TSTP Solution File: GRP553-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP553-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n154.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 00:23:27 EDT 2014
% Result : Unsatisfiable 1.18s
% Output : Refutation 1.18s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP553-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n154.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 19:11:58 CDT 2014
% % CPUTime : 1.18
% Processing problem /tmp/CiME_61783_n154.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " b1,a1 : constant; multiply : 2; inverse : 1; divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B;
% multiply(A,B) = divide(A,inverse(B));
% ";
%
% let s1 = status F "
% b1 lr_lex;
% a1 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > divide > inverse > a1 > b1";
%
% let s2 = status F "
% b1 mul;
% a1 mul;
% multiply mul;
% inverse mul;
% divide mul;
% ";
%
% let p2 = precedence F "
% multiply > 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 = { divide(divide(A,inverse(divide(B,divide(A,C)))),C)
% = B,
% multiply(A,B) = divide(A,inverse(B)) }
% (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) -> divide(A,inverse(B))
% The conjecture has been reduced.
% Conjecture is now:
% divide(inverse(a1),inverse(a1)) = divide(inverse(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] divide(divide(A,inverse(divide(B,divide(A,C)))),C) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [3]
% divide(divide(A,inverse(B)),C) <->
% divide(V_3,inverse(divide(B,divide(V_3,divide(A,C)))))
% Rule [2] divide(divide(A,inverse(divide(B,divide(A,C)))),C) -> B collapsed.
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 2
% New rule produced :
% [4]
% divide(b1,inverse(divide(divide(B,divide(A,C)),divide(b1,divide(A,C))))) -> B
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [5] divide(b1,inverse(divide(divide(A,B),divide(b1,B)))) -> A
% Rule
% [4]
% divide(b1,inverse(divide(divide(B,divide(A,C)),divide(b1,divide(A,C))))) -> B
% collapsed.
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced :
% [6]
% divide(V_3,inverse(divide(divide(divide(B,divide(A,C)),divide(b1,divide(A,
% inverse(
% divide(V_3,B))))),
% divide(V_3,divide(b1,C))))) -> V_3
% Current number of equations to process: 4
% Current number of ordered equations: 0
% Current number of rules: 4
% New rule produced :
% [7] divide(A,divide(B,divide(B,inverse(divide(b1,A))))) -> b1
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [8]
% divide(divide(A,divide(A,inverse(divide(b1,b1)))),divide(B,divide(B,inverse(b1))))
% -> b1
% Current number of equations to process: 29
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [9]
% divide(b1,inverse(divide(b1,divide(b1,divide(A,divide(A,inverse(divide(b1,B))))))))
% -> B
% Current number of equations to process: 33
% Current number of ordered equations: 2
% Current number of rules: 7
% New rule produced :
% [10]
% divide(b1,inverse(divide(divide(A,divide(B,divide(B,inverse(divide(b1,b1))))),b1)))
% -> A
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [11]
% divide(inverse(divide(divide(A,B),divide(b1,B))),divide(C,divide(C,inverse(A))))
% -> b1
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [12]
% divide(b1,divide(B,divide(B,inverse(divide(b1,A))))) <->
% divide(b1,inverse(divide(b1,divide(b1,divide(b1,A)))))
% Current number of equations to process: 37
% Current number of ordered equations: 1
% Current number of rules: 10
% New rule produced :
% [13]
% divide(b1,inverse(divide(b1,divide(b1,divide(b1,A))))) <->
% divide(b1,divide(B,divide(B,inverse(divide(b1,A)))))
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [14] divide(b1,inverse(divide(b1,b1))) -> b1
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [15]
% divide(divide(b1,divide(A,divide(A,inverse(divide(b1,B))))),divide(b1,B)) ->
% b1
% Current number of equations to process: 44
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [16] inverse(divide(divide(divide(b1,b1),A),divide(b1,A))) -> b1
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [17]
% divide(b1,divide(A,divide(A,inverse(B)))) <->
% divide(b1,inverse(divide(b1,divide(b1,B))))
% Rule
% [12]
% divide(b1,divide(B,divide(B,inverse(divide(b1,A))))) <->
% divide(b1,inverse(divide(b1,divide(b1,divide(b1,A))))) collapsed.
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [18]
% inverse(divide(b1,divide(b1,divide(b1,B)))) <->
% divide(A,divide(A,inverse(divide(b1,B))))
% Rule
% [13]
% divide(b1,inverse(divide(b1,divide(b1,divide(b1,A))))) <->
% divide(b1,divide(B,divide(B,inverse(divide(b1,A))))) collapsed.
