TSTP Solution File: GRP462-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP462-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n159.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 00:23:13 EDT 2014
% Result : Unsatisfiable 1.39s
% Output : Refutation 1.39s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP462-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n159.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 : Fri Jun 6 13:56:38 CDT 2014
% % CPUTime : 1.39
% Processing problem /tmp/CiME_42435_n159.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c3,b3,a3,identity : constant; inverse : 1; multiply : 2; divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B;
% multiply(A,B) = divide(A,divide(identity,B));
% inverse(A) = divide(identity,A);
% identity = divide(A,A);
% ";
%
% let s1 = status F "
% c3 lr_lex;
% b3 lr_lex;
% a3 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% divide lr_lex;
% identity lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > divide > identity > a3 > b3 > c3";
%
% let s2 = status F "
% c3 mul;
% b3 mul;
% a3 mul;
% inverse mul;
% multiply mul;
% divide mul;
% identity mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > divide > identity = a3 = b3 = c3";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3));"
% ;
% (*
% 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 = { divide(A,divide(divide(divide(identity,B),C),
% divide(divide(divide(A,A),A),C))) = B,
% multiply(A,B) = divide(A,divide(identity,B)),
% inverse(A) = divide(identity,A),
% identity = divide(A,A) } (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 = { multiply(multiply(a3,b3),c3) =
% multiply(a3,multiply(b3,c3)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] divide(A,A) -> identity
% Current number of equations to process: 1
% Current number of ordered equations: 2
% Current number of rules: 1
% New rule produced : [2] inverse(A) -> divide(identity,A)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 2
% New rule produced : [3] multiply(A,B) -> divide(A,divide(identity,B))
% The conjecture has been reduced.
% Conjecture is now:
% divide(divide(a3,divide(identity,b3)),divide(identity,c3)) = divide(a3,
% divide(identity,
% divide(b3,
% divide(identity,c3))))
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 3
% New rule produced :
% [4]
% divide(A,divide(divide(divide(identity,B),C),divide(divide(identity,A),C)))
% -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced : [5] divide(A,identity) -> A
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] divide(A,divide(divide(identity,B),divide(identity,A))) -> B
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] divide(identity,divide(identity,A)) -> A
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% divide(A,divide(divide(identity,B),divide(divide(identity,A),B))) -> identity
% Current number of equations to process: 2
% Current number of ordered equations: 2
% Current number of rules: 8
% New rule produced :
% [9]
% divide(A,divide(identity,divide(divide(identity,A),divide(identity,B)))) -> B
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced :
% [10]
% divide(identity,divide(divide(divide(identity,A),B),divide(identity,B))) -> A
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11] divide(A,divide(B,divide(identity,A))) <-> divide(identity,B)
% Rule [6] divide(A,divide(divide(identity,B),divide(identity,A))) -> B
% collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [12] divide(divide(identity,A),divide(divide(identity,B),A)) -> B
% Rule
% [8]
% divide(A,divide(divide(identity,B),divide(divide(identity,A),B))) -> identity
% collapsed.
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [13]
% divide(A,divide(divide(B,C),divide(divide(identity,A),C))) ->
% divide(identity,B)
% Rule
% [4]
% divide(A,divide(divide(divide(identity,B),C),divide(divide(identity,A),C)))
% -> B collapsed.
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [14]
% divide(A,divide(identity,divide(divide(identity,A),B))) -> divide(identity,B)
% Rule
% [9]
% divide(A,divide(identity,divide(divide(identity,A),divide(identity,B)))) -> B
% collapsed.
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [15]
% divide(identity,divide(divide(A,B),divide(identity,B))) -> divide(identity,A)
% Rule
% [10]
% divide(identity,divide(divide(divide(identity,A),B),divide(identity,B))) -> A
% collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [16] divide(divide(identity,A),divide(B,A)) -> divide(identity,B)
% Rule [12] divide(divide(identity,A),divide(divide(identity,B),A)) -> B
% collapsed.
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [17]
% divide(divide(identity,A),divide(identity,divide(A,divide(identity,B)))) -> B
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [18]
% divide(identity,divide(divide(divide(identity,A),divide(identity,B)),B)) -> A
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [19]
% divide(divide(identity,A),divide(identity,divide(A,B))) -> divide(identity,B)
% Rule
% [17]
% divide(divide(identity,A),divide(identity,divide(A,divide(identity,B)))) -> B
% collapsed.
