TSTP Solution File: GRP449-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP449-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n125.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 00:23:12 EDT 2014
% Result : Unsatisfiable 1.14s
% Output : Refutation 1.14s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP449-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n125.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 13:43:03 CDT 2014
% % CPUTime : 1.14
% Processing problem /tmp/CiME_37117_n125.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; inverse : 1; multiply : 2; divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C))) = B;
% multiply(A,B) = divide(A,divide(divide(C,C),B));
% inverse(A) = divide(divide(B,B),A);
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > divide > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% inverse mul;
% multiply mul;
% divide mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > divide > b2 = a2";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(multiply(inverse(b2),b2),a2) = a2;"
% ;
% (*
% 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(divide(B,B),B),C),
% divide(divide(divide(B,B),A),C))) = B,
% multiply(A,B) = divide(A,divide(divide(C,C),B)),
% inverse(A) = divide(divide(B,B),A) }
% (3 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(inverse(b2),b2),a2) = a2 }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] inverse(A) <-> divide(divide(B,B),A)
% The conjecture has been reduced.
% Conjecture is now:
% multiply(multiply(divide(divide(a2,a2),b2),b2),a2) = a2
%
% Current number of equations to process: 1
% Current number of ordered equations: 3
% Current number of rules: 1
% New rule produced : [2] divide(divide(B,B),A) <-> divide(divide(a2,a2),A)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 2
% New rule produced : [3] divide(divide(a2,a2),A) <-> divide(divide(B,B),A)
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 3
% New rule produced : [4] multiply(A,B) <-> divide(A,divide(divide(C,C),B))
% The conjecture has been reduced.
% Conjecture is now:
% divide(divide(a2,a2),divide(divide(a2,a2),a2)) = a2
%
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced :
% [5]
% divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C)))
% -> B
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] divide(divide(divide(a2,a2),divide(A,A)),B) -> divide(divide(a2,a2),B)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7] divide(divide(divide(A,A),divide(a2,a2)),B) -> divide(divide(a2,a2),B)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8] divide(divide(divide(A,A),divide(B,B)),C) -> divide(divide(a2,a2),C)
% Rule
% [6] divide(divide(divide(a2,a2),divide(A,A)),B) -> divide(divide(a2,a2),B)
% collapsed.
% Rule
% [7] divide(divide(divide(A,A),divide(a2,a2)),B) -> divide(divide(a2,a2),B)
% collapsed.
% Current number of equations to process: 14
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [9]
% divide(divide(divide(a2,a2),divide(divide(a2,a2),divide(A,A))),B) ->
% divide(divide(a2,a2),B)
% Current number of equations to process: 20
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [10]
% divide(divide(divide(a2,a2),divide(divide(A,A),divide(a2,a2))),B) ->
% divide(divide(a2,a2),B)
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [11]
% divide(divide(divide(a2,a2),divide(divide(A,A),divide(B,B))),C) ->
% divide(divide(a2,a2),C)
% Rule
% [9]
% divide(divide(divide(a2,a2),divide(divide(a2,a2),divide(A,A))),B) ->
% divide(divide(a2,a2),B) collapsed.
% Rule
% [10]
% divide(divide(divide(a2,a2),divide(divide(A,A),divide(a2,a2))),B) ->
% divide(divide(a2,a2),B) collapsed.
% Current number of equations to process: 17
% Current number of ordered equations: 1
% Current number of rules: 7
% New rule produced :
% [12]
% divide(divide(divide(A,A),divide(divide(a2,a2),divide(B,B))),C) ->
% divide(divide(a2,a2),C)
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [13]
% divide(divide(divide(A,A),divide(divide(B,B),divide(a2,a2))),C) ->
% divide(divide(a2,a2),C)
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [14]
% divide(divide(divide(A,A),divide(divide(B,B),divide(C,C))),V_3) ->
% divide(divide(a2,a2),V_3)
% Rule
% [11]
% divide(divide(divide(a2,a2),divide(divide(A,A),divide(B,B))),C) ->
% divide(divide(a2,a2),C) collapsed.
