TSTP Solution File: BOO016-2 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : BOO016-2 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n111.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 00:19:11 EDT 2014
% Result : Unsatisfiable 1.22s
% Output : Refutation 1.22s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : BOO016-2 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n111.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 17:30:13 CDT 2014
% % CPUTime : 1.22
% Processing problem /tmp/CiME_15592_n111.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " multiply,add : infix commutative; z,y,x,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;
% x multiply y = z;
% ";
%
% let s1 = status F "
% z lr_lex;
% y lr_lex;
% x 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 > x > y > z";
%
% let s2 = status F "
% z mul;
% y mul;
% x mul;
% additive_identity mul;
% multiplicative_identity mul;
% inverse mul;
% multiply mul;
% add mul;
% ";
%
% let p2 = precedence F "
% add > multiply > inverse > multiplicative_identity = additive_identity = x = y = z";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " x add z = x;"
% ;
% (*
% 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,
% y multiply x = z } (13 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 = { z add x = x } (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: 8
% Current number of rules: 1
% New rule produced : [2] y multiply x -> z
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 2
% New rule produced : [3] additive_identity add X -> X
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 3
% New rule produced : [4] inverse(X) multiply X -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 4
% New rule produced : [5] inverse(X) add X -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 5
% New rule produced : [6] (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: 6
% New rule produced :
% [7] (Y add Z) multiply X -> (X multiply Y) add (X multiply Z)
% Rule [6] (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: 6
% New rule produced :
% [8]
% ((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: 7
% New rule produced : [9] inverse(multiplicative_identity) -> additive_identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [10] inverse(additive_identity) -> multiplicative_identity
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [11] (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: 10
% New rule produced :
% [12] (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: 11
% New rule produced :
% [13]
% (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: 12
% New rule produced : [14] (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: 13
% New rule produced :
% [15] (inverse(X) multiply Y) add X -> (X multiply X) add Y
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [16]
% (X multiply Y) add inverse(X) <->
% ((additive_identity multiply additive_identity) add inverse(X)) add Y
% Current number of equations to process: 17
% Current number of ordered equations: 1
% Current number of rules: 15
% New rule produced :
% [17]
% ((additive_identity multiply additive_identity) add inverse(X)) add Y <->
% (X multiply Y) add inverse(X)
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [18]
% ((X multiply Y) add Y) add (multiplicative_identity add X) ->
% (X multiply Y) add multiplicative_identity
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [19] ((X multiply X) add X) add ((X multiply Y) add Y) -> X add Y
% Current number of equations to process: 11
% Current number of ordered equations: 2
% Current number of rules: 18
% New rule produced :
% [20] ((X multiply X) add (X multiply Y)) add (X add Y) -> X add Y
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [21] (X multiply Y) add ((inverse(X) multiply Y) add (Y multiply Y)) -> Y
% Current number of equations to process: 9
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [22] (inverse(X) multiply Y) add ((X multiply Y) add (Y multiply Y)) -> Y
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [23] (additive_identity multiply X) add X -> X
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 22
% Rule [16]
% (X multiply Y) add inverse(X) <->
% ((additive_identity multiply additive_identity) add inverse(X)) add Y is composed into
% [16]
% (X multiply Y) add inverse(X) <-> (additive_identity add inverse(X)) add Y
% Rule [15] (inverse(X) multiply Y) add X -> (X multiply X) add Y is composed into
% [15] (inverse(X) multiply Y) add X -> X add Y
% New rule produced : [24] X multiply X -> X
% Rule
% [8]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add (Z multiply Z))
% -> (X multiply Y) add Z collapsed.
% Rule [14] (X multiply X) add Y <-> (Y multiply Y) add X collapsed.
% Rule
% [17]
% ((additive_identity multiply additive_identity) add inverse(X)) add Y <->
% (X multiply Y) add inverse(X) collapsed.
% Rule [19] ((X multiply X) add X) add ((X multiply Y) add Y) -> X add Y
% collapsed.
% Rule [20] ((X multiply X) add (X multiply Y)) add (X add Y) -> X add Y
% collapsed.
% Rule
% [21] (X multiply Y) add ((inverse(X) multiply Y) add (Y multiply Y)) -> Y
% collapsed.
% Rule
% [22] (inverse(X) multiply Y) add ((X multiply Y) add (Y multiply Y)) -> Y
% collapsed.
