TSTP Solution File: BOO014-4 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : BOO014-4 : TPTP v6.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n075.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 00:19:10 EDT 2014
% Result : Unsatisfiable 1.90s
% Output : Refutation 1.90s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : BOO014-4 : TPTP v6.0.0. Released v1.1.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n075.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 17:15:48 CDT 2014
% % CPUTime : 1.90
% Processing problem /tmp/CiME_21943_n075.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " multiply,add : infix commutative; b,a,multiplicative_identity,additive_identity : constant; inverse : 1;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% X add (Y multiply Z) = (X add Y) multiply (X add Z);
% X multiply (Y add Z) = (X multiply Y) add (X multiply Z);
% X add additive_identity = X;
% X multiply multiplicative_identity = X;
% X add inverse(X) = multiplicative_identity;
% X multiply inverse(X) = additive_identity;
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% inverse lr_lex;
% multiplicative_identity lr_lex;
% additive_identity lr_lex;
% multiply mul;
% add mul;
% ";
%
% let p1 = precedence F "
% add > multiply > inverse > additive_identity > multiplicative_identity > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% inverse mul;
% multiplicative_identity mul;
% additive_identity mul;
% multiply mul;
% add mul;
% ";
%
% let p2 = precedence F "
% add > multiply > inverse > additive_identity = multiplicative_identity = a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " inverse(a add b) = inverse(a) multiply inverse(b);"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
%
% let Red_Conjectures = normalize_equations Defining_rules Conjectures;
% *)
% #time on;
%
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
%
% #time off;
%
%
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
%
% F : signature = <signature>
% X : variable_set = <variable set>
%
% Axioms : (F,X) equations = { (Y multiply Z) add X =
% (X add Y) multiply (X add Z),
% (Y add Z) multiply X =
% (X multiply Y) add (X multiply Z),
% additive_identity add X = X,
% multiplicative_identity multiply X = X,
% inverse(X) add X = multiplicative_identity,
% inverse(X) multiply X = additive_identity }
% (6 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 = { inverse(b add a) =
% inverse(b) multiply inverse(a) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] multiplicative_identity multiply X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 5
% 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: 4
% Current number of rules: 2
% New rule produced : [3] inverse(X) multiply X -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 3
% New rule produced : [4] inverse(X) add X -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 4
% New rule produced : [5] (Y multiply Z) add X -> (X add Y) multiply (X add Z)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% ((X add X) multiply (X add Z)) multiply ((X add Y) multiply (Y add Z)) ->
% (Y add Z) multiply X
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] inverse(multiplicative_identity) -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] inverse(additive_identity) -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9] (multiplicative_identity add Y) multiply (X add Y) -> X add Y
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [10] (inverse(Y) add X) multiply (X add Y) -> X
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] (X add X) multiply Y <-> (Y add Y) multiply X
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] (inverse(X) add Y) multiply X -> (X add X) multiply Y
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] (multiplicative_identity add X) multiply X -> X
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] multiplicative_identity add X -> multiplicative_identity
% Rule [9] (multiplicative_identity add Y) multiply (X add Y) -> X add Y
% collapsed.
% Rule [13] (multiplicative_identity add X) multiply X -> X collapsed.
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 12
% Rule [12] (inverse(X) add Y) multiply X -> (X add X) multiply Y is composed into
% [12] (inverse(X) add Y) multiply X -> X multiply Y
% New rule produced : [15] X add X -> X
% Rule
% [6]
% ((X add X) multiply (X add Z)) multiply ((X add Y) multiply (Y add Z)) ->
% (Y add Z) multiply X collapsed.
% Rule [11] (X add X) multiply Y <-> (Y add Y) multiply X collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [16]
% ((X add Y) multiply (Y add Z)) multiply ((X add Z) multiply X) ->
% (Y add Z) multiply X
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [17] inverse(inverse(X)) add X -> X
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [18] inverse(inverse(X)) -> X
% Rule [17] inverse(inverse(X)) add X -> X collapsed.
