TSTP Solution File: BOO005-2 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : BOO005-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n091.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 00:19:07 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 : BOO005-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n091.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jun 5 15:42:53 CDT 2014
% % CPUTime : 1.13
% Processing problem /tmp/CiME_56982_n091.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " multiply,add : infix commutative; a,additive_identity,multiplicative_identity : constant; inverse : 1;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% (X multiply Y) add Z = (X add Z) multiply (Y add Z);
% X add (Y multiply Z) = (X add Y) multiply (X add Z);
% (X add Y) multiply Z = (X multiply Z) add (Y multiply Z);
% X multiply (Y add Z) = (X multiply Y) add (X multiply Z);
% X add inverse(X) = multiplicative_identity;
% inverse(X) add X = multiplicative_identity;
% X multiply inverse(X) = additive_identity;
% inverse(X) multiply X = additive_identity;
% X multiply multiplicative_identity = X;
% multiplicative_identity multiply X = X;
% X add additive_identity = X;
% additive_identity add X = X;
% ";
%
% let s1 = status F "
% a lr_lex;
% additive_identity lr_lex;
% multiplicative_identity lr_lex;
% inverse lr_lex;
% multiply mul;
% add mul;
% ";
%
% let p1 = precedence F "
% add > multiply > inverse > multiplicative_identity > additive_identity > a";
%
% let s2 = status F "
% a mul;
% additive_identity mul;
% multiplicative_identity mul;
% inverse mul;
% multiply mul;
% add mul;
% ";
%
% let p2 = precedence F "
% add > multiply > inverse > multiplicative_identity = additive_identity = a";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " a add multiplicative_identity = multiplicative_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 = { (X multiply Y) add Z =
% (X add Z) multiply (Y add Z),
% (Y multiply Z) add X =
% (X add Y) multiply (X add Z),
% (X add Y) multiply Z =
% (X multiply Z) add (Y multiply Z),
% (Y add Z) multiply X =
% (X multiply Y) add (X multiply Z),
% inverse(X) add X = multiplicative_identity,
% inverse(X) add X = multiplicative_identity,
% inverse(X) multiply X = additive_identity,
% inverse(X) multiply X = additive_identity,
% multiplicative_identity multiply X = X,
% multiplicative_identity multiply X = X,
% additive_identity add X = X,
% additive_identity add X = X } (12 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 = { a add multiplicative_identity =
% multiplicative_identity } (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: 7
% 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: 6
% 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: 5
% 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: 4
% Current number of rules: 4
% New rule produced : [5] (X add Z) multiply (Y add Z) -> (X multiply Y) add Z
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 5
% New rule produced :
% [6] (Y add Z) multiply X -> (X multiply Y) add (X multiply Z)
% Rule [5] (X add Z) multiply (Y add Z) -> (X multiply Y) add Z collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [7]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add (Z multiply Z))
% -> (X multiply Y) add Z
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [8] 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 : [9] 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 : [10] (inverse(Y) multiply X) add (X multiply Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [11] (additive_identity multiply Y) add (X multiply Y) -> X multiply Y
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [12]
% (inverse(X add Y) multiply X) add (inverse(X add Y) multiply Y) ->
% additive_identity
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [13] (X multiply X) add Y <-> (Y multiply Y) add X
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [14] (inverse(X) multiply Y) add X -> (X multiply X) add Y
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [15] (X multiply Y) add inverse(X) <-> (inverse(X) multiply inverse(X)) add Y
% Current number of equations to process: 11
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [16] (inverse(X) multiply inverse(X)) add Y <-> (X multiply Y) add inverse(X)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [17]
% ((X multiply Y) add Y) add (multiplicative_identity add X) ->
% (X multiply Y) add multiplicative_identity
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [18] ((X multiply X) add X) add ((X multiply Y) add Y) -> X add Y
% Current number of equations to process: 5
% Current number of ordered equations: 2
% Current number of rules: 17
% New rule produced :
% [19] ((X multiply X) add (X multiply Y)) add (X add Y) -> X add Y
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [20] (X multiply Y) add ((inverse(X) multiply Y) add (Y multiply Y)) -> Y
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [21] (inverse(X) multiply Y) add ((X multiply Y) add (Y multiply Y)) -> Y
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [22] (additive_identity multiply X) add X -> X
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 21
% Rule [15]
% (X multiply Y) add inverse(X) <-> (inverse(X) multiply inverse(X)) add Y is composed into
% [15] (X multiply Y) add inverse(X) -> inverse(X) add Y
% Rule [14] (inverse(X) multiply Y) add X -> (X multiply X) add Y is composed into
% [14] (inverse(X) multiply Y) add X -> X add Y
% New rule produced : [23] X multiply X -> X
% Rule
% [7]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add (Z multiply Z))
% -> (X multiply Y) add Z collapsed.
% Rule [13] (X multiply X) add Y <-> (Y multiply Y) add X collapsed.
% Rule
% [16] (inverse(X) multiply inverse(X)) add Y <-> (X multiply Y) add inverse(X)
% collapsed.
% Rule [18] ((X multiply X) add X) add ((X multiply Y) add Y) -> X add Y
% collapsed.
% Rule [19] ((X multiply X) add (X multiply Y)) add (X add Y) -> X add Y
% collapsed.
% Rule
% [20] (X multiply Y) add ((inverse(X) multiply Y) add (Y multiply Y)) -> Y
% collapsed.
% Rule
% [21] (inverse(X) multiply Y) add ((X multiply Y) add (Y multiply Y)) -> Y
% collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [24]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add Z) ->
% (X multiply Y) add Z
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [25] inverse(inverse(X)) multiply X -> X
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [26] inverse(inverse(X)) -> X
% Rule [25] inverse(inverse(X)) multiply X -> X collapsed.
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [27] additive_identity multiply X -> additive_identity
% Rule [11] (additive_identity multiply Y) add (X multiply Y) -> X multiply Y
% collapsed.
% Rule [22] (additive_identity multiply X) add X -> X collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [28] ((X multiply Y) add Y) add (X add X) -> X add Y
% Current number of equations to process: 16
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced : [29] ((X multiply Y) add X) add (X add Y) -> X add Y
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [30] (X multiply Y) add ((inverse(X) multiply Y) add Y) -> Y
% Current number of equations to process: 14
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [31] (inverse(X) multiply Y) add ((X multiply Y) add Y) -> Y
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [32]
% (inverse(multiplicative_identity add X) multiply X) add inverse(multiplicative_identity add X)
% -> additive_identity
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [33] multiplicative_identity add X -> multiplicative_identity
% Rule
% [17]
% ((X multiply Y) add Y) add (multiplicative_identity add X) ->
% (X multiply Y) add multiplicative_identity collapsed.
% Rule
% [32]
% (inverse(multiplicative_identity add X) multiply X) add inverse(multiplicative_identity add X)
% -> additive_identity collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 20
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 5 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
% [7] ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add (Z multiply Z))
% -> (X multiply Y) add Z; trace = in the starting set
% [14] (inverse(X) multiply Y) add X -> X add Y; trace = Cp of 7 and 3
% [33] multiplicative_identity add X -> multiplicative_identity; trace = Cp of 14 and 1
% % 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
%------------------------------------------------------------------------------