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [25]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add Z) ->
% (X multiply Y) add Z
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [26] inverse(inverse(X)) multiply X -> X
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [27] (y multiply inverse(x)) add z -> y
% Current number of equations to process: 23
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced : [28] (x multiply inverse(y)) add z -> x
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [29] inverse(inverse(X)) -> X
% Rule [26] inverse(inverse(X)) multiply X -> X collapsed.
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [30] (x multiply additive_identity) add z -> z
% Current number of equations to process: 24
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced : [31] (y multiply additive_identity) add z -> z
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [32] additive_identity multiply X -> additive_identity
% Rule [12] (additive_identity multiply Y) add (X multiply Y) -> X multiply Y
% collapsed.
% Rule [23] (additive_identity multiply X) add X -> X collapsed.
% Rule [30] (x multiply additive_identity) add z -> z collapsed.
% Rule [31] (y multiply additive_identity) add z -> z collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [33] (X multiply Y) add inverse(X) -> inverse(X) add Y
% Rule
% [16]
% (X multiply Y) add inverse(X) <-> (additive_identity add inverse(X)) add Y
% collapsed.
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [34] ((X multiply Y) add Y) add (X add X) -> X add Y
% Current number of equations to process: 22
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced : [35] ((X multiply Y) add X) add (X add Y) -> X add Y
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [36] (X multiply Y) add ((inverse(X) multiply Y) add Y) -> Y
% Current number of equations to process: 20
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [37] (inverse(X) multiply Y) add ((X multiply Y) add Y) -> Y
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [38]
% (inverse(multiplicative_identity add X) multiply X) add inverse(multiplicative_identity add X)
% -> additive_identity
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [39] multiplicative_identity add X -> multiplicative_identity
% Rule
% [18]
% ((X multiply Y) add Y) add (multiplicative_identity add X) ->
% (X multiply Y) add multiplicative_identity collapsed.
% Rule
% [38]
% (inverse(multiplicative_identity add X) multiply X) add inverse(multiplicative_identity add X)
% -> additive_identity collapsed.
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [40] X add X -> X
% Rule [34] ((X multiply Y) add Y) add (X add X) -> X add Y collapsed.
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [41] ((X multiply Y) add Y) add X -> X add Y
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [42] (inverse(X) multiply Y) add ((X multiply Y) add X) -> X add Y
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [43] ((X multiply Y) add X) add ((X multiply Y) add Y) -> X add Y
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [44] ((y multiply X) add z) add ((x multiply X) add X) -> z add X
% Current number of equations to process: 37
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [45] ((y multiply X) add X) add ((x multiply X) add z) -> z add X
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [46]
% (X multiply Y) add ((inverse(X) multiply Y) add inverse(X)) ->
% inverse(X) add Y
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [47]
% ((inverse(Z) multiply Y) multiply X) add ((Y multiply Z) multiply X) ->
% X multiply Y
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [48]
% ((inverse(X) multiply Y) add (inverse(X) multiply Z)) add X ->
% (Y add Z) add X
% Current number of equations to process: 33
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [49]
% ((inverse(X) multiply Z) multiply Y) add (X multiply Y) ->
% (X multiply Y) add (Y multiply Z)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [50]
% ((y multiply X) add z) add ((x multiply X) add x) -> (y multiply X) add x
% Current number of equations to process: 29
% Current number of ordered equations: 3
% Current number of rules: 33
% New rule produced :
% [51]
% ((y multiply X) add (x multiply X)) add (z add x) -> (y multiply X) add x
% Current number of equations to process: 29
% Current number of ordered equations: 2
% Current number of rules: 34
% New rule produced :
% [52]
% ((y multiply X) add (x multiply X)) add (z add y) -> (x multiply X) add y
% Current number of equations to process: 29
% Current number of ordered equations: 1
% Current number of rules: 35
% New rule produced :
% [53]
% ((y multiply X) add y) add ((x multiply X) add z) -> (x multiply X) add y
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [54] (inverse(X add Y) multiply X) add Y -> (X multiply Y) add Y
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [55]
% (inverse(X add Y) multiply Z) add ((X multiply Z) add (Y multiply Z)) -> Z
% Current number of equations to process: 28
% Current number of ordered equations: 0
% Current number of rules: 38
% Rule [54] (inverse(X add Y) multiply X) add Y -> (X multiply Y) add Y is composed into
% [54] (inverse(X add Y) multiply X) add Y -> Y
% New rule produced : [56] (X multiply Y) add X -> X
% Rule
% [25]
% ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add Z) ->
% (X multiply Y) add Z collapsed.
