TSTP Solution File: GRP708-1 by CiME---2.01
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP708-1 : TPTP v6.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n072.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 00:24:09 EDT 2014
% Result : Unsatisfiable 1.19s
% Output : Refutation 1.19s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP708-1 : TPTP v6.0.0. Released v4.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n072.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 : Sat Jun 7 01:16:33 CDT 2014
% % CPUTime : 1.19
% Processing problem /tmp/CiME_49708_n072.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b,a,op_c,unit : constant; rd : 2; mult : 2; ld : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% mult(A,ld(A,B)) = B;
% ld(A,mult(A,B)) = B;
% mult(rd(A,B),B) = A;
% rd(mult(A,B),B) = A;
% mult(A,unit) = A;
% mult(unit,A) = A;
% mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C);
% mult(op_c,A) = mult(A,op_c);
% mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B);
% ";
%
% let s1 = status F "
% b lr_lex;
% a lr_lex;
% op_c lr_lex;
% unit lr_lex;
% rd lr_lex;
% mult lr_lex;
% ld lr_lex;
% ";
%
% let p1 = precedence F "
% ld > mult > rd > unit > op_c > a > b";
%
% let s2 = status F "
% b mul;
% a mul;
% op_c mul;
% unit mul;
% rd mul;
% mult mul;
% ld mul;
% ";
%
% let p2 = precedence F "
% ld > mult > rd > unit = op_c = a = b";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " mult(a,mult(b,op_c)) = mult(mult(a,b),op_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 = { mult(A,ld(A,B)) = B,
% ld(A,mult(A,B)) = B,
% mult(rd(A,B),B) = A,
% rd(mult(A,B),B) = A,
% mult(A,unit) = A,
% mult(unit,A) = A,
% mult(A,mult(B,mult(A,C))) =
% mult(mult(A,mult(B,A)),C),
% mult(op_c,A) = mult(A,op_c),
% mult(mult(op_c,op_c),mult(A,B)) =
% mult(mult(mult(op_c,op_c),A),B) }
% (9 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 = { mult(a,mult(b,op_c)) = mult(mult(a,b),op_c) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] mult(A,unit) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 1
% New rule produced : [2] mult(unit,A) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 2
% New rule produced : [3] mult(A,op_c) <-> mult(op_c,A)
% The conjecture has been reduced.
% Conjecture is now:
% mult(a,mult(b,op_c)) = mult(op_c,mult(a,b))
%
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 3
% New rule produced : [4] mult(op_c,A) <-> mult(A,op_c)
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 4
% New rule produced : [5] rd(mult(A,B),B) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 5
% New rule produced : [6] mult(A,ld(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 6
% New rule produced : [7] mult(rd(A,B),B) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 7
% New rule produced : [8] ld(A,mult(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced :
% [9] mult(mult(A,mult(B,A)),C) -> mult(A,mult(B,mult(A,C)))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [10] mult(mult(mult(op_c,op_c),A),B) -> mult(mult(op_c,op_c),mult(A,B))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] rd(A,unit) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [12] rd(A,A) -> unit
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [13] ld(unit,A) -> A
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [14] ld(A,A) -> unit
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [15] rd(mult(op_c,A),op_c) -> A
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced : [16] rd(mult(A,op_c),A) -> op_c
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [17] rd(A,ld(B,A)) -> B
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] mult(op_c,rd(A,op_c)) -> A
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] ld(A,mult(op_c,A)) -> op_c
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] ld(op_c,mult(A,op_c)) -> A
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [21] ld(rd(A,B),A) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [22] mult(mult(A,A),B) -> mult(A,mult(A,B))
% Rule [10] mult(mult(mult(op_c,op_c),A),B) -> mult(mult(op_c,op_c),mult(A,B))
% collapsed.
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [23] mult(mult(op_c,mult(op_c,A)),B) -> mult(op_c,mult(op_c,mult(A,B)))
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [24] ld(op_c,A) -> rd(A,op_c)
% Rule [20] ld(op_c,mult(A,op_c)) -> A collapsed.
