TSTP Solution File: BOO010-4 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : BOO010-4 : TPTP v6.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n097.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 00:19:09 EDT 2014
% Result : Unsatisfiable 1.13s
% Output : Refutation 1.13s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : BOO010-4 : TPTP v6.0.0. Released v1.1.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n097.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 16:33:03 CDT 2014
% % CPUTime : 1.13
% Processing problem /tmp/CiME_1862_n097.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 " a add (a multiply b) = 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 = { (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 = { (b multiply a) add a = 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)
% The conjecture has been reduced.
% Conjecture is now:
% (b add a) multiply (a add a) = a
%
% 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.
% The conjecture has been reduced.
% Conjecture is now:
% (b add a) multiply a = a
%
% 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.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 21
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 10 rules have been used:
% [1]
% multiplicative_identity multiply X -> X; trace = in the starting set
% [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
% [9] (multiplicative_identity add Y) multiply (X add Y) -> X add Y; trace = Cp of 5 and 1
% [10] (inverse(Y) add X) multiply (X add Y) -> X; trace = Cp of 5 and 3
% [14] multiplicative_identity add X -> multiplicative_identity; trace = Cp of 9 and 4
% [15] X add X -> X; trace = Cp of 10 and 4
% [16] ((X add Y) multiply (Y add Z)) multiply ((X add Z) multiply X) ->
% (Y add Z) multiply X; trace = in the starting set
% [33] (X add Y) multiply X -> X; trace = Cp of 16 and 14
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.030000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------