TSTP Solution File: BOO013-2 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : BOO013-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n120.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 1.15s
% Output : Refutation 1.15s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : BOO013-2 : TPTP v6.0.0. Bugfixed v1.2.1.
% % Command : tptp2X_and_run_cime %s
% % Computer : n120.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 17:00:03 CDT 2014
% % CPUTime : 1.15
% Processing problem /tmp/CiME_48117_n120.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " multiply,add : infix commutative; c,b,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;
% a add b = multiplicative_identity;
% a add c = multiplicative_identity;
% a multiply b = additive_identity;
% a multiply c = additive_identity;
% ";
%
% let s1 = status F "
% c lr_lex;
% b lr_lex;
% 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 > b > c";
%
% let s2 = status F "
% c mul;
% b mul;
% 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 = b = c";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " b = c;"
% ;
% (*
% 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,
% b add a = multiplicative_identity,
% c add a = multiplicative_identity,
% b multiply a = additive_identity,
% c multiply a = additive_identity }
% (16 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 = c } (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: 11
% Current number of rules: 1
% New rule produced : [2] b multiply a -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 2
% New rule produced : [3] c multiply a -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 3
% New rule produced : [4] additive_identity add X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 4
% New rule produced : [5] b add a -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 5
% New rule produced : [6] c add a -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 6
% New rule produced : [7] inverse(X) multiply X -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 7
% New rule produced : [8] inverse(X) add X -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 8
% New rule produced : [9] (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: 9
% New rule produced :
% [10] (Y add Z) multiply X -> (X multiply Y) add (X multiply Z)
% Rule [9] (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: 9
% New rule produced :
% [11]
% ((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: 10
% New rule produced :
% [12] inverse(multiplicative_identity) -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [13] inverse(additive_identity) -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [14] (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: 13
% New rule produced : [15] (b multiply X) add (a multiply X) -> X
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [16] (c multiply X) add (a multiply X) -> X
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [17] (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: 16
% New rule produced :
% [18]
% (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: 17
% New rule produced : [19] (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: 18
% New rule produced : [20] (b multiply X) add a <-> (a multiply a) add X
% Current number of equations to process: 11
% Current number of ordered equations: 2
% Current number of rules: 19
% New rule produced : [21] (a multiply X) add b -> (b multiply b) add X
% Current number of equations to process: 11
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced : [22] (a multiply a) add X <-> (b multiply X) add a
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [23] (a multiply X) add c -> (c multiply c) add X
% Current number of equations to process: 15
% Current number of ordered equations: 2
% Current number of rules: 22
% New rule produced : [24] (c multiply X) add a <-> (a multiply a) add X
% Current number of equations to process: 15
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced : [25] (a multiply a) add X <-> (c multiply X) add a
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [26] (inverse(X) multiply Y) add X -> (X multiply X) add Y
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [27] (X multiply Y) add inverse(X) <-> (inverse(X) multiply inverse(X)) add Y
% Current number of equations to process: 19
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [28] (inverse(X) multiply inverse(X)) add Y <-> (X multiply Y) add inverse(X)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [29]
% ((X multiply Y) add Y) add (multiplicative_identity add X) ->
% (X multiply Y) add multiplicative_identity
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [30] (b multiply X) add ((a multiply X) add (X multiply X)) -> X
% Current number of equations to process: 15
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced :
% [31] (a multiply X) add ((b multiply X) add (X multiply X)) -> X
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [32] (a multiply X) add ((c multiply X) add (X multiply X)) -> X
% Current number of equations to process: 13
