TSTP Solution File: RNG025-6 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : RNG025-6 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n167.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 00:31:45 EDT 2014
% Result : Unsatisfiable 48.44s
% Output : Refutation 48.44s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : RNG025-6 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n167.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 17:49:28 CDT 2014
% % CPUTime : 48.44
% Processing problem /tmp/CiME_57437_n167.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " add : AC; y,x,additive_identity : constant; commutator : 2; associator : 3; additive_inverse : 1; multiply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% additive_identity add X = X;
% X add additive_identity = X;
% multiply(additive_identity,X) = additive_identity;
% multiply(X,additive_identity) = additive_identity;
% additive_inverse(X) add X = additive_identity;
% X add additive_inverse(X) = additive_identity;
% additive_inverse(additive_inverse(X)) = X;
% multiply(X,Y add Z) = multiply(X,Y) add multiply(X,Z);
% multiply(X add Y,Z) = multiply(X,Z) add multiply(Y,Z);
% multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y));
% multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y));
% associator(X,Y,Z) = multiply(multiply(X,Y),Z) add additive_inverse(multiply(X,multiply(Y,Z)));
% commutator(X,Y) = multiply(Y,X) add additive_inverse(multiply(X,Y));
% ";
%
% let s1 = status F "
% y lr_lex;
% x lr_lex;
% commutator lr_lex;
% associator lr_lex;
% additive_inverse lr_lex;
% additive_identity lr_lex;
% multiply mul;
% add mul;
% ";
%
% let p1 = precedence F "
% associator > commutator > multiply > additive_inverse > add > additive_identity > x > y";
%
% let s2 = status F "
% y mul;
% x mul;
% commutator mul;
% associator mul;
% additive_inverse mul;
% multiply mul;
% add mul;
% additive_identity mul;
% ";
%
% let p2 = precedence F "
% associator > commutator > multiply > additive_inverse > add > additive_identity = x = y";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " associator(x,y,x) = additive_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 = { additive_identity add X = X,
% additive_identity add X = X,
% multiply(additive_identity,X) =
% additive_identity,
% multiply(X,additive_identity) =
% additive_identity,
% additive_inverse(X) add X = additive_identity,
% additive_inverse(X) add X = additive_identity,
% additive_inverse(additive_inverse(X)) = X,
% multiply(X,Y add Z) =
% multiply(X,Y) add multiply(X,Z),
% multiply(X add Y,Z) =
% multiply(X,Z) add multiply(Y,Z),
% multiply(multiply(X,Y),Y) =
% multiply(X,multiply(Y,Y)),
% multiply(multiply(X,X),Y) =
% multiply(X,multiply(X,Y)),
% associator(X,Y,Z) =
% additive_inverse(multiply(X,multiply(Y,Z))) add
% multiply(multiply(X,Y),Z),
% commutator(X,Y) =
% additive_inverse(multiply(X,Y)) add multiply(Y,X) }
% (13 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 = { associator(x,y,x) = additive_identity }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] additive_inverse(additive_inverse(X)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 1
% New rule produced : [2] additive_identity add 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(X,additive_identity) -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 3
% New rule produced : [4] multiply(additive_identity,X) -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 4
% New rule produced : [5] additive_inverse(X) add X -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 5
% New rule produced :
% [6] multiply(multiply(X,Y),Y) -> multiply(X,multiply(Y,Y))
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 6
% New rule produced :
% [7] multiply(multiply(X,X),Y) -> multiply(X,multiply(X,Y))
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 7
% New rule produced :
% [8] commutator(X,Y) -> additive_inverse(multiply(X,Y)) add multiply(Y,X)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 8
% New rule produced :
% [9] multiply(X,Y add Z) -> multiply(X,Y) add multiply(X,Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 9
% New rule produced :
% [10] multiply(X add Y,Z) -> multiply(X,Z) add multiply(Y,Z)
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [11]
% associator(X,Y,Z) ->
% additive_inverse(multiply(X,multiply(Y,Z))) add multiply(multiply(X,Y),Z)
% The conjecture has been reduced.
