TSTP Solution File: BOO028-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : BOO028-1 : TPTP v6.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n119.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 00:19:14 EDT 2014
% Result : Unsatisfiable 14.59s
% Output : Refutation 14.59s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : BOO028-1 : TPTP v6.0.0. Released v2.2.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n119.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 18:08:08 CDT 2014
% % CPUTime : 14.59
% Processing problem /tmp/CiME_11190_n119.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " add,multiply : AC; c,b,a : constant; inverse : 1;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% X add (Y multiply (X multiply Z)) = X;
% ((X multiply Y) add (Y multiply Z)) add Y = Y;
% (X add Y) multiply (X add inverse(Y)) = X;
% X multiply (Y add (X add Z)) = X;
% ((X add Y) multiply (Y add Z)) multiply Y = Y;
% (X multiply Y) add (X multiply inverse(Y)) = X;
% ";
%
% let s1 = status F "
% c lr_lex;
% b lr_lex;
% a lr_lex;
% inverse lr_lex;
% add mul;
% multiply mul;
% ";
%
% let p1 = precedence F "
% inverse > multiply > add > a > b > c";
%
% let s2 = status F "
% c mul;
% b mul;
% a mul;
% inverse mul;
% add mul;
% multiply mul;
% ";
%
% let p2 = precedence F "
% inverse > multiply > add > a = b = c";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " a multiply (b add c) = (b multiply a) add (c multiply a);"
% ;
% (*
% 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 = { (X multiply Y multiply Z) add X = X,
% (X multiply Y) add (Y multiply Z) add Y = Y,
% (inverse(Y) add X) multiply (X add Y) = X,
% (X add Y add Z) multiply X = X,
% (X add Y) multiply (Y add Z) multiply Y = Y,
% (inverse(Y) multiply X) add (X multiply Y) = X }
% (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 = { (c add b) multiply a =
% (c multiply a) add (b multiply a) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] (X multiply Y multiply Z) add X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 1
% New rule produced : [2] (X add Y add Z) multiply 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(Y) multiply X) add (X multiply Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 3
% New rule produced : [4] (inverse(Y) add X) multiply (X add Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 4
% New rule produced : [5] (X add Y) multiply (Y add Z) multiply Y -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced : [6] (X multiply Y) add (Y multiply Z) add Y -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] (X multiply Y) add X -> X
% Rule [1] (X multiply Y multiply Z) add X -> X collapsed.
% Rule [6] (X multiply Y) add (Y multiply Z) add Y -> Y collapsed.
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [8] (X add Y) multiply X -> X
% Rule [2] (X add Y add Z) multiply X -> X collapsed.
% Rule [5] (X add Y) multiply (Y add Z) multiply Y -> Y collapsed.
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [9] X add X -> X
% Current number of equations to process: 266
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [10] X multiply X -> X
% Current number of equations to process: 328
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [11] (inverse(Y) multiply X) add Y -> X add Y
% Current number of equations to process: 410
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [12] (inverse(Y) add X) multiply Y -> X multiply Y
% Current number of equations to process: 409
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [13] (X multiply Y) add inverse(X) -> inverse(X) add Y
% Current number of equations to process: 626
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [14] (X add Y) multiply inverse(X) -> inverse(X) multiply Y
% Current number of equations to process: 625
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [15] inverse(X) add X <-> inverse(Y) add X add Y
% Current number of equations to process: 624
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced : [16] inverse(Y) add X add Y <-> inverse(X) add X
% Current number of equations to process: 624
% Current number of ordered equations: 0
% Current number of rules: 12
% Rule [15] inverse(X) add X <-> inverse(Y) add X add Y is composed into
% [15] inverse(X) add X <-> inverse(Y) add Y
% New rule produced : [17] inverse(X) add X add Y -> inverse(X) add X
% Rule [16] inverse(Y) add X add Y <-> inverse(X) add X collapsed.
% Current number of equations to process: 623
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [18] inverse(Y) multiply X multiply Y <-> inverse(X) multiply X
% Current number of equations to process: 622
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced :
% [19] inverse(X) multiply X <-> inverse(Y) multiply X multiply Y
% Current number of equations to process: 622
% Current number of ordered equations: 0
% Current number of rules: 14
% Rule [19] inverse(X) multiply X <-> inverse(Y) multiply X multiply Y is composed into
% [19] inverse(X) multiply X <-> inverse(Y) multiply Y
% New rule produced :
% [20] inverse(X) multiply X multiply Y -> inverse(X) multiply X
% Rule [18] inverse(Y) multiply X multiply Y <-> inverse(X) multiply X
% collapsed.
