%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP597-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n038.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 00:23:34 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 : GRP597-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n038.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 21:24:08 CDT 2014
% % CPUTime : 1.14
% Processing problem /tmp/CiME_3102_n038.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b1,a1 : constant; multiply : 2; inverse : 1; double_divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B))))) = C;
% multiply(A,B) = inverse(double_divide(B,A));
% ";
%
% let s1 = status F "
% b1 lr_lex;
% a1 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% double_divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > double_divide > inverse > a1 > b1";
%
% let s2 = status F "
% b1 mul;
% a1 mul;
% multiply mul;
% inverse mul;
% double_divide mul;
% ";
%
% let p2 = precedence F "
% multiply > double_divide > inverse > a1 = b1";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(inverse(a1),a1) = multiply(inverse(b1),b1);"
% ;
% (*
% 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 = { double_divide(double_divide(A,B),inverse(
% double_divide(A,
% inverse(
% double_divide(
% inverse(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(inverse(a1),a1) =
% multiply(inverse(b1),b1) } (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(a1,inverse(a1))) = inverse(double_divide(b1,inverse(b1)))
%
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 1
% New rule produced :
% [2]
% double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(
% inverse(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]
% double_divide(double_divide(double_divide(inverse(A),B),inverse(double_divide(
% inverse(C),B))),
% inverse(C)) -> A
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [4]
% double_divide(double_divide(double_divide(double_divide(inverse(A),B),
% inverse(double_divide(inverse(double_divide(
% inverse(C),V_3)),B))),V_3),
% inverse(A)) -> C
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [5]
% double_divide(A,inverse(double_divide(double_divide(B,C),inverse(double_divide(
% inverse(V_3),
% inverse(
% double_divide(B,
% inverse(
% double_divide(
% inverse(A),C)))))))))
% -> V_3
% Current number of equations to process: 3
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6] double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) -> B
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(A)) -> B
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [8] double_divide(double_divide(A,inverse(A)),inverse(B)) -> B
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% double_divide(A,inverse(B)) <-> double_divide(inverse(B),inverse(inverse(A)))
% Rule
% [3]
% double_divide(double_divide(double_divide(inverse(A),B),inverse(double_divide(
% inverse(C),B))),
% inverse(C)) -> A collapsed.
% Rule
% [4]
% double_divide(double_divide(double_divide(double_divide(inverse(A),B),
% inverse(double_divide(inverse(double_divide(
% inverse(C),V_3)),B))),V_3),
% inverse(A)) -> C collapsed.
% Rule
% [7]
% double_divide(double_divide(inverse(A),inverse(inverse(B))),inverse(A)) -> B
% collapsed.
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [10]
% double_divide(inverse(A),inverse(inverse(double_divide(inverse(A),inverse(
% inverse(B))))))
% -> B
% Current number of equations to process: 30
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [11]
% double_divide(double_divide(double_divide(A,inverse(A)),B),inverse(double_divide(
% inverse(C),B)))
% -> C
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [12] double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) -> A
% Current number of equations to process: 32
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [13]
% double_divide(A,inverse(double_divide(inverse(A),inverse(inverse(inverse(B))))))
% -> B
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [14]
% double_divide(inverse(inverse(B)),inverse(inverse(inverse(double_divide(
% inverse(A),
% inverse(B)))))) ->
% A
% Current number of equations to process: 36
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [15]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) -> A
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [16]
% double_divide(inverse(A),inverse(inverse(inverse(double_divide(inverse(B),
% inverse(inverse(A))))))) ->
% B
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [17]
% double_divide(inverse(C),inverse(inverse(double_divide(double_divide(
% inverse(double_divide(
% inverse(A),B)),
% inverse(inverse(C))),B))))
% -> A
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [18]
% double_divide(double_divide(A,B),inverse(double_divide(inverse(double_divide(
% inverse(C),B)),
% inverse(inverse(A))))) -> C
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [19]
% double_divide(inverse(C),inverse(inverse(double_divide(double_divide(
% inverse(A),B),
% inverse(double_divide(inverse(C),B))))))
% -> A
% Current number of equations to process: 41
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [20]
% double_divide(double_divide(double_divide(double_divide(A,inverse(A)),B),B),
% inverse(C)) -> C
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [21]
% double_divide(inverse(A),inverse(inverse(double_divide(inverse(inverse(B)),
% inverse(inverse(inverse(A))))))) ->
% B
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [22]
% double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),
% inverse(double_divide(
% inverse(A),inverse(B))))))))
% -> C
% Current number of equations to process: 42
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [23]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(inverse(double_divide(A,
% inverse(
% double_divide(
% inverse(B),
% inverse(
% inverse(C))))))))
% -> C
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [24]
% double_divide(inverse(inverse(inverse(A))),inverse(inverse(inverse(inverse(
% double_divide(
% inverse(A),
% inverse(
% inverse(B))))))))
% -> B
% Current number of equations to process: 40
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [25] double_divide(A,inverse(double_divide(inverse(A),inverse(B)))) -> B
% Rule
% [13]
% double_divide(A,inverse(double_divide(inverse(A),inverse(inverse(inverse(B))))))
% -> B collapsed.
