TSTP Solution File: GRP594-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP594-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n166.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 00:23:33 EDT 2014
% Result : Unsatisfiable 1.17s
% Output : Refutation 1.17s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP594-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n166.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 21:18:33 CDT 2014
% % CPUTime : 1.17
% Processing problem /tmp/CiME_35593_n166.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; multiply : 2; inverse : 1; double_divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B)))))) = C;
% multiply(A,B) = inverse(double_divide(B,A));
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% double_divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > double_divide > inverse > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% multiply mul;
% inverse mul;
% double_divide mul;
% ";
%
% let p2 = precedence F "
% multiply > double_divide > inverse > 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 = { inverse(double_divide(double_divide(A,B),
% inverse(double_divide(A,inverse(
% double_divide(C,B))))))
% = C,
% multiply(A,B) = inverse(double_divide(B,A)) }
% (2 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] multiply(A,B) -> inverse(double_divide(B,A))
% The conjecture has been reduced.
% Conjecture is now:
% inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) = a2
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced :
% [2]
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(
% double_divide(C,B))))))
% -> C
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% inverse(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C))
% -> A
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4]
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))) <->
% double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3)))
% Current number of equations to process: 4
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced :
% [5]
% double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))) <->
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C))))
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(
% double_divide(A,C)))),B))
% -> C
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% inverse(double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),B))))
% -> C
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8]
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))) <->
% inverse(double_divide(double_divide(V_3,B),inverse(double_divide(V_3,C))))
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% inverse(double_divide(inverse(inverse(double_divide(double_divide(A,B),
% inverse(double_divide(A,B))))),C)) -> C
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10]
% inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(
% double_divide(A,B)))),C))
% -> C
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [11]
% inverse(double_divide(double_divide(double_divide(A,B),inverse(double_divide(A,B))),C))
% -> C
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12]
% inverse(double_divide(double_divide(B,C),inverse(double_divide(A,inverse(
% double_divide(B,C))))))
% -> A
% Current number of equations to process: 101
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [13]
% inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),A)) ->
% double_divide(B,C)
% Current number of equations to process: 102
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [14]
% inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)) ->
% double_divide(A,C)
% Rule
% [3]
% inverse(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C))
% -> A collapsed.
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced : [15] double_divide(double_divide(A,B),B) -> A
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 14
% Rule [5]
% double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))) <->
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))) is composed into
% [5]
% double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))) <->
% inverse(double_divide(A,inverse(double_divide(double_divide(A,B),C))))
% New rule produced :
% [16]
% inverse(double_divide(A,inverse(double_divide(B,C)))) <->
% inverse(double_divide(B,inverse(double_divide(A,C))))
% Rule
% [2]
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(
% double_divide(C,B))))))
% -> C collapsed.
% Rule
% [4]
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))) <->
% double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))) collapsed.
% Rule
% [6]
% inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(
% double_divide(A,C)))),B))
% -> C collapsed.
% Rule
% [8]
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))) <->
% inverse(double_divide(double_divide(V_3,B),inverse(double_divide(V_3,C))))
% collapsed.
% Rule
% [9]
% inverse(double_divide(inverse(inverse(double_divide(double_divide(A,B),
% inverse(double_divide(A,B))))),C)) -> C
% collapsed.
% Rule
% [10]
% inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(
% double_divide(A,B)))),C))
% -> C collapsed.
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [17]
% inverse(double_divide(A,inverse(double_divide(double_divide(A,B),inverse(
% double_divide(C,B))))))
% -> C
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [18]
% inverse(double_divide(double_divide(inverse(double_divide(double_divide(A,B),C)),B),C))
% -> A
% Current number of equations to process: 118
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [19]
% inverse(double_divide(A,inverse(A))) <->
% double_divide(double_divide(B,C),inverse(double_divide(B,C)))
% Current number of equations to process: 119
% Current number of ordered equations: 1
% Current number of rules: 12
% Rule [19]
% inverse(double_divide(A,inverse(A))) <->
% double_divide(double_divide(B,C),inverse(double_divide(B,C))) is composed into
% [19]
% inverse(double_divide(A,inverse(A))) <->
% inverse(double_divide(a2,inverse(a2)))
% New rule produced :
% [20]
% double_divide(double_divide(B,C),inverse(double_divide(B,C))) <->
% inverse(double_divide(A,inverse(A)))
% Rule
% [11]
% inverse(double_divide(double_divide(double_divide(A,B),inverse(double_divide(A,B))),C))
% -> C collapsed.