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [20]
% divide(divide(divide(identity,A),B),divide(identity,B)) -> divide(identity,A)
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [21] divide(divide(A,B),divide(identity,B)) -> A
% Rule
% [15]
% divide(identity,divide(divide(A,B),divide(identity,B))) -> divide(identity,A)
% collapsed.
% Rule
% [20]
% divide(divide(divide(identity,A),B),divide(identity,B)) -> divide(identity,A)
% collapsed.
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [22] divide(A,B) <-> divide(identity,divide(B,A))
% Rule
% [18]
% divide(identity,divide(divide(divide(identity,A),divide(identity,B)),B)) -> A
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% divide(identity,divide(divide(identity,c3),divide(a3,divide(identity,b3)))) =
% divide(a3,divide(identity,divide(b3,divide(identity,c3))))
%
% Current number of equations to process: 12
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced : [23] divide(identity,divide(B,A)) <-> divide(A,B)
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [24] divide(identity,divide(A,divide(B,divide(identity,A)))) -> B
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [25] divide(divide(identity,divide(A,B)),divide(B,A)) -> identity
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [26] divide(divide(A,B),divide(identity,divide(B,A))) -> identity
% Current number of equations to process: 24
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced : [27] divide(divide(A,divide(B,C)),divide(C,B)) -> A
% Rule [25] divide(divide(identity,divide(A,B)),divide(B,A)) -> identity
% collapsed.
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [28] divide(divide(A,B),divide(C,divide(B,A))) -> divide(identity,C)
% Rule [26] divide(divide(A,B),divide(identity,divide(B,A))) -> identity
% collapsed.
% Current number of equations to process: 26
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [29]
% divide(identity,divide(C,divide(B,A))) <->
% divide(divide(identity,divide(A,B)),C)
% Current number of equations to process: 29
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [30]
% divide(divide(identity,divide(A,B)),C) <->
% divide(identity,divide(C,divide(B,A)))
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [31] divide(divide(A,B),divide(C,divide(B,divide(identity,C)))) -> A
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [32]
% divide(identity,divide(divide(identity,divide(A,B)),C)) <->
% divide(C,divide(B,A))
% Current number of equations to process: 63
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [33]
% divide(C,divide(B,A)) <->
% divide(identity,divide(divide(identity,divide(A,B)),C))
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [34]
% divide(divide(identity,A),divide(divide(B,C),divide(A,C))) ->
% divide(identity,B)
% Current number of equations to process: 113
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [35] divide(A,B) <-> divide(identity,divide(divide(B,C),divide(A,C)))
% Current number of equations to process: 126
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [36] divide(identity,divide(divide(B,C),divide(A,C))) <-> divide(A,B)
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 24
% Rule [35] divide(A,B) <-> divide(identity,divide(divide(B,C),divide(A,C))) is composed into
% [35] divide(A,B) <-> divide(identity,divide(B,A))
% New rule produced : [37] divide(divide(A,B),divide(C,B)) -> divide(A,C)
% Rule
% [13]
% divide(A,divide(divide(B,C),divide(divide(identity,A),C))) ->
% divide(identity,B) collapsed.
% Rule [16] divide(divide(identity,A),divide(B,A)) -> divide(identity,B)
% collapsed.
% Rule [21] divide(divide(A,B),divide(identity,B)) -> A collapsed.
% Rule
% [34]
% divide(divide(identity,A),divide(divide(B,C),divide(A,C))) ->
% divide(identity,B) collapsed.
% Rule [36] divide(identity,divide(divide(B,C),divide(A,C))) <-> divide(A,B)
% collapsed.
% Current number of equations to process: 167
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [38] divide(divide(A,B),divide(identity,divide(B,C))) -> divide(A,C)
% Rule
% [19]
% divide(divide(identity,A),divide(identity,divide(A,B))) -> divide(identity,B)
% collapsed.
% Current number of equations to process: 198
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [39] divide(divide(identity,divide(A,B)),divide(C,A)) -> divide(B,C)
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [40] divide(A,divide(V_3,divide(C,B))) <-> divide(divide(A,divide(B,C)),V_3)
% Rule
% [29]
% divide(identity,divide(C,divide(B,A))) <->
% divide(divide(identity,divide(A,B)),C) collapsed.