% Conjecture is now:
% additive_inverse(multiply(x,multiply(y,x))) add multiply(multiply(x,y),x) = additive_identity
%
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] additive_inverse(additive_identity) -> additive_identity
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13] additive_inverse(X add Y) add Y -> additive_inverse(X)
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] multiply(X,additive_inverse(Y)) add multiply(X,Y) -> additive_identity
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [15] multiply(additive_inverse(X),Y) add multiply(X,Y) -> additive_identity
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [16]
% multiply(multiply(X,multiply(Y,Y)),Y) ->
% multiply(multiply(X,Y),multiply(Y,Y))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [17]
% multiply(multiply(X,multiply(X,Y)),Y) ->
% multiply(X,multiply(X,multiply(Y,Y)))
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [18]
% multiply(multiply(X,multiply(X,multiply(X,X))),Y) ->
% multiply(X,multiply(X,multiply(X,multiply(X,Y))))
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [19] additive_inverse(X add Y) -> additive_inverse(X) add additive_inverse(Y)
% Rule [13] additive_inverse(X add Y) add Y -> additive_inverse(X) collapsed.
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [20] multiply(X,additive_inverse(Y)) -> additive_inverse(multiply(X,Y))
% Rule
% [14] multiply(X,additive_inverse(Y)) add multiply(X,Y) -> additive_identity
% collapsed.
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [21] multiply(additive_inverse(X),Y) -> additive_inverse(multiply(X,Y))
% Rule
% [15] multiply(additive_inverse(X),Y) add multiply(X,Y) -> additive_identity
% collapsed.
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [22]
% multiply(multiply(X,multiply(X,multiply(Y,Y))),Y) ->
% multiply(multiply(X,multiply(X,Y)),multiply(Y,Y))
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [23]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(Y,Y)))),Y) ->
% multiply(multiply(X,Y),multiply(Y,multiply(Y,multiply(Y,Y))))
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [24]
% multiply(multiply(multiply(X,Y),multiply(X,multiply(Y,Y))),Y) ->
% multiply(multiply(X,Y),multiply(multiply(X,Y),multiply(Y,Y)))
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [25]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,Y)))),Y) ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,Y)))))
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [26]
% multiply(multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(Y,Y))))),Y) ->
% multiply(multiply(X,multiply(X,Y)),multiply(Y,multiply(Y,multiply(Y,Y))))
% Current number of equations to process: 61
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [27]
% multiply(X,multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))) ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,X))))))
% Current number of equations to process: 73
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [28]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,Y))))),Y) ->
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,Y)))),multiply(Y,Y))
% Current number of equations to process: 79
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [29]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(Y,Y)))),multiply(Y,Y)) ->
% multiply(multiply(X,multiply(Y,Y)),multiply(Y,multiply(Y,multiply(Y,Y))))
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [30]
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(multiply(X,Y),multiply(Y,Y))),Y)
% ->
% multiply(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,multiply(Y,multiply(Y,Y)))))
% Current number of equations to process: 98
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [31]
% multiply(multiply(multiply(X,multiply(X,Y)),multiply(X,multiply(X,multiply(Y,Y)))),Y)
% ->
% multiply(multiply(X,multiply(X,Y)),multiply(multiply(X,multiply(X,Y)),
% multiply(Y,Y)))
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [32]
% multiply(multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(Y,Y))))),
% multiply(Y,Y)) ->
% multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(Y,multiply(Y,
% multiply(Y,Y))))
% Current number of equations to process: 139
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [33]
% multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,multiply(X,multiply(X,X)))))
% ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,X)))))))
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [34]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,X))))))),Y)
% ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,Y))))))))
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [35]
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(multiply(X,Y),multiply(Y,Y))),
% multiply(Y,Y)) ->
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,multiply(Y,
% multiply(Y,Y))))),Y)
% Current number of equations to process: 187
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [36]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,multiply(Y,
% multiply(Y,Y))))))),Y)
% ->
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,Y)))),multiply(Y,
% multiply(Y,
% multiply(Y,Y))))
% Current number of equations to process: 214
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [37]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(X,Y)))))))),Y)
% ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(Y,Y)))))))))
