TSTP Solution File: BOO001-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : BOO001-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n161.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 00:19:06 EDT 2014
% Result : Unsatisfiable 1.29s
% Output : Refutation 1.29s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : BOO001-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n161.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 15:11:08 CDT 2014
% % CPUTime : 1.29
% Processing problem /tmp/CiME_55320_n161.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a : constant; inverse : 1; multiply : 3;";
% let X = vars "V W X Y Z";
% let Axioms = equations F X "
% multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z));
% multiply(Y,X,X) = X;
% multiply(X,X,Y) = X;
% multiply(inverse(Y),Y,X) = X;
% multiply(X,Y,inverse(Y)) = X;
% ";
%
% let s1 = status F "
% a lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > a";
%
% let s2 = status F "
% a mul;
% inverse mul;
% multiply mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > a";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " inverse(inverse(a)) = a;"
% ;
% (*
% 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 = { multiply(multiply(V,W,X),Y,multiply(V,W,Z)) =
% multiply(V,W,multiply(X,Y,Z)),
% multiply(Y,X,X) = X,
% multiply(X,X,Y) = X,
% multiply(inverse(Y),Y,X) = X,
% multiply(X,Y,inverse(Y)) = X } (5 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [a] = 1;
% [inverse](x1) = 1 + x1;
% [multiply](x1,x2,x3) = 1 + x1 + x2 + x3;o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { inverse(inverse(a)) = a } (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] multiply(X,X,Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced : [2] multiply(Y,X,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 2
% New rule produced : [3] multiply(X,Y,inverse(Y)) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 3
% New rule produced : [4] multiply(inverse(Y),Y,X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced :
% [5]
% multiply(multiply(V,W,X),Y,multiply(V,W,Z)) -> multiply(V,W,multiply(X,Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] multiply(V,W,V) -> V
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7] multiply(V,W,multiply(X,V,Y)) <-> multiply(X,V,multiply(V,W,Y))
% Current number of equations to process: 8
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced :
% [8] multiply(X,V,multiply(V,W,Y)) <-> multiply(V,W,multiply(X,V,Y))
% Current number of equations to process: 8
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [9] multiply(multiply(V,W,X),Y,W) -> multiply(V,W,multiply(X,Y,W))
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10] multiply(V,W,X) <-> multiply(X,V,multiply(V,W,inverse(V)))
% Current number of equations to process: 10
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [11] multiply(X,V,multiply(V,W,inverse(V))) <-> multiply(V,W,X)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] multiply(V,W,multiply(V,X,Y)) <-> multiply(V,X,multiply(V,W,Y))
% Current number of equations to process: 8
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [13] multiply(multiply(V,W,X),Y,V) -> multiply(V,W,multiply(X,Y,V))
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14] multiply(V,W,multiply(V,X,Y)) <-> multiply(V,X,multiply(inverse(X),W,Y))
% Current number of equations to process: 6
% Current number of ordered equations: 3
% Current number of rules: 14
% New rule produced :
% [15] multiply(V,W,multiply(X,Y,inverse(W))) <-> multiply(V,W,multiply(X,Y,V))
% Current number of equations to process: 6
% Current number of ordered equations: 2
% Current number of rules: 15
% New rule produced :
% [16] multiply(V,W,multiply(X,Y,V)) <-> multiply(V,W,multiply(X,Y,inverse(W)))
% Current number of equations to process: 6
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [17] multiply(V,X,multiply(inverse(X),W,Y)) <-> multiply(V,W,multiply(V,X,Y))
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [18] multiply(X,V,multiply(V,W,X)) -> multiply(V,W,X)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [19] multiply(V,W,multiply(X,V,inverse(W))) -> V