% Rule
% [12]
% divide(divide(divide(A,A),divide(divide(a2,a2),divide(B,B))),C) ->
% divide(divide(a2,a2),C) collapsed.
% Rule
% [13]
% divide(divide(divide(A,A),divide(divide(B,B),divide(a2,a2))),C) ->
% divide(divide(a2,a2),C) collapsed.
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [15]
% divide(A,divide(divide(divide(a2,a2),B),divide(divide(divide(a2,a2),A),B)))
% <-> divide(C,C)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [16] divide(C,C) <-> divide(a2,a2)
% Rule [2] divide(divide(B,B),A) <-> divide(divide(a2,a2),A) collapsed.
% Current number of equations to process: 24
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [17] divide(B,B) <-> divide(divide(A,A),divide(a2,a2))
% Current number of equations to process: 36
% Current number of ordered equations: 1
% Current number of rules: 9
% Rule [17] divide(B,B) <-> divide(divide(A,A),divide(a2,a2)) is composed into
% [17] divide(B,B) <-> divide(a2,a2)
% New rule produced : [18] divide(divide(A,A),divide(a2,a2)) <-> divide(B,B)
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [19]
% divide(A,divide(divide(a2,a2),divide(divide(divide(a2,a2),A),divide(B,B))))
% <-> divide(C,C)
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [20]
% divide(A,divide(divide(divide(B,B),C),divide(divide(divide(a2,a2),A),C))) <->
% divide(V_3,V_3)
% Rule
% [15]
% divide(A,divide(divide(divide(a2,a2),B),divide(divide(divide(a2,a2),A),B)))
% <-> divide(C,C) collapsed.
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [21] divide(A,divide(a2,a2)) -> A
% Rule [18] divide(divide(A,A),divide(a2,a2)) <-> divide(B,B) collapsed.
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [22] divide(B,B) <-> divide(A,A)
% Rule [3] divide(divide(a2,a2),A) <-> divide(divide(B,B),A) collapsed.
% Rule [16] divide(C,C) <-> divide(a2,a2) collapsed.
% Rule [17] divide(B,B) <-> divide(a2,a2) collapsed.
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [23]
% divide(C,C) <->
% divide(divide(A,A),divide(divide(a2,a2),divide(divide(a2,a2),divide(B,B))))
% Current number of equations to process: 40
% Current number of ordered equations: 1
% Current number of rules: 10
% Rule [23]
% divide(C,C) <->
% divide(divide(A,A),divide(divide(a2,a2),divide(divide(a2,a2),divide(B,B)))) is composed into
% [23] divide(C,C) <-> divide(a2,a2)
% New rule produced :
% [24]
% divide(divide(A,A),divide(divide(a2,a2),divide(divide(a2,a2),divide(B,B))))
% <-> divide(C,C)
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [25]
% divide(V_3,V_3) <->
% divide(divide(A,A),divide(divide(divide(B,B),C),divide(divide(a2,a2),C)))
% Current number of equations to process: 48
% Current number of ordered equations: 1
% Current number of rules: 12
% Rule [25]
% divide(V_3,V_3) <->
% divide(divide(A,A),divide(divide(divide(B,B),C),divide(divide(a2,a2),C))) is composed into
% [25] divide(V_3,V_3) <-> divide(a2,a2)
% New rule produced :
% [26]
% divide(divide(A,A),divide(divide(divide(B,B),C),divide(divide(a2,a2),C))) <->
% divide(V_3,V_3)
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [27] divide(divide(A,A),divide(B,B)) -> divide(a2,a2)
% Rule [8] divide(divide(divide(A,A),divide(B,B)),C) -> divide(divide(a2,a2),C)
% collapsed.
% Rule
% [14]
% divide(divide(divide(A,A),divide(divide(B,B),divide(C,C))),V_3) ->
% divide(divide(a2,a2),V_3) collapsed.