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [21] inverse(inverse(double_divide(A,B))) -> double_divide(A,B)
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [22] inverse(double_divide(double_divide(A,inverse(B)),A)) -> B
% Rule
% [13]
% inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),A)) ->
% double_divide(B,C) collapsed.
% Current number of equations to process: 147
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [23] inverse(double_divide(A,double_divide(a2,inverse(a2)))) -> A
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [24] inverse(double_divide(inverse(double_divide(A,inverse(A))),C)) -> C
% Current number of equations to process: 161
% Current number of ordered equations: 1
% Current number of rules: 15
% New rule produced :
% [25] inverse(double_divide(A,inverse(double_divide(inverse(A),B)))) -> B
% Current number of equations to process: 160
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [26] inverse(double_divide(A,inverse(double_divide(B,inverse(A))))) -> B
% Rule
% [12]
% inverse(double_divide(double_divide(B,C),inverse(double_divide(A,inverse(
% double_divide(B,C))))))
% -> A collapsed.
% Current number of equations to process: 159
% Current number of ordered equations: 1
% Current number of rules: 16
% New rule produced :
% [27]
% inverse(double_divide(double_divide(A,B),inverse(C))) <->
% double_divide(C,inverse(double_divide(A,B)))
% Current number of equations to process: 157
% Current number of ordered equations: 2
% Current number of rules: 17
% New rule produced :
% [28]
% double_divide(C,inverse(double_divide(A,B))) <->
% inverse(double_divide(double_divide(A,B),inverse(C)))
% Current number of equations to process: 157
% Current number of ordered equations: 1
% Current number of rules: 18
% New rule produced :
% [29]
% double_divide(double_divide(A,inverse(double_divide(B,C))),C) ->
% inverse(double_divide(A,B))
% Current number of equations to process: 156
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [30]
% inverse(double_divide(A,double_divide(A,inverse(double_divide(B,C))))) ->
% double_divide(B,C)
% Current number of equations to process: 155
% Current number of ordered equations: 1
% Current number of rules: 20
% New rule produced :
% [31]
% inverse(double_divide(double_divide(A,inverse(B)),double_divide(B,C))) ->
% double_divide(A,C)
% Current number of equations to process: 154
% Current number of ordered equations: 1
% Current number of rules: 21
% Rule [5]
% double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))) <->
% inverse(double_divide(A,inverse(double_divide(double_divide(A,B),C)))) is composed into
% [5]
% double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))) <->
% inverse(inverse(double_divide(B,inverse(C))))
% New rule produced :
% [32]
% double_divide(A,inverse(double_divide(double_divide(A,B),C))) ->
% inverse(double_divide(B,inverse(C)))
% Rule
% [17]
% inverse(double_divide(A,inverse(double_divide(double_divide(A,B),inverse(
% double_divide(C,B))))))
% -> C collapsed.