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [19] additive_identity multiply X -> additive_identity
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [20] X multiply X -> X
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [21] (X add Y) multiply inverse(X) -> inverse(X) multiply Y
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [22] ((X add Y) multiply X) multiply Y -> X multiply Y
% Current number of equations to process: 20
% Current number of ordered equations: 2
% Current number of rules: 17
% New rule produced :
% [23] ((X add Y) multiply X) multiply (X multiply Y) -> X multiply Y
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [24] ((X add Y) multiply Y) multiply (inverse(X) add Y) -> Y
% Current number of equations to process: 18
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [25] ((inverse(X) add Y) multiply Y) multiply (X add Y) -> Y
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [26] ((X add Y) multiply X) multiply ((X add Y) multiply Y) -> X multiply Y
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [27]
% (inverse(X multiply Y) add X) multiply (inverse(X multiply Y) add Y) ->
% multiplicative_identity
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [28] ((inverse(Z) add Y) add X) multiply ((Y add Z) add X) -> X add Y
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [29]
% ((inverse(X) add Y) multiply (inverse(X) add Z)) multiply X ->
% (Y multiply Z) multiply X
% Current number of equations to process: 13
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [30]
% ((inverse(X) add Z) add Y) multiply (X add Y) -> (X add Y) multiply (Y add Z)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [31]
% ((X add Y) multiply (X add Z)) multiply (inverse(Y multiply Z) add X) -> X
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [32] ((X add Y) multiply X) multiply (inverse(X) add Y) -> X multiply Y
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [33] (X add Y) multiply X -> X
% Rule
% [16]
% ((X add Y) multiply (Y add Z)) multiply ((X add Z) multiply X) ->
% (Y add Z) multiply X collapsed.
% Rule [22] ((X add Y) multiply X) multiply Y -> X multiply Y collapsed.
% Rule [23] ((X add Y) multiply X) multiply (X multiply Y) -> X multiply Y
% collapsed.
% Rule [24] ((X add Y) multiply Y) multiply (inverse(X) add Y) -> Y collapsed.
% Rule [25] ((inverse(X) add Y) multiply Y) multiply (X add Y) -> Y collapsed.
% Rule
% [26] ((X add Y) multiply X) multiply ((X add Y) multiply Y) -> X multiply Y
% collapsed.
% Rule [32] ((X add Y) multiply X) multiply (inverse(X) add Y) -> X multiply Y
% collapsed.
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [34] ((X add Y) multiply (Y add Z)) multiply X -> (Y add Z) multiply X
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [35] (X multiply Y) multiply X -> X multiply Y
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [36]
% ((X add Y) multiply (X add Z)) multiply inverse(X) ->
% (Y multiply Z) multiply inverse(X)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [37] (X add Y) add Y -> X add Y
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [38] (inverse(X) add Y) add inverse(X add Y) -> inverse(X add Y) add Y
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [39]
% (X add Y) add inverse(inverse(Y) add X) -> inverse(inverse(Y) add X) add X
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [40] (inverse(inverse(X) add Y) multiply Y) multiply X -> additive_identity
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [41] (inverse(X) multiply Y) multiply X -> additive_identity
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [42] (inverse(inverse(X) multiply Y) add X) multiply (X add Y) -> X
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [43]
% (inverse(X multiply Y) add inverse(X)) multiply (inverse(X) add Y) ->
% inverse(X)
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [44]
% ((X add Z) add Y) multiply (inverse(X) add Y) ->
% (inverse(X) add Y) multiply (Y add Z)
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [45] (X add Y) add inverse(X) -> multiplicative_identity
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [46] ((X add Y) multiply (X add Z)) multiply X -> X
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [47] ((Y add Z) add X) multiply (X add Y) -> X add Y
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [48] ((X add Y) multiply (X add Z)) multiply (Y multiply Z) -> Y multiply Z
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [49] inverse(X add Y) multiply X -> additive_identity
% Rule
% [40] (inverse(inverse(X) add Y) multiply Y) multiply X -> additive_identity
% collapsed.