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [25] rd(A,rd(A,op_c)) -> op_c
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [26] mult(A,mult(A,op_c)) <-> mult(op_c,mult(A,A))
% Current number of equations to process: 18
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced : [27] mult(op_c,mult(A,A)) <-> mult(A,mult(A,op_c))
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [28] rd(mult(A,mult(A,B)),B) -> mult(A,A)
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [29] mult(B,mult(B,ld(mult(B,B),A))) -> A
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [30] ld(mult(A,A),mult(A,mult(A,B))) -> B
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [31] mult(A,mult(op_c,A)) <-> mult(op_c,mult(A,A))
% Current number of equations to process: 27
% Current number of ordered equations: 1
% Current number of rules: 29
% New rule produced : [32] mult(op_c,mult(A,A)) <-> mult(A,mult(op_c,A))
% Current number of equations to process: 27
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced : [33] ld(A,mult(op_c,mult(A,A))) -> mult(A,op_c)
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced : [34] rd(mult(A,mult(op_c,A)),op_c) -> mult(A,A)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced : [35] rd(mult(op_c,mult(A,op_c)),A) -> mult(op_c,op_c)
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [36] rd(mult(A,B),ld(A,B)) -> mult(A,A)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [37] rd(mult(op_c,A),rd(A,op_c)) <-> mult(op_c,op_c)
% Current number of equations to process: 33
% Current number of ordered equations: 1
% Current number of rules: 35
% Rule [37] rd(mult(op_c,A),rd(A,op_c)) <-> mult(op_c,op_c) is composed into
% [37] rd(mult(op_c,A),rd(A,op_c)) <-> rd(mult(op_c,b),rd(b,op_c))
% Rule [35] rd(mult(op_c,mult(A,op_c)),A) -> mult(op_c,op_c) is composed into
% [35] rd(mult(op_c,mult(A,op_c)),A) -> rd(mult(op_c,b),rd(b,op_c))
% New rule produced : [38] mult(op_c,op_c) <-> rd(mult(op_c,A),rd(A,op_c))
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced : [39] rd(mult(op_c,mult(A,A)),mult(A,op_c)) -> A
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [40] rd(mult(A,mult(A,op_c)),mult(A,A)) -> op_c
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [41] mult(A,ld(mult(A,A),B)) -> ld(A,B)
% Rule [29] mult(B,mult(B,ld(mult(B,B),A))) -> A collapsed.
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [42] ld(mult(A,A),mult(A,B)) -> ld(A,B)
% Rule [30] ld(mult(A,A),mult(A,mult(A,B))) -> B collapsed.
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [43] rd(A,ld(A,unit)) -> mult(A,A)
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [44] rd(mult(op_c,A),ld(A,op_c)) -> mult(A,A)
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced : [45] rd(A,ld(B,ld(B,A))) -> mult(B,B)
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced : [46] rd(mult(op_c,mult(A,A)),mult(op_c,A)) -> A
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [47] rd(mult(A,mult(op_c,A)),mult(A,A)) -> op_c
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [48] rd(mult(b,op_c),rd(b,op_c)) -> rd(op_c,rd(unit,op_c))
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced : [49] rd(rd(mult(op_c,A),rd(A,op_c)),op_c) -> op_c
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [50] rd(mult(A,mult(op_c,A)),mult(A,op_c)) -> A
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [51] ld(mult(A,A),B) -> ld(A,ld(A,B))
% Rule [41] mult(A,ld(mult(A,A),B)) -> ld(A,B) collapsed.
% Rule [42] ld(mult(A,A),mult(A,B)) -> ld(A,B) collapsed.