% Current number of equations to process: 228
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [38]
% multiply(multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(multiply(X,
% multiply(X,Y)),
% multiply(Y,Y))),Y) ->
% multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(X,multiply(X,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [39]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,Y)))))))),Y)
% ->
% multiply(multiply(X,Y),multiply(Y,multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))))
% Current number of equations to process: 301
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [40]
% multiply(multiply(multiply(multiply(X,Y),multiply(Y,Y)),multiply(X,multiply(Y,
% multiply(Y,
% multiply(Y,Y))))),Y)
% ->
% multiply(multiply(multiply(X,Y),multiply(Y,Y)),multiply(multiply(X,Y),
% multiply(Y,multiply(Y,
% multiply(Y,Y)))))
% Current number of equations to process: 320
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [41]
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,multiply(Y,
% multiply(Y,Y))))),
% multiply(Y,Y)) ->
% multiply(multiply(X,multiply(Y,Y)),multiply(multiply(X,multiply(Y,Y)),
% multiply(Y,multiply(Y,multiply(Y,Y)))))
% Current number of equations to process: 356
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [42]
% multiply(multiply(multiply(X,Y),multiply(multiply(X,Y),multiply(multiply(X,Y),
% multiply(X,multiply(Y,Y))))),Y)
% ->
% multiply(multiply(X,Y),multiply(multiply(X,Y),multiply(multiply(X,Y),
% multiply(multiply(X,Y),
% multiply(Y,Y)))))
% Current number of equations to process: 385
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [43]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,multiply(Y,
% multiply(Y,Y))))))),
% multiply(Y,Y)) ->
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,Y))))),
% multiply(Y,multiply(Y,multiply(Y,Y))))
% Current number of equations to process: 420
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [44]
% multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),
% multiply(X,multiply(X,multiply(X,X))))) ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(X,X)))))))))
% Current number of equations to process: 431
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [45]
% multiply(multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(multiply(X,
% multiply(X,Y)),
% multiply(Y,Y))),
% multiply(Y,Y)) ->
% multiply(multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(X,multiply(X,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y)))))),Y)
% Current number of equations to process: 451
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [46]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(X,
% multiply(Y,Y))))))))),Y)
% ->
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(X,Y)))))))),
% multiply(Y,Y))
% Current number of equations to process: 490
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [47]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,Y)))))))),
% multiply(Y,Y)) ->
% multiply(multiply(X,multiply(Y,Y)),multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))))
% Current number of equations to process: 512
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [48]
% multiply(multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))))),Y)
% ->
% multiply(multiply(X,multiply(X,Y)),multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))))
% Current number of equations to process: 530
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [49]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,X)))),multiply(multiply(X,
% multiply(X,X)),
% multiply(X,
% multiply(X,X))))
% ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(X,
% multiply(X,X))))))))))
% Current number of equations to process: 552
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [50]
% multiply(multiply(multiply(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,
% multiply(Y,
% multiply(Y,Y))))),Y),
% multiply(Y,Y)) ->
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(multiply(X,Y),multiply(Y,Y))),
% multiply(Y,multiply(Y,multiply(Y,Y))))
% Current number of equations to process: 559
% Current number of ordered equations: 1
% Current number of rules: 47
% New rule produced :
% [51]
% multiply(multiply(multiply(multiply(X,Y),multiply(Y,Y)),multiply(multiply(X,Y),
% multiply(Y,multiply(Y,
% multiply(Y,Y))))),Y)
% ->
% multiply(multiply(multiply(multiply(X,Y),multiply(Y,Y)),multiply(X,multiply(Y,
% multiply(Y,
% multiply(Y,Y))))),
% multiply(Y,Y))
% Current number of equations to process: 559
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [52]
% multiply(multiply(X,Y),Z) add multiply(multiply(X,Z),Y) add multiply(X,
% multiply(Y,Y)) add
% multiply(X,multiply(Z,Z)) ->
% multiply(X,multiply(Y,Y)) add multiply(X,multiply(Y,Z)) add multiply(X,
% multiply(Z,Y)) add
% multiply(X,multiply(Z,Z))
% Current number of equations to process: 616
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [53]
% multiply(multiply(X,Y),Z) add multiply(multiply(X,Z),Y) add multiply(X,
% multiply(Y,Y)) ->
% multiply(X,multiply(Y,Y)) add multiply(X,multiply(Y,Z)) add multiply(X,
% multiply(Z,Y))
% Rule
% [52]
% multiply(multiply(X,Y),Z) add multiply(multiply(X,Z),Y) add multiply(X,
% multiply(Y,Y)) add
% multiply(X,multiply(Z,Z)) ->
% multiply(X,multiply(Y,Y)) add multiply(X,multiply(Y,Z)) add multiply(X,
% multiply(Z,Y)) add
% multiply(X,multiply(Z,Z)) collapsed.
