiply(Y,Z))
% Rule
% [78]
% multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))))) ->
% Z collapsed.
% Rule [90] multiply(X,multiply(j,multiply(X,multiply(j,multiply(X,c))))) -> a
% collapsed.
% Rule [91] multiply(X,multiply(k,multiply(X,multiply(k,multiply(X,j))))) -> h
% collapsed.
% Rule
% [107]
% multiply(X,multiply(k,multiply(X,multiply(k,multiply(X,h))))) ->
% multiply(k,j) collapsed.
% Rule
% [108]
% multiply(X,multiply(j,multiply(X,multiply(j,multiply(X,a))))) ->
% multiply(j,c) collapsed.
% Rule
% [122]
% multiply(X,multiply(c,multiply(X,multiply(c,multiply(X,a))))) ->
% multiply(k,multiply(j,multiply(k,multiply(j,j)))) collapsed.
% Current number of equations to process: 388
% Current number of ordered equations: 0
% Current number of rules: 57
% Rule [111]
% multiply(c,multiply(k,multiply(c,multiply(k,a)))) ->
% multiply(j,multiply(k,multiply(j,j))) is composed into [111]
% multiply(c,
% multiply(k,
% multiply(c,
% multiply(k,a))))
% -> b
% New rule produced : [124] multiply(j,multiply(k,multiply(j,j))) -> b
% Rule [98] multiply(c,multiply(k,multiply(j,multiply(k,multiply(j,j))))) -> a
% collapsed.
% Rule [103] multiply(c,multiply(j,multiply(k,multiply(j,j)))) -> multiply(j,c)
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% multiply(k,multiply(k,b)) = identity
%
% Current number of equations to process: 459
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced : [125] multiply(c,multiply(k,b)) -> a
% Current number of equations to process: 458
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [126] multiply(k,multiply(k,multiply(j,multiply(k,k)))) -> multiply(k,j)
% Current number of equations to process: 460
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced : [127] multiply(j,multiply(k,b)) -> h
% Current number of equations to process: 463
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced : [128] multiply(j,multiply(k,k)) -> h
% Rule
% [92]
% multiply(j,multiply(k,multiply(j,multiply(k,k)))) ->
% multiply(k,multiply(j,h)) collapsed.
% Rule [126] multiply(k,multiply(k,multiply(j,multiply(k,k)))) -> multiply(k,j)
% collapsed.
% Current number of equations to process: 466
% Current number of ordered equations: 0
% Current number of rules: 58
% Rule [71] multiply(j,multiply(j,k)) -> multiply(k,multiply(k,multiply(j,h))) is composed into
% [71] multiply(j,multiply(j,k)) -> multiply(k,multiply(j,j))
% New rule produced : [129] multiply(k,multiply(j,h)) -> multiply(j,j)
% Rule [75] multiply(j,multiply(k,multiply(k,multiply(j,h)))) -> k collapsed.
% Current number of equations to process: 466
% Current number of ordered equations: 0
% Current number of rules: 58
% Rule [124] multiply(j,multiply(k,multiply(j,j))) -> b is composed into
% [124] multiply(j,multiply(k,multiply(j,j))) -> k
% Rule [121] multiply(j,multiply(k,multiply(k,multiply(j,j)))) -> multiply(k,b) is composed into
% [121] multiply(j,multiply(k,multiply(k,multiply(j,j)))) -> multiply(k,k)
% Rule [111] multiply(c,multiply(k,multiply(c,multiply(k,a)))) -> b is composed into
% [111] multiply(c,multiply(k,multiply(c,multiply(k,a)))) -> k
% New rule produced : [130] b -> k
% Rule [39] multiply(c,b) -> multiply(j,c) collapsed.
% Rule [40] multiply(j,b) -> multiply(k,j) collapsed.
% Rule
% [58]
% multiply(b,X) ->
% multiply(k,multiply(k,multiply(j,multiply(k,multiply(k,multiply(j,multiply(j,X)))))))
% collapsed.
% Rule [125] multiply(c,multiply(k,b)) -> a collapsed.
% Rule [127] multiply(j,multiply(k,b)) -> h collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 469
% Current number of ordered equations: 0
% Current number of rules: 54
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 29 rules have been used:
% [1]
% multiply(X,identity) -> X; trace = in the starting set
% [3] multiply(a,b) -> c; trace = in the starting set
% [4] multiply(h,b) -> j; trace = in the starting set
% [5] multiply(X,inverse(X)) -> identity; trace = in the starting set
% [6] multiply(inverse(X),X) -> identity; trace = in the starting set
% [8] multiply(d,inverse(b)) -> h; trace = in the starting set
% [9] multiply(j,inverse(h)) -> k; trace = in the starting set
% [10] multiply(X,multiply(X,X)) -> identity; trace = in the starting set
% [11] multiply(multiply(X,Y),Z) -> multiply(X,multiply(Y,Z)); trace = in the starting set
% [16] multiply(h,multiply(b,X)) -> multiply(j,X); trace = Cp of 11 and 4
% [17] multiply(Y,multiply(inverse(Y),X)) -> X; trace = Cp of 11 and 5
% [18] multiply(inverse(Y),multiply(Y,X)) -> X; trace = Cp of 11 and 6
% [20] multiply(j,multiply(b,b)) -> h; trace = Cp of 16 and 10
% [26] inverse(b) -> multiply(inverse(d),h); trace = Cp of 18 and 8
% [28] inverse(X) -> multiply(X,X); trace = Cp of 18 and 10
% [30] multiply(j,multiply(d,multiply(d,h))) -> h; trace = Cp of 16 and 5
% [31] multiply(c,multiply(c,multiply(d,c))) -> b; trace = Cp of 18 and 3
% [36] multiply(Y,multiply(Y,multiply(Y,X))) -> X; trace = Cp of 11 and 6
% [39] multiply(c,b) -> multiply(j,c); trace = Cp of 36 and 31
% [48] multiply(d,multiply(d,h)) -> multiply(j,multiply(j,h)); trace = Cp of 36 and 30
% [55] multiply(h,X) -> multiply(k,multiply(k,multiply(j,X))); trace = Cp of 20 and 11
% [63] multiply(k,multiply(k,j)) -> h; trace = Cp of 55 and 1
% [68] multiply(k,h) -> j; trace = Cp of 63 and 36
% [71] multiply(j,multiply(j,k)) -> multiply(k,multiply(k,multiply(j,h))); trace = Cp of 18 and 9
% [78] multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z))))))
% -> Z; trace = Cp of 17 and 11
% [91] multiply(X,multiply(k,multiply(X,multiply(k,multiply(X,j))))) -> h; trace = Cp of 78 and 68
% [97] multiply(X,multiply(X,h)) <->
% multiply(k,multiply(X,multiply(k,multiply(X,j)))); trace = Cp of 91 and 36
% [124] multiply(j,multiply(k,multiply(j,j))) -> b; trace = Cp of 78 and 39
% [130] b -> k; trace = Cp of 71 and 36
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.250000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------