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced : [19] divide(b1,divide(b1,b1)) -> b1
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [20] divide(divide(b1,b1),divide(A,divide(A,inverse(b1)))) -> b1
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [21] divide(b1,inverse(divide(divide(A,divide(b1,b1)),b1))) -> A
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced :
% [22] divide(inverse(divide(b1,b1)),divide(A,divide(A,inverse(b1)))) -> b1
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [23]
% divide(B,inverse(divide(divide(b1,b1),divide(B,divide(b1,A))))) ->
% divide(b1,A)
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [24] divide(divide(b1,divide(A,divide(A,inverse(B)))),B) -> b1
% Rule
% [15]
% divide(divide(b1,divide(A,divide(A,inverse(divide(b1,B))))),divide(b1,B)) ->
% b1 collapsed.
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [25] inverse(divide(b1,divide(b1,A))) <-> divide(B,divide(B,inverse(A)))
% Rule
% [18]
% inverse(divide(b1,divide(b1,divide(b1,B)))) <->
% divide(A,divide(A,inverse(divide(b1,B)))) collapsed.
% Current number of equations to process: 106
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [26] divide(B,divide(B,inverse(A))) <-> inverse(divide(b1,divide(b1,A)))
% Rule
% [17]
% divide(b1,divide(A,divide(A,inverse(B)))) <->
% divide(b1,inverse(divide(b1,divide(b1,B)))) collapsed.
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [27] inverse(divide(divide(divide(b1,b1),divide(b1,b1)),b1)) -> b1
% Current number of equations to process: 113
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [28] inverse(divide(b1,divide(b1,divide(A,divide(A,inverse(b1)))))) -> b1
% Current number of equations to process: 117
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [29] inverse(divide(b1,b1)) -> divide(b1,b1)
% Rule
% [8]
% divide(divide(A,divide(A,inverse(divide(b1,b1)))),divide(B,divide(B,inverse(b1))))
% -> b1 collapsed.
% Rule
% [10]
% divide(b1,inverse(divide(divide(A,divide(B,divide(B,inverse(divide(b1,b1))))),b1)))
% -> A collapsed.
% Rule [14] divide(b1,inverse(divide(b1,b1))) -> b1 collapsed.
% Rule
% [22] divide(inverse(divide(b1,b1)),divide(A,divide(A,inverse(b1)))) -> b1
% collapsed.
% Current number of equations to process: 129
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [30] divide(b1,divide(A,divide(A,divide(b1,b1)))) -> b1
% Current number of equations to process: 128
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [31] divide(A,inverse(divide(divide(b1,b1),divide(A,B)))) -> B
% Rule
% [23]
% divide(B,inverse(divide(divide(b1,b1),divide(B,divide(b1,A))))) ->
% divide(b1,A) collapsed.
% Current number of equations to process: 130
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [32] divide(A,divide(A,inverse(b1))) -> inverse(b1)
% Rule [20] divide(divide(b1,b1),divide(A,divide(A,inverse(b1)))) -> b1
% collapsed.
% Rule
% [28] inverse(divide(b1,divide(b1,divide(A,divide(A,inverse(b1)))))) -> b1
% collapsed.
% Current number of equations to process: 161
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [33] inverse(inverse(b1)) -> b1
% Current number of equations to process: 160
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [34] divide(divide(b1,b1),inverse(b1)) -> b1
% Current number of equations to process: 159
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [35] divide(A,divide(A,divide(b1,b1))) -> divide(b1,b1)
% Rule [30] divide(b1,divide(A,divide(A,divide(b1,b1)))) -> b1 collapsed.
% Current number of equations to process: 158
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [36] divide(A,inverse(divide(b1,divide(b1,divide(b1,A))))) -> b1
% Current number of equations to process: 174
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [37]
% inverse(inverse(divide(b1,divide(b1,A)))) <->
% divide(B,divide(B,inverse(inverse(A))))
% Current number of equations to process: 184
% Current number of ordered equations: 1
% Current number of rules: 22
% New rule produced :
% [38]
% divide(B,divide(B,inverse(inverse(A)))) <->
% inverse(inverse(divide(b1,divide(b1,A))))
% Current number of equations to process: 184
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [39] divide(divide(A,divide(b1,b1)),B) -> divide(A,B)
% Rule [21] divide(b1,inverse(divide(divide(A,divide(b1,b1)),b1))) -> A
% collapsed.