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [50] (inverse(X add Y) add Y) multiply X -> X multiply Y
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [51] (inverse(X multiply Y) add Y) multiply X -> X
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [52] (inverse(X) multiply Y) multiply (X add Y) -> inverse(X) multiply Y
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [53] (X multiply Y) multiply (inverse(X) add Y) -> X multiply Y
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [54] inverse(X multiply Y) add X -> multiplicative_identity
% Rule
% [27]
% (inverse(X multiply Y) add X) multiply (inverse(X multiply Y) add Y) ->
% multiplicative_identity collapsed.
% Rule [51] (inverse(X multiply Y) add Y) multiply X -> X collapsed.
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [55] ((inverse(Z) add Y) add X) multiply Z -> (X add Y) multiply Z
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [56] (X multiply Y) multiply inverse(X) -> additive_identity
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [57]
% ((inverse(Z) add Y) add X) multiply (Y add Z) -> (X add Y) multiply (Y add Z)
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [58] ((X add Y) add Z) add X -> (X add Y) add Z
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [59] ((X add Y) add Z) multiply X -> X
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [60] (X multiply Y) multiply inverse(X add Z) -> additive_identity
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [61] ((inverse(Z) add X) multiply Y) multiply Z -> (X multiply Y) multiply Z
% Rule
% [29]
% ((inverse(X) add Y) multiply (inverse(X) add Z)) multiply X ->
% (Y multiply Z) multiply X collapsed.
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [62]
% ((X add Z) multiply Y) multiply inverse(Z) ->
% (X multiply Y) multiply inverse(Z)
% Rule
% [36]
% ((X add Y) multiply (X add Z)) multiply inverse(X) ->
% (Y multiply Z) multiply inverse(X) collapsed.
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [63] (inverse(X add Y) add Y) multiply (inverse(X) add Y) -> inverse(X) add Y
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [64] (inverse(inverse(X) add Y) add Y) multiply (X add Y) -> X add Y
% Current number of equations to process: 111
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [65] ((inverse(Y) add X) multiply (X add Z)) multiply (X add Y) -> X
% Current number of equations to process: 110
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [66] (inverse(inverse(Y) multiply X) add Y) multiply X -> X multiply Y
% Current number of equations to process: 112
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [67]
% (X add Y) multiply inverse(inverse(X) multiply Y) ->
% inverse(inverse(X) multiply Y) multiply X
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [68]
% (inverse(X multiply Y) add inverse(X)) multiply Y -> inverse(X) multiply Y
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [69]
% (inverse(X) add Y) multiply inverse(X multiply Y) ->
% inverse(X multiply Y) multiply inverse(X)
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [70] inverse(inverse(X) multiply Y) add X -> inverse(inverse(X) multiply Y)
% Rule [42] (inverse(inverse(X) multiply Y) add X) multiply (X add Y) -> X
% collapsed.
% Rule [66] (inverse(inverse(Y) multiply X) add Y) multiply X -> X multiply Y
% collapsed.
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [71] inverse(inverse(Y) multiply X) multiply X -> X multiply Y
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 52
% Rule [67]
% (X add Y) multiply inverse(inverse(X) multiply Y) ->
% inverse(inverse(X) multiply Y) multiply X is composed into [67]
% (X add Y) multiply
% inverse(
% inverse(X) multiply Y)
% -> X
% New rule produced : [72] inverse(inverse(X) multiply Y) multiply X -> X
% Current number of equations to process: 124
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [73]
% ((X add Y) add Z) multiply (inverse(X) add Y) ->
% (inverse(X) add Y) multiply (Y add Z)
% Current number of equations to process: 130
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [74]
% (inverse(X add Y) add Y) add (inverse(X) add Y) -> inverse(X add Y) add Y
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced : [75] (inverse(Y add Z) add X) multiply (X add Z) -> X
% Current number of equations to process: 133
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [76] ((Y add Z) add X) multiply inverse(Z) -> (X add Y) multiply inverse(Z)
% Current number of equations to process: 132
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced : [77] (inverse(X) add Y) add X -> multiplicative_identity
% Current number of equations to process: 143
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced : [78] inverse(X add Y) add inverse(X) -> inverse(X)
% Current number of equations to process: 142
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [79] inverse(X add Y) multiply inverse(X) -> inverse(X add Y)
% Current number of equations to process: 141
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced : [80] (X add Y) add (X add Z) -> (X add Y) add Z
% Rule
% [74]
% (inverse(X add Y) add Y) add (inverse(X) add Y) -> inverse(X add Y) add Y
% collapsed.
