TSTP Solution File: GRP467-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP467-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n134.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 00:23:14 EDT 2014
% Result : Unsatisfiable 3.08s
% Output : Refutation 3.08s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP467-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n134.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 14:01:28 CDT 2014
% % CPUTime : 3.08
% Processing problem /tmp/CiME_54061_n134.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " a2,b2 : constant; multiply : 2; inverse : 1; divide : 2;";
% let X = vars "A B C D";
% let Axioms = equations F X "
% divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = C;
% multiply(A,B) = divide(A,inverse(B));
% ";
%
% let s1 = status F "
% a2 lr_lex;
% b2 lr_lex;
% multiply lr_lex;
% inverse lr_lex;
% divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > divide > inverse > b2 > a2";
%
% let s2 = status F "
% a2 mul;
% b2 mul;
% multiply mul;
% inverse mul;
% divide mul;
% ";
%
% let p2 = precedence F "
% multiply > 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 = { divide(divide(A,A),divide(B,divide(divide(C,
% divide(D,B)),
% inverse(D)))) = C,
% 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(multiply(inverse(b2),b2),a2) = a2 }
% (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(divide(inverse(b2),inverse(b2)),inverse(a2)) = a2
%
% 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,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) -> C
% 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,A),divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,
% inverse(D))))
% <-> divide(V_4,V_4)
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 3
% New rule produced : [4] divide(a2,a2) <-> divide(V_4,V_4)
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 4
% New rule produced : [5] divide(V_4,V_4) <-> divide(a2,a2)
% The conjecture has been reduced.
% Conjecture is now:
% divide(divide(a2,a2),inverse(a2)) = a2
%
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced :
% [6]
% divide(divide(A,A),divide(a2,divide(divide(B,divide(C,C)),inverse(a2)))) -> B
% Current number of equations to process: 6
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced :
% [7]
% divide(C,B) <->
% divide(divide(A,A),divide(B,divide(divide(a2,a2),inverse(C))))
% Rule
% [3]
% divide(divide(A,A),divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,
% inverse(D))))
% <-> divide(V_4,V_4) collapsed.
% Current number of equations to process: 9
% Current number of ordered equations: 1
% Current number of rules: 6
% New rule produced :
% [8]
% divide(divide(A,A),divide(B,divide(divide(a2,a2),inverse(C)))) <->
% divide(C,B)
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [9]
% divide(divide(A,A),divide(B,divide(divide(C,divide(a2,a2)),inverse(B)))) -> C
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [10]
% divide(divide(A,A),divide(B,divide(divide(C,C),inverse(D)))) <-> divide(D,B)
% Rule
% [8]
% divide(divide(A,A),divide(B,divide(divide(a2,a2),inverse(C)))) <->
% divide(C,B) collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [11]
% divide(divide(A,A),divide(B,divide(divide(C,divide(D,D)),inverse(B)))) -> C
% Rule
% [6]
% divide(divide(A,A),divide(a2,divide(divide(B,divide(C,C)),inverse(a2)))) -> B
% collapsed.
% Rule
% [9]
% divide(divide(A,A),divide(B,divide(divide(C,divide(a2,a2)),inverse(B)))) -> C
% collapsed.
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced :
% [12]
% divide(divide(A,A),divide(a2,a2)) <->
% divide(B,divide(divide(C,C),inverse(B)))
% Current number of equations to process: 18
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced :
% [13]
% divide(B,divide(divide(C,C),inverse(B))) <->
% divide(divide(A,A),divide(a2,a2))
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [14] divide(A,A) <-> divide(B,B)
% Rule [4] divide(a2,a2) <-> divide(V_4,V_4) collapsed.
% Rule [5] divide(V_4,V_4) <-> divide(a2,a2) collapsed.