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [33] double_divide(B,double_divide(C,B)) -> C
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [34]
% inverse(double_divide(A,inverse(B))) <->
% inverse(double_divide(double_divide(B,C),inverse(double_divide(A,C))))
% Current number of equations to process: 152
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [35]
% inverse(double_divide(double_divide(B,C),inverse(double_divide(A,C)))) <->
% inverse(double_divide(A,inverse(B)))
% Current number of equations to process: 152
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [36]
% inverse(double_divide(double_divide(A,double_divide(B,C)),A)) <->
% double_divide(double_divide(V_3,inverse(double_divide(B,C))),V_3)
% Current number of equations to process: 151
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [37]
% double_divide(double_divide(V_3,inverse(double_divide(B,C))),V_3) <->
% inverse(double_divide(double_divide(A,double_divide(B,C)),A))
% Current number of equations to process: 151
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [38]
% inverse(double_divide(double_divide(A,double_divide(B,C)),A)) <->
% double_divide(double_divide(B,inverse(double_divide(V_3,C))),V_3)
% Current number of equations to process: 150
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [39]
% double_divide(double_divide(B,inverse(double_divide(V_3,C))),V_3) <->
% inverse(double_divide(double_divide(A,double_divide(B,C)),A))
% Current number of equations to process: 150
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [40]
% inverse(double_divide(A,double_divide(double_divide(B,C),inverse(double_divide(A,C)))))
% -> B
% Current number of equations to process: 153
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [41]
% double_divide(double_divide(A,B),double_divide(double_divide(A,B),C)) -> C
% Current number of equations to process: 154
% Current number of ordered equations: 0
% Current number of rules: 30
% Rule [5]
% double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))) <->
% inverse(inverse(double_divide(B,inverse(C)))) is composed into [5]
% double_divide(
% double_divide(C,V_3),
% inverse(
% double_divide(B,V_3)))
% <->
% double_divide(B,
% inverse(C))
% New rule produced : [42] inverse(inverse(A)) -> A
% Rule [21] inverse(inverse(double_divide(A,B))) -> double_divide(A,B)
% collapsed.
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [43]
% inverse(double_divide(double_divide(inverse(double_divide(A,B)),C),B)) ->
% double_divide(A,C)
% Rule
% [18]
% inverse(double_divide(double_divide(inverse(double_divide(double_divide(A,B),C)),B),C))
% -> A collapsed.
% Current number of equations to process: 155
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [44] inverse(double_divide(A,inverse(double_divide(a2,inverse(a2))))) -> A
% Current number of equations to process: 157
% Current number of ordered equations: 0
% Current number of rules: 31
% Rule [20]
% double_divide(double_divide(B,C),inverse(double_divide(B,C))) <->
% inverse(double_divide(A,inverse(A))) is composed into [20]
% double_divide(
% double_divide(B,C),
% inverse(double_divide(B,C)))
% <->
% double_divide(A,
% inverse(A))
% New rule produced :
% [45] inverse(double_divide(B,inverse(B))) <-> double_divide(A,inverse(A))
% Rule
% [19]
% inverse(double_divide(A,inverse(A))) <->
% inverse(double_divide(a2,inverse(a2))) collapsed.
% Rule [24] inverse(double_divide(inverse(double_divide(A,inverse(A))),C)) -> C
% collapsed.
% Rule
% [44] inverse(double_divide(A,inverse(double_divide(a2,inverse(a2))))) -> A
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 161
% Current number of ordered equations: 1
% Current number of rules: 29
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 12 rules have been used:
% [1]
% multiply(A,B) -> inverse(double_divide(B,A)); trace = in the starting set
% [2] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,
% inverse(double_divide(C,B))))))
% -> C; trace = in the starting set
% [3] inverse(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C))
% -> A; trace = Self cp of 2
% [4] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C))))
% <-> double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))); trace = Cp of 3 and 2
% [5] double_divide(double_divide(C,V_3),inverse(double_divide(B,V_3))) <->
% inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))); trace = Cp of 3 and 2
% [6] inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(
% double_divide(A,C)))),B))
% -> C; trace = Cp of 5 and 3
% [9] inverse(double_divide(inverse(inverse(double_divide(double_divide(A,B),
% inverse(double_divide(A,B))))),C))
% -> C; trace = Cp of 6 and 5
% [10] inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(
% double_divide(A,B)))),C))
% -> C; trace = Cp of 9 and 4
% [11] inverse(double_divide(double_divide(double_divide(A,B),inverse(double_divide(A,B))),C))
% -> C; trace = Cp of 10 and 4
% [12] inverse(double_divide(double_divide(B,C),inverse(double_divide(A,
% inverse(double_divide(B,C))))))
% -> A; trace = Cp of 11 and 2
% [20] double_divide(double_divide(B,C),inverse(double_divide(B,C))) <->
% inverse(double_divide(A,inverse(A))); trace = Cp of 12 and 11
% [45] inverse(double_divide(B,inverse(B))) <-> double_divide(A,inverse(A)); trace = Cp of 20 and 5
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.060000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------