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [33] (c multiply X) add ((a multiply X) add (X multiply X)) -> X
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [34] ((X multiply X) add X) add ((X multiply Y) add Y) -> X add Y
% Current number of equations to process: 9
% Current number of ordered equations: 2
% Current number of rules: 33
% New rule produced :
% [35] ((X multiply X) add (X multiply Y)) add (X add Y) -> X add Y
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [36] (X multiply Y) add ((inverse(X) multiply Y) add (Y multiply Y)) -> Y
% Current number of equations to process: 7
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [37] (inverse(X) multiply Y) add ((X multiply Y) add (Y multiply Y)) -> Y
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [38] (additive_identity multiply X) add X -> X
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [39] a multiply inverse(b) -> a
% Current number of equations to process: 14
% Current number of ordered equations: 1
% Current number of rules: 38
% New rule produced : [40] b multiply inverse(a) -> b
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [41] a multiply inverse(c) -> a
% Current number of equations to process: 14
% Current number of ordered equations: 1
% Current number of rules: 40
% New rule produced : [42] c multiply inverse(a) -> c
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 41
% Rule [27]
% (X multiply Y) add inverse(X) <-> (inverse(X) multiply inverse(X)) add Y is composed into
% [27] (X multiply Y) add inverse(X) -> inverse(X) add Y
% Rule [26] (inverse(X) multiply Y) add X -> (X multiply X) add Y is composed into
% [26] (inverse(X) multiply Y) add X -> X add Y
% Rule [24] (c multiply X) add a <-> (a multiply a) add X is composed into
% [24] (c multiply X) add a -> a add X
% Rule [23] (a multiply X) add c -> (c multiply c) add X is composed into
% [23] (a multiply X) add c -> c add X
% Rule [21] (a multiply X) add b -> (b multiply b) add X is composed into
% [21] (a multiply X) add b -> b add X
% Rule [20] (b multiply X) add a <-> (a multiply a) add X is composed into
% [20] (b multiply X) add a -> a add X
% New rule produced : [43] X multiply X -> X
% Rule
% [11]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add (Z multiply Z))
% -> (X multiply Y) add Z collapsed.
% Rule [19] (X multiply X) add Y <-> (Y multiply Y) add X collapsed.
% Rule [22] (a multiply a) add X <-> (b multiply X) add a collapsed.
% Rule [25] (a multiply a) add X <-> (c multiply X) add a collapsed.
% Rule
% [28] (inverse(X) multiply inverse(X)) add Y <-> (X multiply Y) add inverse(X)
% collapsed.
% Rule [30] (b multiply X) add ((a multiply X) add (X multiply X)) -> X
% collapsed.
% Rule [31] (a multiply X) add ((b multiply X) add (X multiply X)) -> X
% collapsed.
% Rule [32] (a multiply X) add ((c multiply X) add (X multiply X)) -> X
% collapsed.
% Rule [33] (c multiply X) add ((a multiply X) add (X multiply X)) -> X
% collapsed.
% Rule [34] ((X multiply X) add X) add ((X multiply Y) add Y) -> X add Y
% collapsed.
% Rule [35] ((X multiply X) add (X multiply Y)) add (X add Y) -> X add Y
% collapsed.
% Rule
% [36] (X multiply Y) add ((inverse(X) multiply Y) add (Y multiply Y)) -> Y
% collapsed.
% Rule
% [37] (inverse(X) multiply Y) add ((X multiply Y) add (Y multiply Y)) -> Y
% collapsed.
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [44]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add Z) ->
% (X multiply Y) add Z
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [45] inverse(inverse(X)) multiply X -> X
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [46] inverse(inverse(X)) -> X
% Rule [45] inverse(inverse(X)) multiply X -> X collapsed.
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [47] c multiply b -> c
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [48] inverse(a) -> b
% Rule [40] b multiply inverse(a) -> b collapsed.
% Rule [42] c multiply inverse(a) -> c collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced : [49] inverse(b) -> a
% Rule [39] a multiply inverse(b) -> a collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 31
% Rule [48] inverse(a) -> b is composed into [48] inverse(a) -> c
% New rule produced : [50] b -> c
% Rule [2] b multiply a -> additive_identity collapsed.
% Rule [5] b add a -> multiplicative_identity collapsed.
% Rule [15] (b multiply X) add (a multiply X) -> X collapsed.
% Rule [20] (b multiply X) add a -> a add X collapsed.
% Rule [21] (a multiply X) add b -> b add X collapsed.
% Rule [47] c multiply b -> c collapsed.
% Rule [49] inverse(b) -> a collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 25
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 5 rules have been used:
% [2]
% b multiply a -> additive_identity; trace = in the starting set
% [6] c add a -> multiplicative_identity; trace = in the starting set
% [10] (Y add Z) multiply X -> (X multiply Y) add (X multiply Z); trace = in the starting set
% [16] (c multiply X) add (a multiply X) -> X; trace = Cp of 10 and 6
% [50] b -> c; trace = Cp of 16 and 2
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.040000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------