% Rule [35] ((X multiply Y) add X) add (X add Y) -> X add Y collapsed.
% Rule [36] (X multiply Y) add ((inverse(X) multiply Y) add Y) -> Y collapsed.
% Rule [37] (inverse(X) multiply Y) add ((X multiply Y) add Y) -> Y collapsed.
% Rule [41] ((X multiply Y) add Y) add X -> X add Y collapsed.
% Rule [42] (inverse(X) multiply Y) add ((X multiply Y) add X) -> X add Y
% collapsed.
% Rule [43] ((X multiply Y) add X) add ((X multiply Y) add Y) -> X add Y
% collapsed.
% Rule [44] ((y multiply X) add z) add ((x multiply X) add X) -> z add X
% collapsed.
% Rule [45] ((y multiply X) add X) add ((x multiply X) add z) -> z add X
% collapsed.
% Rule
% [46]
% (X multiply Y) add ((inverse(X) multiply Y) add inverse(X)) ->
% inverse(X) add Y collapsed.
% Rule
% [50]
% ((y multiply X) add z) add ((x multiply X) add x) -> (y multiply X) add x
% collapsed.
% Rule
% [53]
% ((y multiply X) add y) add ((x multiply X) add z) -> (x multiply X) add y
% collapsed.
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [57] ((X multiply Y) add (X multiply Z)) add Z -> (X multiply Y) add Z
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [58] (X add Y) add X -> X add Y
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [59] ((y multiply X) add z) add X -> z add X
% Current number of equations to process: 32
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced : [60] ((x multiply X) add z) add X -> z add X
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [61] ((y multiply X) add z) add x -> (y multiply X) add x
% Current number of equations to process: 33
% Current number of ordered equations: 1
% Current number of rules: 32
% New rule produced : [62] ((x multiply X) add z) add y -> (x multiply X) add y
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [63] x add inverse(y) -> z add inverse(y)
% Current number of equations to process: 34
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced : [64] y add inverse(x) -> z add inverse(x)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [65] ((y multiply inverse(x)) multiply X) add (z multiply X) -> y multiply X
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [66] ((x multiply inverse(y)) multiply X) add (z multiply X) -> x multiply X
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [67]
% ((X multiply Y) add (X multiply Z)) add inverse(X) ->
% (Y add Z) add inverse(X)
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [68] (X multiply Y) multiply Y -> X multiply Y
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced :
% [69]
% (inverse(X) multiply Y) multiply inverse(X multiply Y) ->
% inverse(X multiply Y) multiply Y
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [70]
% (X multiply Y) multiply inverse(inverse(Y) multiply X) ->
% inverse(inverse(Y) multiply X) multiply X
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [71] (inverse(inverse(X) multiply Y) add Y) add X -> multiplicative_identity
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [72] (inverse(X) add Y) add X -> multiplicative_identity
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [73] ((inverse(y) multiply X) multiply x) add z -> (x multiply X) add z
% Current number of equations to process: 42
% Current number of ordered equations: 1
% Current number of rules: 44
% New rule produced :
% [74] ((inverse(x) multiply X) multiply y) add z -> (y multiply X) add z
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [75] z add x -> x
% Rule
% [51]
% ((y multiply X) add (x multiply X)) add (z add x) -> (y multiply X) add x
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 45
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [2]
% y multiply x -> z; trace = in the starting set
% [4] inverse(X) multiply X -> additive_identity; trace = in the starting set
% [7] (Y add Z) multiply X -> (X multiply Y) add (X multiply Z); trace = in the starting set
% [13] (inverse(X add Y) multiply X) add (inverse(X add Y) multiply Y) ->
% additive_identity; trace = Cp of 7 and 4
% [25] ((X multiply Y) add (X multiply Z)) add ((Y multiply Z) add Z) ->
% (X multiply Y) add Z; trace = in the starting set
% [51] ((y multiply X) add (x multiply X)) add (z add x) ->
% (y multiply X) add x; trace = Cp of 25 and 2
% [75] z add x -> x; trace = Cp of 51 and 13
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.110000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------