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [15] divide(C,C) <-> divide(divide(A,A),divide(divide(B,B),divide(a2,a2)))
% Current number of equations to process: 33
% Current number of ordered equations: 1
% Current number of rules: 9
% Rule [15]
% divide(C,C) <-> divide(divide(A,A),divide(divide(B,B),divide(a2,a2))) is composed into
% [15] divide(C,C) <-> divide(a2,a2)
% New rule produced :
% [16] divide(divide(A,A),divide(divide(B,B),divide(a2,a2))) <-> divide(C,C)
% Current number of equations to process: 33
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced :
% [17] divide(C,C) <-> divide(A,divide(divide(B,B),inverse(A)))
% Current number of equations to process: 35
% Current number of ordered equations: 1
% Current number of rules: 11
% Rule [17] divide(C,C) <-> divide(A,divide(divide(B,B),inverse(A))) is composed into
% [17] divide(C,C) <-> divide(a2,a2)
% Rule [12]
% divide(divide(A,A),divide(a2,a2)) <->
% divide(B,divide(divide(C,C),inverse(B))) is composed into [12]
% divide(
% divide(A,A),
% divide(a2,a2))
% <->
% divide(C,C)
% New rule produced :
% [18] divide(A,divide(divide(B,B),inverse(A))) <-> divide(C,C)
% Rule
% [13]
% divide(B,divide(divide(C,C),inverse(B))) <->
% divide(divide(A,A),divide(a2,a2)) collapsed.
% Current number of equations to process: 35
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced : [19] divide(C,C) <-> divide(divide(A,A),divide(B,B))
% Current number of equations to process: 34
% Current number of ordered equations: 1
% Current number of rules: 12
% Rule [19] divide(C,C) <-> divide(divide(A,A),divide(B,B)) is composed into
% [19] divide(C,C) <-> divide(a2,a2)
% New rule produced : [20] divide(divide(A,A),divide(B,B)) <-> divide(C,C)
% Rule [12] divide(divide(A,A),divide(a2,a2)) <-> divide(C,C) collapsed.
% Rule
% [16] divide(divide(A,A),divide(divide(B,B),divide(a2,a2))) <-> divide(C,C)
% collapsed.
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [21]
% divide(divide(A,A),divide(divide(B,B),divide(divide(a2,a2),inverse(divide(C,C)))))
% <-> divide(D,D)
% Current number of equations to process: 34
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [22]
% divide(divide(A,A),divide(divide(B,B),divide(divide(C,C),inverse(divide(D,D)))))
% <-> divide(V_4,V_4)
% Rule
% [21]
% divide(divide(A,A),divide(divide(B,B),divide(divide(a2,a2),inverse(divide(C,C)))))
% <-> divide(D,D) collapsed.
% Current number of equations to process: 37
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced :
% [23]
% divide(divide(A,A),divide(divide(a2,a2),divide(divide(B,inverse(a2)),
% divide(divide(a2,a2),inverse(
% divide(divide(B,
% divide(C,C)),
% inverse(a2)))))))
% <-> divide(D,D)
% Current number of equations to process: 39
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [24]
% divide(A,divide(divide(B,B),divide(inverse(A),divide(divide(a2,a2),inverse(
% divide(C,C))))))
% <-> divide(D,D)
% Current number of equations to process: 47
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [25]
% divide(A,divide(divide(B,B),divide(inverse(A),divide(divide(C,C),inverse(
% divide(D,D))))))
% <-> divide(V_4,V_4)
% Rule
% [24]
% divide(A,divide(divide(B,B),divide(inverse(A),divide(divide(a2,a2),inverse(
% divide(C,C))))))
% <-> divide(D,D) collapsed.
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [26]
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(inverse(D),divide(
% divide(a2,a2),
% inverse(
% divide(V_4,V_4)))))))
% <-> divide(D,B)
% Current number of equations to process: 45
% Current number of ordered equations: 3
% Current number of rules: 15
% New rule produced :
% [27]
% divide(divide(A,A),divide(divide(B,B),divide(divide(divide(C,C),inverse(D)),
% divide(divide(a2,a2),inverse(V_4)))))
% -> divide(D,V_4)
% Current number of equations to process: 45
% Current number of ordered equations: 2
% Current number of rules: 16
% New rule produced :
% [28]
% divide(divide(A,A),divide(divide(B,divide(divide(C,C),inverse(D))),divide(
% divide(a2,a2),
% inverse(
% divide(V_4,V_4)))))
% -> divide(D,B)
% Current number of equations to process: 45
% Current number of ordered equations: 1
% Current number of rules: 17
% New rule produced :
% [29]
% divide(D,B) <->
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(inverse(D),divide(
% divide(a2,a2),
% inverse(
% divide(V_4,V_4)))))))
% Current number of equations to process: 45
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [30]
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(inverse(D),divide(
% divide(V_4,V_4),
% inverse(
% divide(V_5,V_5)))))))
% <-> divide(D,B)
% Rule
% [26]
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(inverse(D),divide(
% divide(a2,a2),
% inverse(
% divide(V_4,V_4)))))))
% <-> divide(D,B) collapsed.