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [81] (inverse(X add Y) add Z) add inverse(X) -> inverse(X) add Z
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 61
% Rule [39]
% (X add Y) add inverse(inverse(Y) add X) ->
% inverse(inverse(Y) add X) add X is composed into [39]
% (X add Y) add inverse(
% inverse(Y) add X)
% ->
% inverse(inverse(Y)) add X
% Rule [38] (inverse(X) add Y) add inverse(X add Y) -> inverse(X add Y) add Y is composed into
% [38] (inverse(X) add Y) add inverse(X add Y) -> inverse(X) add Y
% New rule produced : [82] inverse(X add Y) add Y -> inverse(X) add Y
% Rule [50] (inverse(X add Y) add Y) multiply X -> X multiply Y collapsed.
% Rule
% [63] (inverse(X add Y) add Y) multiply (inverse(X) add Y) -> inverse(X) add Y
% collapsed.
% Rule [64] (inverse(inverse(X) add Y) add Y) multiply (X add Y) -> X add Y
% collapsed.
% Current number of equations to process: 156
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced : [83] inverse(inverse(X) add Y) add X -> X
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [84] (inverse(X) add Y) add (X add Z) -> multiplicative_identity
% Current number of equations to process: 159
% Current number of ordered equations: 1
% Current number of rules: 61
% New rule produced :
% [85] ((X add Y) add Z) add inverse(X) -> multiplicative_identity
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced : [86] (X multiply Y) multiply (X add Z) -> X multiply Y
% Rule [52] (inverse(X) multiply Y) multiply (X add Y) -> inverse(X) multiply Y
% collapsed.
% Rule [53] (X multiply Y) multiply (inverse(X) add Y) -> X multiply Y
% collapsed.
% Current number of equations to process: 163
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [87]
% (inverse(X multiply Y) multiply Y) multiply inverse(X) ->
% inverse(X multiply Y) multiply Y
% Current number of equations to process: 168
% Current number of ordered equations: 0
% Current number of rules: 62
% Rule [69]
% (inverse(X) add Y) multiply inverse(X multiply Y) ->
% inverse(X multiply Y) multiply inverse(X) is composed into [69]
% (inverse(X) add Y) multiply
% inverse(
% X multiply Y)
% -> inverse(X)
% New rule produced :
% [88] inverse(X multiply Y) multiply inverse(X) -> inverse(X)
% Current number of equations to process: 178
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [89] inverse(X multiply Y) add inverse(X) -> inverse(X multiply Y)
% Rule
% [43]
% (inverse(X multiply Y) add inverse(X)) multiply (inverse(X) add Y) ->
% inverse(X) collapsed.
% Rule
% [68]
% (inverse(X multiply Y) add inverse(X)) multiply Y -> inverse(X) multiply Y
% collapsed.
% Current number of equations to process: 178
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [90] inverse(X multiply Y) multiply Y -> inverse(X) multiply Y
% Rule [71] inverse(inverse(Y) multiply X) multiply X -> X multiply Y
% collapsed.
% Rule
% [87]
% (inverse(X multiply Y) multiply Y) multiply inverse(X) ->
% inverse(X multiply Y) multiply Y collapsed.
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [91] (X add Y) add inverse(inverse(X) multiply Y) -> multiplicative_identity
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [92] (inverse(X) add Y) add inverse(X multiply Y) -> multiplicative_identity
% Current number of equations to process: 175
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [93] (X add Y) add inverse(X multiply Z) -> multiplicative_identity
% Rule
% [91] (X add Y) add inverse(inverse(X) multiply Y) -> multiplicative_identity
% collapsed.
% Rule
% [92] (inverse(X) add Y) add inverse(X multiply Y) -> multiplicative_identity
% collapsed.