% Rule
% [24]
% divide(divide(A,A),divide(divide(a2,a2),divide(divide(a2,a2),divide(B,B))))
% <-> divide(C,C) collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [28] divide(A,divide(B,B)) -> A
% Rule
% [19]
% divide(A,divide(divide(a2,a2),divide(divide(divide(a2,a2),A),divide(B,B))))
% <-> divide(C,C) collapsed.
% Rule [21] divide(A,divide(a2,a2)) -> A collapsed.
% Rule [27] divide(divide(A,A),divide(B,B)) -> divide(a2,a2) collapsed.
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [29] divide(A,divide(divide(a2,a2),divide(divide(a2,a2),A))) <-> divide(C,C)
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [30] divide(A,divide(divide(B,B),divide(divide(a2,a2),A))) <-> divide(C,C)
% Rule
% [29] divide(A,divide(divide(a2,a2),divide(divide(a2,a2),A))) <-> divide(C,C)
% collapsed.
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [31] divide(A,divide(divide(divide(B,B),B),divide(divide(B,B),A))) -> B
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [32]
% divide(A,divide(divide(divide(B,B),C),divide(divide(divide(V_3,V_3),A),C)))
% <-> divide(V_4,V_4)
% Rule
% [20]
% divide(A,divide(divide(divide(B,B),C),divide(divide(divide(a2,a2),A),C))) <->
% divide(V_3,V_3) collapsed.
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [33] divide(C,C) <-> divide(divide(divide(A,A),B),divide(divide(a2,a2),B))
% Current number of equations to process: 63
% Current number of ordered equations: 1
% Current number of rules: 12
% Rule [33]
% divide(C,C) <-> divide(divide(divide(A,A),B),divide(divide(a2,a2),B)) is composed into
% [33] divide(C,C) <-> divide(a2,a2)
% New rule produced :
% [34] divide(divide(divide(A,A),B),divide(divide(a2,a2),B)) <-> divide(C,C)
% Rule
% [26]
% divide(divide(A,A),divide(divide(divide(B,B),C),divide(divide(a2,a2),C))) <->
% divide(V_3,V_3) collapsed.
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [35] divide(A,divide(divide(B,B),divide(divide(C,C),A))) <-> divide(V_3,V_3)
% Rule
% [30] divide(A,divide(divide(B,B),divide(divide(a2,a2),A))) <-> divide(C,C)
% collapsed.
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [36] divide(divide(A,A),divide(divide(B,B),B)) -> B
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 13
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 14 rules have been used:
% [1]
% inverse(A) <-> divide(divide(B,B),A); trace = in the starting set
% [2] divide(divide(B,B),A) <-> divide(divide(a2,a2),A); trace = in the starting set
% [3] divide(divide(a2,a2),A) <-> divide(divide(B,B),A); trace = in the starting set
% [4] multiply(A,B) <-> divide(A,divide(divide(C,C),B)); trace = in the starting set
% [5] divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C)))
% -> B; trace = in the starting set
% [6] divide(divide(divide(a2,a2),divide(A,A)),B) -> divide(divide(a2,a2),B); trace = Self cp of 2
% [8] divide(divide(divide(A,A),divide(B,B)),C) -> divide(divide(a2,a2),C); trace = Cp of 6 and 3
% [15] divide(A,divide(divide(divide(a2,a2),B),divide(divide(divide(a2,a2),A),B)))
% <-> divide(C,C); trace = Cp of 5 and 2
% [16] divide(C,C) <-> divide(a2,a2); trace = Cp of 5 and 2
% [21] divide(A,divide(a2,a2)) -> A; trace = Cp of 16 and 5
% [22] divide(B,B) <-> divide(A,A); trace = Cp of 15 and 8
% [28] divide(A,divide(B,B)) -> A; trace = Cp of 22 and 5
% [31] divide(A,divide(divide(divide(B,B),B),divide(divide(B,B),A))) -> B; trace = Cp of 21 and 5
% [36] divide(divide(A,A),divide(divide(B,B),B)) -> B; trace = Cp of 31 and 28
% % 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
%------------------------------------------------------------------------------