% Current number of equations to process: 667
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [54]
% multiply(multiply(X,Y),Z) add multiply(multiply(X,Z),Y) ->
% multiply(X,multiply(Y,Z)) add multiply(X,multiply(Z,Y))
% Rule
% [53]
% multiply(multiply(X,Y),Z) add multiply(multiply(X,Z),Y) add multiply(X,
% multiply(Y,Y)) ->
% multiply(X,multiply(Y,Y)) add multiply(X,multiply(Y,Z)) add multiply(X,
% multiply(Z,Y))
% collapsed.
% Current number of equations to process: 698
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [55]
% multiply(multiply(X,Y),X) add multiply(X,multiply(X,Y)) ->
% multiply(X,multiply(X,Y)) add multiply(X,multiply(Y,X))
% Current number of equations to process: 744
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [56]
% additive_inverse(multiply(multiply(X,Y),Z)) add additive_inverse(multiply(
% multiply(X,Z),Y))
% ->
% additive_inverse(multiply(X,multiply(Y,Z))) add additive_inverse(multiply(X,
% multiply(Z,Y)))
% Current number of equations to process: 768
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [57]
% additive_inverse(multiply(multiply(X,Z),Y)) add multiply(X,multiply(Y,Z)) add
% multiply(X,multiply(Z,Y)) <-> multiply(multiply(X,Y),Z)
% Current number of equations to process: 767
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [58]
% multiply(multiply(X,Y),Z) <->
% additive_inverse(multiply(multiply(X,Z),Y)) add multiply(X,multiply(Y,Z)) add
% multiply(X,multiply(Z,Y))
% Rule
% [16]
% multiply(multiply(X,multiply(Y,Y)),Y) ->
% multiply(multiply(X,Y),multiply(Y,Y)) collapsed.
% Rule
% [17]
% multiply(multiply(X,multiply(X,Y)),Y) ->
% multiply(X,multiply(X,multiply(Y,Y))) collapsed.
% Rule
% [22]
% multiply(multiply(X,multiply(X,multiply(Y,Y))),Y) ->
% multiply(multiply(X,multiply(X,Y)),multiply(Y,Y)) collapsed.
% Rule
% [23]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(Y,Y)))),Y) ->
% multiply(multiply(X,Y),multiply(Y,multiply(Y,multiply(Y,Y)))) collapsed.
% Rule
% [24]
% multiply(multiply(multiply(X,Y),multiply(X,multiply(Y,Y))),Y) ->
% multiply(multiply(X,Y),multiply(multiply(X,Y),multiply(Y,Y))) collapsed.
% Rule
% [25]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,Y)))),Y) ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,Y))))) collapsed.
% Rule
% [26]
% multiply(multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(Y,Y))))),Y) ->
% multiply(multiply(X,multiply(X,Y)),multiply(Y,multiply(Y,multiply(Y,Y))))
% collapsed.
% Rule
% [28]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,Y))))),Y) ->
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,Y)))),multiply(Y,Y))
% collapsed.
% Rule
% [29]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(Y,Y)))),multiply(Y,Y)) ->
% multiply(multiply(X,multiply(Y,Y)),multiply(Y,multiply(Y,multiply(Y,Y))))
% collapsed.
% Rule
% [30]
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(multiply(X,Y),multiply(Y,Y))),Y)
% ->
% multiply(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,multiply(Y,multiply(Y,Y)))))
% collapsed.
% Rule
% [31]
% multiply(multiply(multiply(X,multiply(X,Y)),multiply(X,multiply(X,multiply(Y,Y)))),Y)
% ->
% multiply(multiply(X,multiply(X,Y)),multiply(multiply(X,multiply(X,Y)),
% multiply(Y,Y))) collapsed.
% Rule
% [32]
% multiply(multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(Y,Y))))),
% multiply(Y,Y)) ->
% multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(Y,multiply(Y,
% multiply(Y,Y))))
% collapsed.