% Current number of equations to process: 192
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [94] (inverse(X multiply Y) add Z) add X -> multiplicative_identity
% Current number of equations to process: 192
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [95] inverse((X add Y) multiply (X add Z)) multiply X -> additive_identity
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [96] inverse(inverse(X) add Y) multiply inverse(X add Y) -> additive_identity
% Current number of equations to process: 193
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [97] ((X add Y) add Z) add inverse(X add Z) -> multiplicative_identity
% Current number of equations to process: 192
% Current number of ordered equations: 0
% Current number of rules: 66
% New rule produced :
% [98]
% (inverse(X) add Y) add inverse(X multiply Z) -> inverse(X multiply Z) add Y
% Current number of equations to process: 188
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [99] (inverse(inverse(X) multiply Y) add Z) multiply X -> X
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [100] (X add Y) multiply inverse((Y add Z) add X) -> additive_identity
% Current number of equations to process: 205
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [101] (inverse((inverse(X) add Y) multiply Z) add Y) multiply X -> X
% Current number of equations to process: 204
% Current number of ordered equations: 0
% Current number of rules: 70
% New rule produced :
% [102] (((X add Y) add Z) add V_3) multiply (X add Z) -> X add Z
% Current number of equations to process: 206
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [103]
% (X multiply Y) multiply inverse((X add Z) multiply (Y add Z)) ->
% additive_identity
% Current number of equations to process: 205
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [104] (inverse(inverse(Y) multiply Z) add X) multiply (X add Y) -> X add Y
% Current number of equations to process: 204
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [105]
% (X add Y) add inverse(inverse(X) multiply Z) ->
% inverse(inverse(X) multiply Z) add Y
% Current number of equations to process: 203
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [106] ((inverse(X add Z) add Y) add X) multiply Z -> (X add Y) multiply Z
% Current number of equations to process: 202
% Current number of ordered equations: 0
% Current number of rules: 75
% New rule produced :
% [107] ((X add Y) multiply (X add Z)) multiply (inverse(Y) add X) -> X
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [108]
% (inverse(X multiply Z) add Y) multiply (inverse(X) add Y) -> inverse(X) add Y
% Current number of equations to process: 199
% Current number of ordered equations: 0
% Current number of rules: 77
% New rule produced :
% [109] (((X add Y) multiply (X add Z)) multiply (X add V_3)) multiply X -> X
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [110]
% (inverse(inverse(X multiply Y) multiply Z) add X) multiply (X add Z) -> X
% Current number of equations to process: 197
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [111]
% ((inverse(X) add Y) add Z) add inverse((Y add Z) multiply X) ->
% multiplicative_identity
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 80
% New rule produced :
% [112]
% ((X add Y) multiply Z) multiply inverse((inverse(Z) add Y) add X) ->
% additive_identity
% Current number of equations to process: 195
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [113] inverse((X add Y) add Z) multiply X -> additive_identity
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced : [114] (((X add Y) add Z) add V_3) multiply X -> X
% Current number of equations to process: 208
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [115] ((inverse(X) add Y) add Z) add X -> multiplicative_identity
% Current number of equations to process: 210
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [116] (X multiply Y) multiply ((X add Z) add V_3) -> X multiply Y
% Current number of equations to process: 218
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [117] (X multiply Y) multiply inverse((X add Z) add V_3) -> additive_identity
% Current number of equations to process: 241
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [118] inverse(((X add Y) add Z) add V_3) multiply X -> additive_identity
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [119] (((X add Y) add Z) multiply (X add V_3)) multiply X -> X
% Current number of equations to process: 239
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [120]
% ((inverse(inverse(X) add Y) multiply Z) multiply Y) multiply X ->
% additive_identity
% Current number of equations to process: 244
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced : [121] ((Y add Z) multiply X) multiply Y -> X multiply Y
% Rule [34] ((X add Y) multiply (Y add Z)) multiply X -> (Y add Z) multiply X
% collapsed.
% Rule [46] ((X add Y) multiply (X add Z)) multiply X -> X collapsed.
% Rule
% [109] (((X add Y) multiply (X add Z)) multiply (X add V_3)) multiply X -> X
% collapsed.
% Rule [119] (((X add Y) add Z) multiply (X add V_3)) multiply X -> X
% collapsed.