% Current number of equations to process: 621
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [21] inverse(X multiply Y) add Y -> inverse(X) add X
% Current number of equations to process: 749
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [22] inverse(X add Y) multiply Y -> inverse(X) multiply X
% Current number of equations to process: 909
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [23] (inverse(X) add X) multiply Y -> Y
% Current number of equations to process: 979
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [24] inverse(inverse(X)) multiply X -> X
% Current number of equations to process: 991
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [25] (inverse(inverse(X)) add Y) multiply X -> X
% Current number of equations to process: 990
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [26] inverse(inverse(X)) -> X
% Rule [24] inverse(inverse(X)) multiply X -> X collapsed.
% Rule [25] (inverse(inverse(X)) add Y) multiply X -> X collapsed.
% Current number of equations to process: 1020
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [27] inverse(inverse(X) add Y) add X -> X
% Current number of equations to process: 1077
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [28] inverse(X add Y) add inverse(X) -> inverse(X)
% Current number of equations to process: 1076
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [29] (inverse(X) multiply X) add Y -> Y
% Current number of equations to process: 1226
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [30] inverse(inverse(X) multiply Y) multiply X -> X
% Current number of equations to process: 1364
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced : [31] inverse(inverse(X) multiply X) multiply Y -> Y
% Current number of equations to process: 1364
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [32] inverse(X multiply Y) multiply inverse(X) -> inverse(X)
% Current number of equations to process: 1446
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [33] inverse(inverse(X) multiply X) -> inverse(X) add X
% Rule [31] inverse(inverse(X) multiply X) multiply Y -> Y collapsed.
% Current number of equations to process: 1587
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [34] inverse(inverse(X) add X) -> inverse(X) multiply X
% Current number of equations to process: 1613
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [35] inverse(X add Y) multiply inverse(Y) -> inverse(X add Y)
% Current number of equations to process: 2313
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [36] inverse(X multiply Y) add inverse(Y) -> inverse(X multiply Y)
% Current number of equations to process: 2431
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [37] (inverse(Y multiply Z) multiply X) add Y -> X add Y
% Current number of equations to process: 2549
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [38] (inverse(Y add Z) add X) multiply Y -> X multiply Y
% Current number of equations to process: 2872
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [39] ((inverse(X) add Z) multiply Y) add X -> X add Y
% Current number of equations to process: 3231
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [40] ((inverse(X) multiply Z) add Y) multiply X -> X multiply Y
% Current number of equations to process: 3544
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [41] ((X multiply Z) add Y) multiply Z -> (X add Y) multiply Z
% Current number of equations to process: 3883
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [42] ((X add Z) multiply Y) add Z -> (X multiply Y) add Z
% Current number of equations to process: 4296
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [43] (inverse(inverse(X) add Y) add Y) multiply X -> X
% Current number of equations to process: 4721
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [44] inverse(inverse(X) add Y) add Y -> X add Y
% Rule [43] (inverse(inverse(X) add Y) add Y) multiply X -> X collapsed.
% Current number of equations to process: 4846
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [45] inverse(X add Y) add Y -> inverse(X) add Y
% Rule [44] inverse(inverse(X) add Y) add Y -> X add Y collapsed.
% Current number of equations to process: 4867
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [46] inverse(X multiply Y) -> inverse(X) add inverse(Y)
% Rule [21] inverse(X multiply Y) add Y -> inverse(X) add X collapsed.
% Rule [30] inverse(inverse(X) multiply Y) multiply X -> X collapsed.
% Rule [32] inverse(X multiply Y) multiply inverse(X) -> inverse(X) collapsed.
% Rule [33] inverse(inverse(X) multiply X) -> inverse(X) add X collapsed.
% Rule [36] inverse(X multiply Y) add inverse(Y) -> inverse(X multiply Y)
% collapsed.
% Rule [37] (inverse(Y multiply Z) multiply X) add Y -> X add Y collapsed.