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [31]
% divide(divide(A,A),divide(divide(B,B),divide(divide(divide(C,C),inverse(D)),
% divide(divide(V_4,V_4),inverse(V_5)))))
% -> divide(D,V_5)
% Rule
% [27]
% divide(divide(A,A),divide(divide(B,B),divide(divide(divide(C,C),inverse(D)),
% divide(divide(a2,a2),inverse(V_4)))))
% -> divide(D,V_4) collapsed.
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [32]
% divide(divide(A,A),divide(divide(B,divide(divide(C,C),inverse(D))),divide(
% divide(V_4,V_4),
% inverse(
% divide(V_5,V_5)))))
% -> divide(D,B)
% Rule
% [28]
% divide(divide(A,A),divide(divide(B,divide(divide(C,C),inverse(D))),divide(
% divide(a2,a2),
% inverse(
% divide(V_4,V_4)))))
% -> divide(D,B) collapsed.
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [33]
% divide(divide(A,A),divide(divide(B,divide(divide(C,divide(D,B)),inverse(D))),
% divide(divide(V_4,C),inverse(divide(V_5,V_5))))) -> V_4
% Current number of equations to process: 113
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced :
% [34]
% divide(divide(A,A),divide(divide(B,inverse(C)),divide(divide(D,D),inverse(
% divide(
% divide(B,
% divide(V_4,C)),
% inverse(V_4))))))
% <-> divide(V_5,V_5)
% Current number of equations to process: 146
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [35]
% divide(divide(A,inverse(B)),divide(divide(C,C),inverse(divide(divide(A,
% divide(D,B)),
% inverse(D))))) <->
% divide(V_4,V_4)
% Rule
% [34]
% divide(divide(A,A),divide(divide(B,inverse(C)),divide(divide(D,D),inverse(
% divide(
% divide(B,
% divide(V_4,C)),
% inverse(V_4))))))
% <-> divide(V_5,V_5) collapsed.
% Current number of equations to process: 162
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [36]
% divide(V_4,V_4) <->
% divide(divide(divide(A,A),inverse(B)),divide(divide(C,C),inverse(divide(
% divide(D,D),
% inverse(B)))))
% Current number of equations to process: 181
% Current number of ordered equations: 1
% Current number of rules: 21
% Rule [36]
% divide(V_4,V_4) <->
% divide(divide(divide(A,A),inverse(B)),divide(divide(C,C),inverse(
% divide(
% divide(D,D),
% inverse(B))))) is composed into
% [36] divide(V_4,V_4) <-> divide(a2,a2)
% New rule produced :
% [37]
% divide(divide(divide(A,A),inverse(B)),divide(divide(C,C),inverse(divide(
% divide(D,D),
% inverse(B)))))
% <-> divide(V_4,V_4)
% Current number of equations to process: 181
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [38]
% divide(D,D) <->
% divide(divide(A,inverse(B)),divide(divide(C,C),inverse(divide(divide(A,
% divide(a2,a2)),
% inverse(B)))))
% Current number of equations to process: 180
% Current number of ordered equations: 1
% Current number of rules: 23
% Rule [38]
% divide(D,D) <->
% divide(divide(A,inverse(B)),divide(divide(C,C),inverse(divide(divide(A,
% divide(a2,a2)),
% inverse(B))))) is composed into
% [38] divide(D,D) <-> divide(a2,a2)
% New rule produced :
% [39]
% divide(divide(A,inverse(B)),divide(divide(C,C),inverse(divide(divide(A,
% divide(a2,a2)),
% inverse(B))))) <->
% divide(D,D)
% Current number of equations to process: 180
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [40]
% divide(divide(A,inverse(B)),divide(divide(C,C),inverse(divide(divide(A,
% divide(D,D)),
% inverse(B))))) <->
% divide(V_4,V_4)
% Rule
% [23]
% divide(divide(A,A),divide(divide(a2,a2),divide(divide(B,inverse(a2)),
% divide(divide(a2,a2),inverse(
% divide(divide(B,
% divide(C,C)),
% inverse(a2)))))))
% <-> divide(D,D) collapsed.