% Current number of equations to process: 244
% Current number of ordered equations: 0
% Current number of rules: 86
% New rule produced :
% [122] (X multiply Y) multiply (X multiply Z) -> (X multiply Y) multiply Z
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [123] (inverse(inverse(Y) multiply Z) multiply X) multiply Y -> X multiply Y
% Current number of equations to process: 247
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [124] (((X add Y) add Z) add V_3) multiply (X add V_3) -> X add V_3
% Current number of equations to process: 247
% Current number of ordered equations: 1
% Current number of rules: 89
% New rule produced :
% [125] (((X add Y) add Z) add V_3) add X -> ((X add Y) add Z) add V_3
% Current number of equations to process: 247
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [126] (inverse((Y add Z) add V_3) add X) multiply (X add Y) -> X
% Current number of equations to process: 246
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [127]
% (X multiply Y) multiply inverse((X add Z) multiply (X add V_3)) ->
% additive_identity
% Current number of equations to process: 241
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [128]
% (X add Y) multiply inverse(((Y add Z) add X) add V_3) -> additive_identity
% Current number of equations to process: 240
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [129]
% (inverse(X add Y) multiply Z) multiply inverse(inverse(X) add Y) ->
% additive_identity
% Current number of equations to process: 239
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [130]
% (inverse(inverse(X) add Y) multiply Z) multiply inverse(X add Y) ->
% additive_identity
% Current number of equations to process: 238
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [131] (X add Y) multiply inverse(Y add Z) -> inverse(Y add Z) multiply X
% Rule [100] (X add Y) multiply inverse((Y add Z) add X) -> additive_identity
% collapsed.
% Current number of equations to process: 241
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [132]
% ((inverse(X add Y) multiply Z) multiply Y) multiply inverse(X) ->
% additive_identity
% Current number of equations to process: 243
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [133]
% (inverse(X multiply Z) multiply Y) multiply inverse(X) ->
% inverse(X) multiply Y
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [134]
% (inverse(X) multiply Z) multiply inverse(X add Y) ->
% inverse(X add Y) multiply Z
% Current number of equations to process: 248
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [135] inverse(inverse(X) add Y) multiply X -> inverse(inverse(X) add Y)
% Current number of equations to process: 251
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [136]
% ((inverse(X) add Y) add Z) multiply inverse(X add Y) -> inverse(X add Y)
% Current number of equations to process: 249
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced : [137] inverse(inverse(Y) add X) -> inverse(X) multiply Y
% Rule
% [39] (X add Y) add inverse(inverse(Y) add X) -> inverse(inverse(Y)) add X
% collapsed.
% Rule [83] inverse(inverse(X) add Y) add X -> X collapsed.
% Rule
% [96] inverse(inverse(X) add Y) multiply inverse(X add Y) -> additive_identity
% collapsed.
% Rule
% [120]
% ((inverse(inverse(X) add Y) multiply Z) multiply Y) multiply X ->
% additive_identity collapsed.
% Rule
% [129]
% (inverse(X add Y) multiply Z) multiply inverse(inverse(X) add Y) ->
% additive_identity collapsed.
% Rule
% [130]
% (inverse(inverse(X) add Y) multiply Z) multiply inverse(X add Y) ->
% additive_identity collapsed.
% Rule [135] inverse(inverse(X) add Y) multiply X -> inverse(inverse(X) add Y)
% collapsed.
% Current number of equations to process: 258
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [138]
% (((inverse(Y) multiply X) multiply Z) multiply Y) multiply X ->
% additive_identity
% Current number of equations to process: 257
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [139]
% (inverse(X add Y) multiply Z) multiply (inverse(Y) multiply X) ->
% additive_identity
% Current number of equations to process: 256
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [140]
% ((inverse(Y) multiply X) multiply Z) multiply inverse(X add Y) ->
% additive_identity
% Current number of equations to process: 255
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [141]
% ((inverse(X) multiply Y) multiply inverse(Z)) multiply X -> additive_identity
% Current number of equations to process: 261
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced : [142] inverse(X add Y) -> inverse(X) multiply inverse(Y)
% Rule [38] (inverse(X) add Y) add inverse(X add Y) -> inverse(X) add Y
% collapsed.