% Current number of equations to process: 198
% Current number of ordered equations: 2
% Current number of rules: 21
% New rule produced :
% [41] divide(A,divide(C,divide(identity,B))) <-> divide(divide(A,B),C)
% Current number of equations to process: 202
% Current number of ordered equations: 3
% Current number of rules: 22
% New rule produced :
% [42] divide(divide(A,B),C) <-> divide(A,divide(C,divide(identity,B)))
% Current number of equations to process: 202
% Current number of ordered equations: 2
% Current number of rules: 23
% New rule produced :
% [43] divide(divide(A,divide(B,C)),V_3) <-> divide(A,divide(V_3,divide(C,B)))
% Rule
% [30]
% divide(divide(identity,divide(A,B)),C) <->
% divide(identity,divide(C,divide(B,A))) collapsed.
% Current number of equations to process: 211
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [44] divide(A,divide(B,C)) <-> divide(divide(A,divide(identity,C)),B)
% Current number of equations to process: 225
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [45] divide(divide(A,divide(identity,C)),B) <-> divide(A,divide(B,C))
% Current number of equations to process: 225
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [46]
% divide(identity,divide(divide(A,B),C)) <->
% divide(divide(C,divide(identity,B)),A)
% Current number of equations to process: 346
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [47]
% divide(divide(C,divide(identity,B)),A) <->
% divide(identity,divide(divide(A,B),C))
% Current number of equations to process: 346
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [48]
% divide(B,divide(A,divide(identity,C))) <->
% divide(identity,divide(A,divide(B,C)))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 344
% Current number of ordered equations: 3
% Current number of rules: 28
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 20 rules have been used:
% [1]
% divide(A,A) -> identity; trace = in the starting set
% [3] multiply(A,B) -> divide(A,divide(identity,B)); trace = in the starting set
% [4] divide(A,divide(divide(divide(identity,B),C),divide(divide(identity,A),C)))
% -> B; trace = in the starting set
% [5] divide(A,identity) -> A; trace = Cp of 4 and 1
% [6] divide(A,divide(divide(identity,B),divide(identity,A))) -> B; trace = Cp of 5 and 4
% [7] divide(identity,divide(identity,A)) -> A; trace = Cp of 6 and 1
% [9] divide(A,divide(identity,divide(divide(identity,A),divide(identity,B))))
% -> B; trace = Cp of 4 and 1
% [11] divide(A,divide(B,divide(identity,A))) <-> divide(identity,B); trace = Cp of 7 and 6
% [12] divide(divide(identity,A),divide(divide(identity,B),A)) -> B; trace = Cp of 7 and 6
% [13] divide(A,divide(divide(B,C),divide(divide(identity,A),C))) ->
% divide(identity,B); trace = Cp of 7 and 4
% [14] divide(A,divide(identity,divide(divide(identity,A),B))) ->
% divide(identity,B); trace = Cp of 9 and 7
% [16] divide(divide(identity,A),divide(B,A)) -> divide(identity,B); trace = Cp of 12 and 7
% [22] divide(A,B) <-> divide(identity,divide(B,A)); trace = Cp of 16 and 14
% [23] divide(identity,divide(B,A)) <-> divide(A,B); trace = Cp of 16 and 14
% [34] divide(divide(identity,A),divide(divide(B,C),divide(A,C))) ->
% divide(identity,B); trace = Cp of 13 and 7
% [35] divide(A,B) <-> divide(identity,divide(divide(B,C),divide(A,C))); trace = Cp of 34 and 14
% [37] divide(divide(A,B),divide(C,B)) -> divide(A,C); trace = Cp of 35 and 23
% [38] divide(divide(A,B),divide(identity,divide(B,C))) -> divide(A,C); trace = Cp of 37 and 22
% [42] divide(divide(A,B),C) <-> divide(A,divide(C,divide(identity,B))); trace = Cp of 38 and 11
% [48] divide(B,divide(A,divide(identity,C))) <->
% divide(identity,divide(A,divide(B,C))); trace = Cp of 42 and 35
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.270000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------