% Current number of equations to process: 2087
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [47] inverse(X add Y) -> inverse(X) multiply inverse(Y)
% Rule [22] inverse(X add Y) multiply Y -> inverse(X) multiply X collapsed.
% Rule [27] inverse(inverse(X) add Y) add X -> X collapsed.
% Rule [28] inverse(X add Y) add inverse(X) -> inverse(X) collapsed.
% Rule [34] inverse(inverse(X) add X) -> inverse(X) multiply X collapsed.
% Rule [35] inverse(X add Y) multiply inverse(Y) -> inverse(X add Y) collapsed.
% Rule [38] (inverse(Y add Z) add X) multiply Y -> X multiply Y collapsed.
% Rule [45] inverse(X add Y) add Y -> inverse(X) add Y collapsed.
% Current number of equations to process: 2098
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [48] ((X add Z) multiply Y) add inverse(X) -> inverse(X) add Y
% Current number of equations to process: 2079
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [49] ((X multiply Z) add Y) multiply inverse(X) -> inverse(X) multiply Y
% Current number of equations to process: 2175
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [50] ((inverse(X) add inverse(Y)) multiply Z) add (Y multiply Z) -> Z
% Current number of equations to process: 2242
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [51] ((inverse(X) multiply inverse(Y)) add Z) multiply (Y add Z) -> Z
% Current number of equations to process: 2380
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [52] ((X add Y) multiply Z) add (inverse(Y) multiply Z) -> Z
% Current number of equations to process: 2503
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [53] (X add Z) multiply Y -> (X multiply Y) add (Y multiply Z)
% Rule [4] (inverse(Y) add X) multiply (X add Y) -> X collapsed.
% Rule [8] (X add Y) multiply X -> X collapsed.
% Rule [12] (inverse(Y) add X) multiply Y -> X multiply Y collapsed.
% Rule [14] (X add Y) multiply inverse(X) -> inverse(X) multiply Y collapsed.
% Rule [23] (inverse(X) add X) multiply Y -> Y collapsed.
% Rule [39] ((inverse(X) add Z) multiply Y) add X -> X add Y collapsed.
% Rule [40] ((inverse(X) multiply Z) add Y) multiply X -> X multiply Y
% collapsed.
% Rule [41] ((X multiply Z) add Y) multiply Z -> (X add Y) multiply Z
% collapsed.
% Rule [42] ((X add Z) multiply Y) add Z -> (X multiply Y) add Z collapsed.
% Rule [48] ((X add Z) multiply Y) add inverse(X) -> inverse(X) add Y
% collapsed.
% Rule [49] ((X multiply Z) add Y) multiply inverse(X) -> inverse(X) multiply Y
% collapsed.
% Rule [50] ((inverse(X) add inverse(Y)) multiply Z) add (Y multiply Z) -> Z
% collapsed.
% Rule [51] ((inverse(X) multiply inverse(Y)) add Z) multiply (Y add Z) -> Z
% collapsed.
% Rule [52] ((X add Y) multiply Z) add (inverse(Y) multiply Z) -> Z collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 2644
% Current number of ordered equations: 0
% Current number of rules: 15
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 11 rules have been used:
% [1]
% (X multiply Y multiply Z) add X -> X; trace = in the starting set
% [2] (X add Y add Z) multiply X -> X; trace = in the starting set
% [3] (inverse(Y) multiply X) add (X multiply Y) -> X; trace = in the starting set
% [4] (inverse(Y) add X) multiply (X add Y) -> X; trace = in the starting set
% [7] (X multiply Y) add X -> X; trace = Cp of 2 and 1
% [8] (X add Y) multiply X -> X; trace = Cp of 3 and 2
% [12] (inverse(Y) add X) multiply Y -> X multiply Y; trace = Cp of 8 and 4
% [13] (X multiply Y) add inverse(X) -> inverse(X) add Y; trace = Cp of 7 and 3
% [48] ((X add Z) multiply Y) add inverse(X) -> inverse(X) add Y; trace = Cp of 13 and 8
% [52] ((X add Y) multiply Z) add (inverse(Y) multiply Z) -> Z; trace = Cp of 48 and 12
% [53] (X add Z) multiply Y -> (X multiply Y) add (Y multiply Z); trace = Cp of 52 and 4
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 13.450000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------