% Rule
% [39]
% divide(divide(A,inverse(B)),divide(divide(C,C),inverse(divide(divide(A,
% divide(a2,a2)),
% inverse(B))))) <->
% divide(D,D) collapsed.
% Current number of equations to process: 179
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [41]
% divide(divide(divide(A,A),inverse(B)),divide(divide(C,C),inverse(B))) ->
% divide(a2,a2)
% Current number of equations to process: 187
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [42]
% divide(divide(A,A),divide(divide(a2,divide(divide(B,divide(C,C)),inverse(a2))),
% divide(divide(D,B),inverse(divide(V_4,V_4))))) -> D
% Current number of equations to process: 206
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [43]
% divide(divide(A,A),divide(divide(a2,a2),divide(divide(B,divide(C,C)),
% inverse(divide(D,D))))) -> B
% Current number of equations to process: 210
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [44]
% divide(divide(A,A),divide(divide(B,B),divide(divide(C,divide(D,D)),inverse(
% divide(V_4,V_4)))))
% -> C
% Rule
% [43]
% divide(divide(A,A),divide(divide(a2,a2),divide(divide(B,divide(C,C)),
% inverse(divide(D,D))))) -> B
% collapsed.
% Current number of equations to process: 229
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [45]
% divide(divide(A,A),divide(a2,divide(divide(a2,a2),divide(inverse(a2),
% divide(divide(a2,a2),
% inverse(divide(B,divide(a2,a2))))))))
% -> B
% Current number of equations to process: 236
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [46]
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(inverse(D),divide(
% divide(a2,a2),
% inverse(
% divide(V_4,
% divide(D,B))))))))
% -> V_4
% Rule
% [45]
% divide(divide(A,A),divide(a2,divide(divide(a2,a2),divide(inverse(a2),
% divide(divide(a2,a2),
% inverse(divide(B,divide(a2,a2))))))))
% -> B collapsed.
% Current number of equations to process: 241
% Current number of ordered equations: 1
% Current number of rules: 27
% New rule produced :
% [47]
% divide(divide(B,B),divide(divide(C,divide(divide(A,divide(D,C)),inverse(D))),
% divide(divide(a2,a2),inverse(divide(V_4,V_4))))) -> A
% Current number of equations to process: 241
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [48]
% divide(divide(A,A),divide(divide(B,B),inverse(divide(C,C)))) <-> divide(D,D)
% Rule
% [22]
% divide(divide(A,A),divide(divide(B,B),divide(divide(C,C),inverse(divide(D,D)))))
% <-> divide(V_4,V_4) collapsed.
% Current number of equations to process: 297
% Current number of ordered equations: 0
% Current number of rules: 28
% Rule [29]
% divide(D,B) <->
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(inverse(D),
% divide(divide(a2,a2),
% inverse(divide(V_4,V_4))))))) is composed into
% [29] divide(D,B) <-> divide(divide(A,A),divide(B,D))
% New rule produced :
% [49]
% divide(divide(A,A),divide(inverse(B),divide(divide(C,C),inverse(divide(D,D)))))
% -> B
% Rule
% [25]
% divide(A,divide(divide(B,B),divide(inverse(A),divide(divide(C,C),inverse(
% divide(D,D))))))
% <-> divide(V_4,V_4) collapsed.
% Rule
% [30]
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(inverse(D),divide(
% divide(V_4,V_4),
% inverse(
% divide(V_5,V_5)))))))
% <-> divide(D,B) collapsed.
% Current number of equations to process: 299
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [50]
% divide(divide(A,A),divide(divide(B,divide(divide(C,divide(D,B)),inverse(D))),
% divide(V_4,V_4))) -> C
% Current number of equations to process: 304
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [51]
% divide(divide(A,A),divide(divide(divide(B,B),C),divide(divide(a2,a2),
% inverse(divide(D,D))))) -> C
% Current number of equations to process: 313
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced : [52] inverse(divide(A,A)) <-> divide(B,B)
% Current number of equations to process: 315
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced : [53] divide(B,B) <-> inverse(divide(A,A))
% Current number of equations to process: 315
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [54]
% divide(divide(A,A),divide(divide(divide(B,B),inverse(divide(C,C))),divide(D,D)))
% <-> divide(V_4,V_4)
% Current number of equations to process: 315
% Current number of ordered equations: 2
% Current number of rules: 32
% New rule produced :
% [55]
% divide(divide(A,A),divide(divide(B,B),divide(inverse(divide(C,C)),divide(D,D))))
% <-> divide(V_4,V_4)
% Current number of equations to process: 315
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [56] divide(divide(A,A),divide(inverse(B),divide(C,C))) -> B
% Rule
% [55]
% divide(divide(A,A),divide(divide(B,B),divide(inverse(divide(C,C)),divide(D,D))))
% <-> divide(V_4,V_4) collapsed.
