TSTP Solution File: LDA001-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : LDA001-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n064.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 00:28:18 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 : LDA001-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n064.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 15:12:03 CDT 2014
% % CPUTime : 1.15
% Processing problem /tmp/CiME_24637_n064.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " u,n3,n1,n2 : constant; f : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% f(X,f(Y,Z)) = f(f(X,Y),f(X,Z));
% n2 = f(n1,n1);
% n3 = f(n2,n1);
% u = f(n2,n2);
% ";
%
% let s1 = status F "
% u lr_lex;
% n3 lr_lex;
% n1 lr_lex;
% n2 lr_lex;
% f mul;
% ";
%
% let p1 = precedence F "
% f > n2 > n1 > n3 > u";
%
% let s2 = status F "
% u mul;
% n3 mul;
% n1 mul;
% n2 mul;
% f mul;
% ";
%
% let p2 = precedence F "
% f > n2 = n1 = n3 = u";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " f(f(n3,n2),u) = f(f(u,u),u);"
% ;
% (*
% 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 = { f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
% n2 = f(n1,n1),
% n3 = f(n2,n1),
% u = f(n2,n2) } (4 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 = { f(f(n3,n2),u) = f(f(u,u),u) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] f(n1,n1) -> n2
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced : [2] f(n2,n1) -> n3
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 2
% New rule produced : [3] f(n2,n2) -> u
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 3
% New rule produced : [4] f(X,f(Y,Z)) <-> f(f(X,Y),f(X,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced : [5] f(f(X,Y),f(X,Z)) <-> f(X,f(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] f(f(X,n1),f(X,n1)) -> f(X,n2)
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] f(f(X,n2),f(X,n1)) -> f(X,n3)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] f(f(X,n2),f(X,n2)) -> f(X,u)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [9] f(n2,f(n1,X)) -> f(n1,f(n1,X))
% Current number of equations to process: 7
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [10] f(f(n1,X),n2) -> f(n1,f(X,n1))
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] f(n3,f(n2,X)) -> f(n1,f(n1,X))
% Current number of equations to process: 5
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced : [12] f(f(n2,X),n3) -> f(n2,f(X,n1))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] f(n2,f(X,n2)) -> f(f(n2,X),u)
% Current number of equations to process: 3
% Current number of ordered equations: 1
% Current number of rules: 13
% New rule produced : [14] f(n2,f(n2,X)) -> f(u,f(n2,X))
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] f(n1,n2) -> u
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] f(n3,n3) -> u
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] f(u,n2) -> f(n1,n3)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] f(n2,n3) -> f(u,n3)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] f(n2,u) -> f(u,u)
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] f(n1,u) -> f(n3,u)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 20
% Rule [20] f(n1,u) -> f(n3,u) is composed into [20] f(n1,u) -> f(u,u)
% New rule produced : [21] f(n3,u) -> f(u,u)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] f(n1,f(X,n2)) -> f(f(n1,X),u)
% Current number of equations to process: 80
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced : [23] f(n1,f(n2,X)) -> f(u,f(n1,X))
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] f(n3,f(X,n3)) -> f(f(n3,X),u)
% Current number of equations to process: 78
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced : [25] f(n3,f(n3,X)) -> f(u,f(n3,X))
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] f(n1,f(n1,n3)) -> f(f(u,u),u)
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [27] f(n2,f(n3,n1)) -> f(f(u,n3),n3)
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [28] f(n2,f(u,n3)) -> f(u,f(u,n3))
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [29] f(n1,f(u,u)) -> f(n3,f(u,u))
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [30] f(n2,f(u,n1)) -> f(f(u,u),n3)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [31] f(n2,f(u,u)) -> f(u,f(u,u))
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 31
% Rule [29] f(n1,f(u,u)) -> f(n3,f(u,u)) is composed into [29]
% f(n1,f(u,u)) ->
% f(u,f(u,u))
% New rule produced : [32] f(n3,f(u,u)) -> f(u,f(u,u))
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [33] f(n1,f(u,n1)) -> f(f(u,u),n2)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [34] f(f(n3,n2),u) -> f(f(u,u),u)
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 34
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 10 rules have been used:
% [1]
% f(n1,n1) -> n2; trace = in the starting set
% [2] f(n2,n1) -> n3; trace = in the starting set
% [4] f(X,f(Y,Z)) <-> f(f(X,Y),f(X,Z)); trace = in the starting set
% [5] f(f(X,Y),f(X,Z)) <-> f(X,f(Y,Z)); trace = in the starting set
% [6] f(f(X,n1),f(X,n1)) -> f(X,n2); trace = Cp of 4 and 1
% [7] f(f(X,n2),f(X,n1)) -> f(X,n3); trace = Cp of 4 and 2
% [16] f(n3,n3) -> u; trace = Cp of 6 and 2
% [18] f(n2,n3) -> f(u,n3); trace = Cp of 7 and 2
% [24] f(n3,f(X,n3)) -> f(f(n3,X),u); trace = Cp of 16 and 5
% [34] f(f(n3,n2),u) -> f(f(u,u),u); trace = Cp of 24 and 18
% % 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
%------------------------------------------------------------------------------