% Rule [27] inverse(divide(divide(divide(b1,b1),divide(b1,b1)),b1)) -> b1
% collapsed.
% Current number of equations to process: 191
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [40] divide(b1,inverse(divide(A,b1))) -> A
% Current number of equations to process: 190
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced : [41] inverse(divide(divide(b1,b1),b1)) -> b1
% Current number of equations to process: 189
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [42] divide(B,divide(B,inverse(divide(b1,A)))) <-> divide(A,b1)
% Current number of equations to process: 195
% Current number of ordered equations: 1
% Current number of rules: 25
% New rule produced :
% [43] divide(A,b1) <-> divide(B,divide(B,inverse(divide(b1,A))))
% Rule [41] inverse(divide(divide(b1,b1),b1)) -> b1 collapsed.
% Current number of equations to process: 195
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [44] divide(A,divide(A,inverse(B))) <-> divide(C,divide(C,inverse(B)))
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [45]
% inverse(divide(divide(A,B),divide(b1,B))) <->
% divide(b1,inverse(divide(divide(b1,b1),A)))
% Rule [16] inverse(divide(divide(divide(b1,b1),A),divide(b1,A))) -> b1
% collapsed.
% Current number of equations to process: 196
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [46]
% divide(b1,inverse(divide(divide(b1,b1),A))) <->
% inverse(divide(divide(A,B),divide(b1,B)))
% Current number of equations to process: 196
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [47] divide(A,divide(A,b1)) -> b1
% Rule [19] divide(b1,divide(b1,b1)) -> b1 collapsed.
% Current number of equations to process: 216
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [48] divide(inverse(divide(divide(b1,A),divide(b1,A))),inverse(b1)) -> b1
% Current number of equations to process: 217
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced : [49] divide(A,divide(b1,b1)) -> A
% Rule [35] divide(A,divide(A,divide(b1,b1))) -> divide(b1,b1) collapsed.
% Rule [39] divide(divide(A,divide(b1,b1)),B) -> divide(A,B) collapsed.
% Current number of equations to process: 220
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced : [50] divide(A,A) <-> divide(b1,b1)
% Rule
% [48] divide(inverse(divide(divide(b1,A),divide(b1,A))),inverse(b1)) -> b1
% collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 219
% Current number of ordered equations: 1
% Current number of rules: 27
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 13 rules have been used:
% [1]
% multiply(A,B) -> divide(A,inverse(B)); trace = in the starting set
% [2] divide(divide(A,inverse(divide(B,divide(A,C)))),C) -> B; trace = in the starting set
% [4] divide(b1,inverse(divide(divide(B,divide(A,C)),divide(b1,divide(A,C)))))
% -> B; trace = in the starting set
% [5] divide(b1,inverse(divide(divide(A,B),divide(b1,B)))) -> A; trace = Self cp of 4
% [6] divide(V_3,inverse(divide(divide(divide(B,divide(A,C)),divide(b1,
% divide(A,inverse(
% divide(V_3,B))))),
% divide(V_3,divide(b1,C))))) -> V_3; trace = Self cp of 2
% [7] divide(A,divide(B,divide(B,inverse(divide(b1,A))))) -> b1; trace = Cp of 6 and 5
% [9] divide(b1,inverse(divide(b1,divide(b1,divide(A,divide(A,inverse(divide(b1,B))))))))
% -> B; trace = Cp of 7 and 5
% [12] divide(b1,divide(B,divide(B,inverse(divide(b1,A))))) <->
% divide(b1,inverse(divide(b1,divide(b1,divide(b1,A))))); trace = Self cp of 9
% [14] divide(b1,inverse(divide(b1,b1))) -> b1; trace = Cp of 9 and 7
% [17] divide(b1,divide(A,divide(A,inverse(B)))) <->
% divide(b1,inverse(divide(b1,divide(b1,B)))); trace = Cp of 12 and 5
% [19] divide(b1,divide(b1,b1)) -> b1; trace = Cp of 14 and 7
% [25] inverse(divide(b1,divide(b1,A))) <-> divide(B,divide(B,inverse(A))); trace = Cp of 17 and 9
% [50] divide(A,A) <-> divide(b1,b1); trace = Cp of 25 and 19
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 0.080000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------