% Rule
% [35]
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(multiply(X,Y),multiply(Y,Y))),
% multiply(Y,Y)) ->
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,multiply(Y,
% multiply(Y,Y))))),Y)
% collapsed.
% Rule
% [36]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,multiply(Y,
% multiply(Y,Y))))))),Y)
% ->
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,Y)))),multiply(Y,
% multiply(Y,
% multiply(Y,Y))))
% collapsed.
% Rule
% [37]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(X,Y)))))))),Y)
% ->
% multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(Y,Y)))))))))
% collapsed.
% Rule
% [38]
% multiply(multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(multiply(X,
% multiply(X,Y)),
% multiply(Y,Y))),Y) ->
% multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(X,multiply(X,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))
% collapsed.
% Rule
% [39]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,Y)))))))),Y)
% ->
% multiply(multiply(X,Y),multiply(Y,multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))))
% collapsed.
% Rule
% [40]
% multiply(multiply(multiply(multiply(X,Y),multiply(Y,Y)),multiply(X,multiply(Y,
% multiply(Y,
% multiply(Y,Y))))),Y)
% ->
% multiply(multiply(multiply(X,Y),multiply(Y,Y)),multiply(multiply(X,Y),
% multiply(Y,multiply(Y,
% multiply(Y,Y)))))
% collapsed.
% Rule
% [41]
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,multiply(Y,
% multiply(Y,Y))))),
% multiply(Y,Y)) ->
% multiply(multiply(X,multiply(Y,Y)),multiply(multiply(X,multiply(Y,Y)),
% multiply(Y,multiply(Y,multiply(Y,Y)))))
% collapsed.
% Rule
% [42]
% multiply(multiply(multiply(X,Y),multiply(multiply(X,Y),multiply(multiply(X,Y),
% multiply(X,multiply(Y,Y))))),Y)
% ->
% multiply(multiply(X,Y),multiply(multiply(X,Y),multiply(multiply(X,Y),
% multiply(multiply(X,Y),
% multiply(Y,Y))))) collapsed.
% Rule
% [43]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,multiply(Y,
% multiply(Y,Y))))))),
% multiply(Y,Y)) ->
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(Y,Y))))),
% multiply(Y,multiply(Y,multiply(Y,Y)))) collapsed.
% Rule
% [45]
% multiply(multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(multiply(X,
% multiply(X,Y)),
% multiply(Y,Y))),
% multiply(Y,Y)) ->
% multiply(multiply(multiply(X,multiply(X,multiply(Y,Y))),multiply(X,multiply(X,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y)))))),Y)
% collapsed.
% Rule
% [46]
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(X,
% multiply(Y,Y))))))))),Y)
% ->
% multiply(multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,multiply(X,
% multiply(X,
% multiply(X,Y)))))))),
% multiply(Y,Y)) collapsed.
% Rule
% [47]
% multiply(multiply(X,multiply(Y,multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,Y)))))))),
% multiply(Y,Y)) ->
% multiply(multiply(X,multiply(Y,Y)),multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))))
% collapsed.
% Rule
% [48]
% multiply(multiply(X,multiply(X,multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))))),Y)
% ->
% multiply(multiply(X,multiply(X,Y)),multiply(Y,multiply(Y,multiply(Y,multiply(Y,
% multiply(Y,
% multiply(Y,
% multiply(Y,Y))))))))
% collapsed.
% Rule
% [50]
% multiply(multiply(multiply(multiply(X,multiply(Y,Y)),multiply(X,multiply(Y,
% multiply(Y,
% multiply(Y,Y))))),Y),
% multiply(Y,Y)) ->
% multiply(multiply(multiply(X,multiply(Y,Y)),multiply(multiply(X,Y),multiply(Y,Y))),
% multiply(Y,multiply(Y,multiply(Y,Y)))) collapsed.
% Rule
% [51]
% multiply(multiply(multiply(multiply(X,Y),multiply(Y,Y)),multiply(multiply(X,Y),
% multiply(Y,multiply(Y,
% multiply(Y,Y))))),Y)
% ->
% multiply(multiply(multiply(multiply(X,Y),multiply(Y,Y)),multiply(X,multiply(Y,
% multiply(Y,
% multiply(Y,Y))))),
% multiply(Y,Y)) collapsed.