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 21
% Rule [9]
% double_divide(A,inverse(B)) <->
% double_divide(inverse(B),inverse(inverse(A))) is composed into [9]
% double_divide(A,
% inverse(B))
% <->
% double_divide(
% inverse(B),A)
% New rule produced : [26] inverse(inverse(B)) -> B
% Rule
% [10]
% double_divide(inverse(A),inverse(inverse(double_divide(inverse(A),inverse(
% inverse(B))))))
% -> B collapsed.
% Rule
% [14]
% double_divide(inverse(inverse(B)),inverse(inverse(inverse(double_divide(
% inverse(A),
% inverse(B)))))) ->
% A collapsed.
% Rule
% [15]
% double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) -> A
% collapsed.
% Rule
% [16]
% double_divide(inverse(A),inverse(inverse(inverse(double_divide(inverse(B),
% inverse(inverse(A))))))) ->
% B collapsed.
% Rule
% [17]
% double_divide(inverse(C),inverse(inverse(double_divide(double_divide(
% inverse(double_divide(
% inverse(A),B)),
% inverse(inverse(C))),B))))
% -> A collapsed.
% Rule
% [18]
% double_divide(double_divide(A,B),inverse(double_divide(inverse(double_divide(
% inverse(C),B)),
% inverse(inverse(A))))) -> C
% collapsed.
% Rule
% [19]
% double_divide(inverse(C),inverse(inverse(double_divide(double_divide(
% inverse(A),B),
% inverse(double_divide(inverse(C),B))))))
% -> A collapsed.
% Rule
% [21]
% double_divide(inverse(A),inverse(inverse(double_divide(inverse(inverse(B)),
% inverse(inverse(inverse(A))))))) ->
% B collapsed.
% Rule
% [23]
% double_divide(inverse(double_divide(A,inverse(B))),inverse(inverse(double_divide(A,
% inverse(
% double_divide(
% inverse(B),
% inverse(
% inverse(C))))))))
% -> C collapsed.
% Rule
% [24]
% double_divide(inverse(inverse(inverse(A))),inverse(inverse(inverse(inverse(
% double_divide(
% inverse(A),
% inverse(
% inverse(B))))))))
% -> B collapsed.