% Rule [49] inverse(X add Y) multiply X -> additive_identity collapsed.
% Rule [60] (X multiply Y) multiply inverse(X add Z) -> additive_identity
% collapsed.
% Rule [75] (inverse(Y add Z) add X) multiply (X add Z) -> X collapsed.
% Rule [78] inverse(X add Y) add inverse(X) -> inverse(X) collapsed.
% Rule [79] inverse(X add Y) multiply inverse(X) -> inverse(X add Y) collapsed.
% Rule [81] (inverse(X add Y) add Z) add inverse(X) -> inverse(X) add Z
% collapsed.
% Rule [82] inverse(X add Y) add Y -> inverse(X) add Y collapsed.
% Rule [97] ((X add Y) add Z) add inverse(X add Z) -> multiplicative_identity
% collapsed.
% Rule
% [106] ((inverse(X add Z) add Y) add X) multiply Z -> (X add Y) multiply Z
% collapsed.
% Rule
% [112]
% ((X add Y) multiply Z) multiply inverse((inverse(Z) add Y) add X) ->
% additive_identity collapsed.
% Rule [113] inverse((X add Y) add Z) multiply X -> additive_identity
% collapsed.
% Rule
% [117] (X multiply Y) multiply inverse((X add Z) add V_3) -> additive_identity
% collapsed.
% Rule [118] inverse(((X add Y) add Z) add V_3) multiply X -> additive_identity
% collapsed.
% Rule [126] (inverse((Y add Z) add V_3) add X) multiply (X add Y) -> X
% collapsed.
% Rule
% [128]
% (X add Y) multiply inverse(((Y add Z) add X) add V_3) -> additive_identity
% collapsed.
% Rule [131] (X add Y) multiply inverse(Y add Z) -> inverse(Y add Z) multiply X
% collapsed.
% Rule
% [132]
% ((inverse(X add Y) multiply Z) multiply Y) multiply inverse(X) ->
% additive_identity collapsed.
% Rule
% [134]
% (inverse(X) multiply Z) multiply inverse(X add Y) ->
% inverse(X add Y) multiply Z collapsed.
% Rule
% [136]
% ((inverse(X) add Y) add Z) multiply inverse(X add Y) -> inverse(X add Y)
% collapsed.
% Rule [137] inverse(inverse(Y) add X) -> inverse(X) multiply Y collapsed.
% Rule
% [139]
% (inverse(X add Y) multiply Z) multiply (inverse(Y) multiply X) ->
% additive_identity collapsed.
% Rule
% [140]
% ((inverse(Y) multiply X) multiply Z) multiply inverse(X add Y) ->
% additive_identity collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 272
% Current number of ordered equations: 0
% Current number of rules: 76
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 11 rules have been used:
% [3]
% inverse(X) multiply X -> additive_identity; trace = in the starting set
% [4] inverse(X) add X -> multiplicative_identity; trace = in the starting set
% [5] (Y multiply Z) add X -> (X add Y) multiply (X add Z); trace = in the starting set
% [6] ((X add X) multiply (X add Z)) multiply ((X add Y) multiply (Y add Z)) ->
% (Y add Z) multiply X; trace = in the starting set
% [10] (inverse(Y) add X) multiply (X add Y) -> X; trace = Cp of 5 and 3
% [21] (X add Y) multiply inverse(X) -> inverse(X) multiply Y; trace = Cp of 6 and 4
% [31] ((X add Y) multiply (X add Z)) multiply (inverse(Y multiply Z) add X) ->
% X; trace = Cp of 10 and 5
% [34] ((X add Y) multiply (Y add Z)) multiply X -> (Y add Z) multiply X; trace = in the starting set
% [43] (inverse(X multiply Y) add inverse(X)) multiply (inverse(X) add Y) ->
% inverse(X); trace = Cp of 31 and 4
% [69] (inverse(X) add Y) multiply inverse(X multiply Y) -> inverse(X); trace = Cp of 43 and 34
% [142] inverse(X add Y) -> inverse(X) multiply inverse(Y); trace = Cp of 69 and 21
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.780000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------