% Current number of equations to process: 97
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced : [52] mult(rd(unit,A),rd(unit,A)) -> rd(rd(unit,A),A)
% Current number of equations to process: 102
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced : [53] rd(A,rd(rd(A,op_c),op_c)) -> rd(op_c,rd(unit,op_c))
% Current number of equations to process: 101
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced : [54] rd(mult(A,mult(A,op_c)),mult(op_c,A)) -> A
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced : [55] rd(rd(op_c,rd(unit,op_c)),op_c) -> op_c
% Current number of equations to process: 116
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced : [56] rd(rd(mult(A,op_c),rd(A,op_c)),op_c) -> op_c
% Current number of equations to process: 115
% Current number of ordered equations: 0
% Current number of rules: 50
% Rule [38] mult(op_c,op_c) <-> rd(mult(op_c,A),rd(A,op_c)) is composed into
% [38] mult(op_c,op_c) -> rd(op_c,rd(unit,op_c))
% Rule [35] rd(mult(op_c,mult(A,op_c)),A) -> rd(mult(op_c,b),rd(b,op_c)) is composed into
% [35] rd(mult(op_c,mult(A,op_c)),A) -> rd(op_c,rd(unit,op_c))
% New rule produced :
% [57] rd(mult(op_c,A),rd(A,op_c)) -> rd(op_c,rd(unit,op_c))
% Rule [37] rd(mult(op_c,A),rd(A,op_c)) <-> rd(mult(op_c,b),rd(b,op_c))
% collapsed.
% Rule [49] rd(rd(mult(op_c,A),rd(A,op_c)),op_c) -> op_c collapsed.
% Current number of equations to process: 114
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced : [58] ld(rd(op_c,rd(unit,op_c)),A) -> rd(rd(A,op_c),op_c)
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [59] rd(mult(A,op_c),rd(A,op_c)) -> rd(op_c,rd(unit,op_c))
% Rule [48] rd(mult(b,op_c),rd(b,op_c)) -> rd(op_c,rd(unit,op_c)) collapsed.
% Rule [56] rd(rd(mult(A,op_c),rd(A,op_c)),op_c) -> op_c collapsed.
% Current number of equations to process: 132
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [60] mult(A,mult(B,mult(A,op_c))) <-> mult(op_c,mult(A,mult(B,A)))
% Current number of equations to process: 146
% Current number of ordered equations: 3
% Current number of rules: 50
% New rule produced :
% [61] mult(op_c,mult(A,mult(B,A))) <-> mult(A,mult(B,mult(A,op_c)))
% Current number of equations to process: 146
% Current number of ordered equations: 2
% Current number of rules: 51
% New rule produced :
% [62] mult(op_c,mult(A,mult(op_c,B))) <-> mult(op_c,mult(op_c,mult(A,B)))
% Current number of equations to process: 146
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [63] mult(op_c,mult(op_c,mult(A,B))) <-> mult(op_c,mult(A,mult(op_c,B)))
% Current number of equations to process: 146
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced : [64] mult(A,mult(op_c,B)) <-> mult(op_c,mult(A,B))
% Rule [31] mult(A,mult(op_c,A)) <-> mult(op_c,mult(A,A)) collapsed.
% Rule [62] mult(op_c,mult(A,mult(op_c,B))) <-> mult(op_c,mult(op_c,mult(A,B)))
% collapsed.
% Current number of equations to process: 194
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced : [65] mult(A,mult(B,op_c)) <-> mult(op_c,mult(A,B))
% Rule [26] mult(A,mult(A,op_c)) <-> mult(op_c,mult(A,A)) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 227
% Current number of ordered equations: 1
% Current number of rules: 52
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [3]
% mult(A,op_c) <-> mult(op_c,A); trace = in the starting set
% [4] mult(op_c,A) <-> mult(A,op_c); trace = in the starting set
% [8] ld(A,mult(A,B)) -> B; trace = in the starting set
% [9] mult(mult(A,mult(B,A)),C) -> mult(A,mult(B,mult(A,C))); trace = in the starting set
% [62] mult(op_c,mult(A,mult(op_c,B))) <-> mult(op_c,mult(op_c,mult(A,B))); trace = Cp of 9 and 3
% [64] mult(A,mult(op_c,B)) <-> mult(op_c,mult(A,B)); trace = Cp of 62 and 8
% [65] mult(A,mult(B,op_c)) <-> mult(op_c,mult(A,B)); trace = Cp of 64 and 4
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.080000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------