% Current number of equations to process: 794
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [59]
% multiply(multiply(multiply(X,Y),Z),Y) add multiply(multiply(X,multiply(Y,Y)),Z)
% ->
% multiply(multiply(X,Y),multiply(Y,Z)) add multiply(multiply(X,Y),multiply(Z,Y))
% Current number of equations to process: 799
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [60]
% multiply(multiply(X,multiply(X,Y)),Z) add multiply(multiply(X,multiply(X,Z)),Y)
% ->
% multiply(X,multiply(X,multiply(Y,Z))) add multiply(X,multiply(X,multiply(Z,Y)))
% Current number of equations to process: 798
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [61]
% multiply(X,multiply(multiply(Y,Z),V_3)) add multiply(X,multiply(multiply(Y,V_3),Z))
% ->
% multiply(X,multiply(Y,multiply(Z,V_3))) add multiply(X,multiply(Y,multiply(V_3,Z)))
% Current number of equations to process: 797
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [62]
% multiply(multiply(multiply(X,Y),Z),V_3) add multiply(multiply(multiply(X,Z),Y),V_3)
% ->
% multiply(multiply(X,multiply(Y,Z)),V_3) add multiply(multiply(X,multiply(Z,Y)),V_3)
% Current number of equations to process: 796
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [63]
% multiply(multiply(X,Y),multiply(Y,Y)) add multiply(multiply(X,Y),multiply(Y,Y))
% ->
% multiply(X,multiply(Y,multiply(Y,Y))) add multiply(X,multiply(Y,multiply(Y,Y)))
% Current number of equations to process: 795
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [64]
% multiply(multiply(X,Y),multiply(X,Y)) add multiply(X,multiply(X,multiply(Y,Y)))
% ->
% multiply(X,multiply(X,multiply(Y,Y))) add multiply(X,multiply(Y,multiply(X,Y)))
% Current number of equations to process: 794
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [65] multiply(multiply(X,Y),X) -> multiply(X,multiply(Y,X))
% Rule
% [55]
% multiply(multiply(X,Y),X) add multiply(X,multiply(X,Y)) ->
% multiply(X,multiply(X,Y)) add multiply(X,multiply(Y,X)) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 797
% Current number of ordered equations: 0
% Current number of rules: 32
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 10 rules have been used:
% [5]
% additive_inverse(X) add X -> additive_identity; trace = in the starting set
% [6] multiply(multiply(X,Y),Y) -> multiply(X,multiply(Y,Y)); trace = in the starting set
% [7] multiply(multiply(X,X),Y) -> multiply(X,multiply(X,Y)); trace = in the starting set
% [9] multiply(X,Y add Z) -> multiply(X,Y) add multiply(X,Z); trace = in the starting set
% [11] associator(X,Y,Z) ->
% additive_inverse(multiply(X,multiply(Y,Z))) add multiply(multiply(X,Y),Z); trace = in the starting set
% [52] multiply(multiply(X,Y),Z) add multiply(multiply(X,Z),Y) add multiply(X,
% multiply(Y,Y)) add
% multiply(X,multiply(Z,Z)) ->
% multiply(X,multiply(Y,Y)) add multiply(X,multiply(Y,Z)) add multiply(X,
% multiply(Z,Y)) add
% multiply(X,multiply(Z,Z)); trace = Cp of 9 and 6
% [53] multiply(multiply(X,Y),Z) add multiply(multiply(X,Z),Y) add multiply(X,
% multiply(Y,Y))
% ->
% multiply(X,multiply(Y,Y)) add multiply(X,multiply(Y,Z)) add multiply(X,
% multiply(Z,Y)); trace = Cp of 52 and 5
% [54] multiply(multiply(X,Y),Z) add multiply(multiply(X,Z),Y) ->
% multiply(X,multiply(Y,Z)) add multiply(X,multiply(Z,Y)); trace = Cp of 53 and 5
% [55] multiply(multiply(X,Y),X) add multiply(X,multiply(X,Y)) ->
% multiply(X,multiply(X,Y)) add multiply(X,multiply(Y,X)); trace = Cp of 54 and 7
% [65] multiply(multiply(X,Y),X) -> multiply(X,multiply(Y,X)); trace = Cp of 55 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 47.270000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------