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [20] multiply(W,X,multiply(V,W,X)) -> multiply(V,W,X)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [21] multiply(V,W,X) <-> multiply(V,X,multiply(inverse(X),W,X))
% Current number of equations to process: 19
% Current number of ordered equations: 1
% Current number of rules: 21
% New rule produced :
% [22] multiply(V,X,multiply(inverse(X),W,X)) <-> multiply(V,W,X)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [23] multiply(V,X,multiply(V,W,X)) -> multiply(V,W,X)
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [24] multiply(inverse(W),V,multiply(V,W,inverse(V))) -> V
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced : [25] multiply(W,inverse(W),V) -> V
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced : [26] multiply(V,W,multiply(V,W,X)) -> multiply(V,W,X)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced : [27] multiply(V,W,multiply(V,X,inverse(W))) -> V
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [28] multiply(V,W,multiply(inverse(W),X,V)) -> V
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [29] multiply(V,W,multiply(inverse(W),V,X)) -> V
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [30]
% multiply(inverse(V),W,multiply(inverse(W),V,X)) -> multiply(inverse(V),W,X)
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [31] multiply(V,W,multiply(X,multiply(V,W,X),Y)) -> multiply(V,W,X)
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [32] multiply(V,W,multiply(Y,multiply(V,W,X),X)) -> multiply(V,W,X)
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [33] multiply(V,W,multiply(multiply(V,W,X),V,X)) -> multiply(V,W,X)
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced : [34] multiply(V,W,multiply(X,inverse(W),V)) -> V
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced : [35] multiply(V,W,multiply(X,W,V)) -> multiply(V,W,X)
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [36] multiply(V,W,multiply(V,X,Y)) <-> multiply(V,W,multiply(inverse(W),X,Y))
% Current number of equations to process: 74
% Current number of ordered equations: 1
% Current number of rules: 36
% New rule produced :
% [37] multiply(V,W,multiply(inverse(W),X,Y)) <-> multiply(V,W,multiply(V,X,Y))
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [38]
% multiply(inverse(V),W,multiply(X,V,inverse(W))) -> multiply(inverse(V),W,X)
% Rule [24] multiply(inverse(W),V,multiply(V,W,inverse(V))) -> V collapsed.
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced : [39] multiply(V,W,multiply(V,inverse(W),X)) -> V
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced : [40] multiply(inverse(V),W,multiply(W,V,X)) -> W
% Current number of equations to process: 111
% Current number of ordered equations: 0
% Current number of rules: 39
% Rule [21] multiply(V,W,X) <-> multiply(V,X,multiply(inverse(X),W,X)) is composed into
% [21] multiply(V,W,X) <-> multiply(V,X,W)
% New rule produced : [41] multiply(inverse(W),V,W) -> V
% Rule [22] multiply(V,X,multiply(inverse(X),W,X)) <-> multiply(V,W,X)
% collapsed.
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 39
% New rule produced : [42] multiply(V,W,multiply(X,W,inverse(V))) -> W
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [43] multiply(V,W,multiply(X,V,multiply(Y,V,inverse(W)))) -> V
% Current number of equations to process: 176
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [44] multiply(V,W,multiply(V,X,multiply(Y,V,inverse(W)))) -> V
% Current number of equations to process: 175
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced :
% [45] multiply(V,W,multiply(X,V,multiply(inverse(W),Y,V))) -> V
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced : [46] multiply(V,W,X) <-> multiply(W,X,V)
% Rule [4] multiply(inverse(Y),Y,X) -> X collapsed.
% Rule [33] multiply(V,W,multiply(multiply(V,W,X),V,X)) -> multiply(V,W,X)
% collapsed.
% Current number of equations to process: 184
% Current number of ordered equations: 1
% Current number of rules: 42
% Rule [10] multiply(V,W,X) <-> multiply(X,V,multiply(V,W,inverse(V))) is composed into
% [10] multiply(V,W,X) <-> multiply(X,V,W)
% New rule produced : [47] multiply(Y,X,inverse(Y)) -> X
% Rule [11] multiply(X,V,multiply(V,W,inverse(V))) <-> multiply(V,W,X)
% collapsed.