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [27] double_divide(inverse(A),double_divide(B,inverse(B))) -> A
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [28] double_divide(inverse(A),double_divide(inverse(A),B)) -> B
% Current number of equations to process: 50
% Current number of ordered equations: 1
% Current number of rules: 14
% New rule produced :
% [29] double_divide(inverse(A),double_divide(B,inverse(A))) -> B
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [30] double_divide(inverse(A),inverse(double_divide(inverse(B),A))) -> B
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [31]
% double_divide(inverse(C),double_divide(double_divide(inverse(double_divide(
% inverse(A),B)),C),B))
% -> A
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [32]
% double_divide(double_divide(A,B),inverse(double_divide(inverse(double_divide(
% inverse(C),B)),A)))
% -> C
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [33]
% double_divide(inverse(C),double_divide(double_divide(inverse(A),B),inverse(
% double_divide(
% inverse(C),B))))
% -> A
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [34]
% double_divide(inverse(double_divide(A,inverse(B))),double_divide(A,inverse(
% double_divide(
% inverse(B),C))))
% -> C
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [35]
% double_divide(double_divide(A,inverse(double_divide(B,inverse(B)))),inverse(
% double_divide(A,
% inverse(C))))
% -> C
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [36] double_divide(inverse(A),inverse(double_divide(inverse(B),B))) -> A
% Current number of equations to process: 47
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [37] double_divide(inverse(double_divide(A,inverse(A))),inverse(B)) -> B
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [38]
% double_divide(A,inverse(double_divide(double_divide(double_divide(inverse(A),B),B),
% inverse(C)))) -> C
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [39]
% double_divide(inverse(A),inverse(double_divide(double_divide(double_divide(B,
% inverse(B)),C),C)))
% -> A
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [40]
% double_divide(inverse(double_divide(inverse(A),B)),double_divide(double_divide(C,
% inverse(C)),B))
% -> A
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [41]
% double_divide(inverse(A),double_divide(double_divide(double_divide(B,
% inverse(B)),C),C)) -> A
% Current number of equations to process: 49
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [42]
% double_divide(double_divide(double_divide(double_divide(inverse(A),A),B),B),
% inverse(C)) -> C
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [43]
% double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),
% inverse(double_divide(
% inverse(B),inverse(A))))))))
% -> C
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [44]
% double_divide(double_divide(double_divide(double_divide(double_divide(
% double_divide(A,
% inverse(A)),B),B),C),C),
% inverse(V_3)) -> V_3
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 30
% New rule produced :
% [45]
% double_divide(inverse(C),double_divide(inverse(B),double_divide(inverse(A),
% inverse(double_divide(
% inverse(B),C)))))
% -> A
% Current number of equations to process: 47
% Current number of ordered equations: 1
% Current number of rules: 31
% New rule produced :
% [46]
% double_divide(inverse(B),double_divide(A,inverse(double_divide(inverse(B),
% inverse(double_divide(
% inverse(A),C))))))
% -> C
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [47]
% double_divide(A,inverse(double_divide(double_divide(inverse(B),A),inverse(
% double_divide(
% inverse(C),
% inverse(B))))))
% -> C
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [48]
% double_divide(double_divide(inverse(A),B),inverse(double_divide(B,inverse(
% double_divide(
% inverse(C),
% inverse(A))))))
% -> C
% Current number of equations to process: 43
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [49]
% double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,inverse(
% double_divide(
% inverse(B),
% inverse(C))))))
% -> C
% Current number of equations to process: 43
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [50]
% double_divide(double_divide(double_divide(double_divide(double_divide(A,
% inverse(A)),B),B),C),
% inverse(double_divide(inverse(V_3),C))) -> V_3
% Current number of equations to process: 42
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [51] double_divide(inverse(double_divide(inverse(A),inverse(B))),A) -> B
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 37
% New rule produced :
% [52] double_divide(A,inverse(A)) <-> double_divide(B,inverse(B))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 38
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 8 rules have been used:
% [1]
% multiply(A,B) -> inverse(double_divide(B,A)); trace = in the starting set
% [2] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(
% double_divide(
% inverse(C),B)))))
% -> C; trace = in the starting set
% [5] double_divide(A,inverse(double_divide(double_divide(B,C),inverse(
% double_divide(
% inverse(V_3),
% inverse(
% double_divide(B,
% inverse(
% double_divide(
% inverse(A),C)))))))))
% -> V_3; trace = Self cp of 2
% [6] double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) -> B; trace = Self cp of 5
% [8] double_divide(double_divide(A,inverse(A)),inverse(B)) -> B; trace = Cp of 6 and 2
% [12] double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) -> A; trace = Cp of 8 and 6
% [25] double_divide(A,inverse(double_divide(inverse(A),inverse(B)))) -> B; trace = Cp of 12 and 2
% [52] double_divide(A,inverse(A)) <-> double_divide(B,inverse(B)); trace = Cp of 25 and 12
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.040000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------