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 42
% New rule produced : [48] multiply(V,W,X) <-> multiply(W,V,X)
% Current number of equations to process: 182
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [49] multiply(V,W,multiply(W,X,Y)) <-> multiply(W,multiply(V,W,Y),X)
% Current number of equations to process: 184
% Current number of ordered equations: 3
% Current number of rules: 44
% New rule produced :
% [50] multiply(V,W,multiply(X,Y,V)) <-> multiply(X,V,multiply(V,W,Y))
% Current number of equations to process: 184
% Current number of ordered equations: 2
% Current number of rules: 45
% New rule produced :
% [51] multiply(W,multiply(V,W,Y),X) <-> multiply(V,W,multiply(W,X,Y))
% Current number of equations to process: 184
% Current number of ordered equations: 1
% Current number of rules: 46
% New rule produced :
% [52] multiply(X,V,multiply(V,W,Y)) <-> multiply(V,W,multiply(X,Y,V))
% Current number of equations to process: 184
% Current number of ordered equations: 0
% Current number of rules: 47
% New rule produced :
% [53] multiply(V,W,multiply(W,X,Y)) <-> multiply(W,Y,multiply(V,W,X))
% Current number of equations to process: 183
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [54] multiply(W,Y,multiply(V,W,X)) <-> multiply(V,W,multiply(W,X,Y))
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [55] multiply(V,W,multiply(X,Y,W)) <-> multiply(W,multiply(V,W,X),Y)
% Current number of equations to process: 181
% Current number of ordered equations: 3
% Current number of rules: 50
% New rule produced :
% [56] multiply(V,X,multiply(W,Y,X)) <-> multiply(X,multiply(V,W,X),Y)
% Current number of equations to process: 181
% Current number of ordered equations: 2
% Current number of rules: 51
% New rule produced :
% [57] multiply(W,multiply(V,W,X),Y) <-> multiply(V,W,multiply(X,Y,W))
% Current number of equations to process: 181
% Current number of ordered equations: 1
% Current number of rules: 52
% New rule produced :
% [58] multiply(X,multiply(V,W,X),Y) <-> multiply(V,X,multiply(W,Y,X))
% Current number of equations to process: 181
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [59] multiply(V,W,multiply(V,X,Y)) <-> multiply(V,Y,multiply(V,W,X))
% Current number of equations to process: 179
% Current number of ordered equations: 3
% Current number of rules: 54
% New rule produced :
% [60] multiply(V,W,multiply(V,X,Y)) <-> multiply(V,multiply(V,W,Y),X)
% Current number of equations to process: 179
% Current number of ordered equations: 2
% Current number of rules: 55
% New rule produced :
% [61] multiply(V,Y,multiply(V,W,X)) <-> multiply(V,W,multiply(V,X,Y))
% Current number of equations to process: 179
% Current number of ordered equations: 1
% Current number of rules: 56
% New rule produced :
% [62] multiply(V,multiply(V,W,Y),X) <-> multiply(V,W,multiply(V,X,Y))
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [63] multiply(V,W,multiply(X,Y,V)) <-> multiply(V,X,multiply(W,Y,V))
% Current number of equations to process: 177
% Current number of ordered equations: 2
% Current number of rules: 58
% New rule produced :
% [64] multiply(V,W,multiply(X,Y,V)) <-> multiply(V,multiply(V,W,X),Y)
% Current number of equations to process: 177
% Current number of ordered equations: 1
% Current number of rules: 59
% New rule produced :
% [65] multiply(V,multiply(V,W,X),Y) <-> multiply(V,W,multiply(X,Y,V))
% Current number of equations to process: 177
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced : [66] multiply(V,W,multiply(W,V,X)) <-> multiply(W,X,V)
% Current number of equations to process: 183
% Current number of ordered equations: 1
% Current number of rules: 61
% New rule produced : [67] multiply(W,X,V) <-> multiply(V,W,multiply(W,V,X))
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced : [68] multiply(V,W,multiply(W,V,X)) <-> multiply(V,X,W)
% Current number of equations to process: 191
% Current number of ordered equations: 1
% Current number of rules: 63
% New rule produced : [69] multiply(V,X,W) <-> multiply(V,W,multiply(W,V,X))
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced : [70] inverse(inverse(V)) -> V
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 201
% Current number of ordered equations: 0
% Current number of rules: 65
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 7 rules have been used:
% [2]
% multiply(Y,X,X) -> X; trace = in the starting set
% [3] multiply(X,Y,inverse(Y)) -> X; trace = in the starting set
% [5] multiply(multiply(V,W,X),Y,multiply(V,W,Z)) ->
% multiply(V,W,multiply(X,Y,Z)); trace = in the starting set
% [7] multiply(V,W,multiply(X,V,Y)) <-> multiply(X,V,multiply(V,W,Y)); trace = Cp of 5 and 2
% [11] multiply(X,V,multiply(V,W,inverse(V))) <-> multiply(V,W,X); trace = Cp of 7 and 3
% [25] multiply(W,inverse(W),V) -> V; trace = Cp of 11 and 2
% [70] inverse(inverse(V)) -> V; trace = Cp of 25 and 3
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.170000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------