% Current number of equations to process: 319
% Current number of ordered equations: 0
% Current number of rules: 33
% Rule [7]
% divide(C,B) <->
% divide(divide(A,A),divide(B,divide(divide(a2,a2),inverse(C)))) is composed into
% [7] divide(C,B) <-> divide(divide(A,A),divide(B,C))
% New rule produced : [57] divide(divide(A,A),inverse(B)) -> B
% Rule
% [10]
% divide(divide(A,A),divide(B,divide(divide(C,C),inverse(D)))) <-> divide(D,B)
% collapsed.
% Rule [18] divide(A,divide(divide(B,B),inverse(A))) <-> divide(C,C) collapsed.
% Rule
% [31]
% divide(divide(A,A),divide(divide(B,B),divide(divide(divide(C,C),inverse(D)),
% divide(divide(V_4,V_4),inverse(V_5)))))
% -> divide(D,V_5) collapsed.
% Rule
% [32]
% divide(divide(A,A),divide(divide(B,divide(divide(C,C),inverse(D))),divide(
% divide(V_4,V_4),
% inverse(
% divide(V_5,V_5)))))
% -> divide(D,B) collapsed.
% Rule
% [35]
% divide(divide(A,inverse(B)),divide(divide(C,C),inverse(divide(divide(A,
% divide(D,B)),
% inverse(D))))) <->
% divide(V_4,V_4) collapsed.
% Rule
% [37]
% divide(divide(divide(A,A),inverse(B)),divide(divide(C,C),inverse(divide(
% divide(D,D),
% inverse(B)))))
% <-> divide(V_4,V_4) collapsed.
% Rule
% [40]
% divide(divide(A,inverse(B)),divide(divide(C,C),inverse(divide(divide(A,
% divide(D,D)),
% inverse(B))))) <->
% divide(V_4,V_4) collapsed.
% Rule
% [41]
% divide(divide(divide(A,A),inverse(B)),divide(divide(C,C),inverse(B))) ->
% divide(a2,a2) collapsed.
% Rule
% [46]
% divide(divide(A,A),divide(B,divide(divide(C,C),divide(inverse(D),divide(
% divide(a2,a2),
% inverse(
% divide(V_4,
% divide(D,B))))))))
% -> V_4 collapsed.
% Rule
% [47]
% divide(divide(B,B),divide(divide(C,divide(divide(A,divide(D,C)),inverse(D))),
% divide(divide(a2,a2),inverse(divide(V_4,V_4))))) -> A
% collapsed.
% Rule
% [48]
% divide(divide(A,A),divide(divide(B,B),inverse(divide(C,C)))) <-> divide(D,D)
% collapsed.
% Rule
% [49]
% divide(divide(A,A),divide(inverse(B),divide(divide(C,C),inverse(divide(D,D)))))
% -> B collapsed.
% Rule
% [51]
% divide(divide(A,A),divide(divide(divide(B,B),C),divide(divide(a2,a2),
% inverse(divide(D,D))))) -> C
% collapsed.
% Rule
% [54]
% divide(divide(A,A),divide(divide(divide(B,B),inverse(divide(C,C))),divide(D,D)))
% <-> divide(V_4,V_4) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 326
% Current number of ordered equations: 0
% Current number of rules: 20
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 17 rules have been used:
% [1]
% multiply(A,B) -> divide(A,inverse(B)); trace = in the starting set
% [2] divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) ->
% C; trace = in the starting set
% [4] divide(a2,a2) <-> divide(V_4,V_4); trace = Self cp of 2
% [5] divide(V_4,V_4) <-> divide(a2,a2); trace = Self cp of 2
% [7] divide(C,B) <->
% divide(divide(A,A),divide(B,divide(divide(a2,a2),inverse(C)))); trace = Cp of 5 and 2
% [8] divide(divide(A,A),divide(B,divide(divide(a2,a2),inverse(C)))) <->
% divide(C,B); trace = Cp of 5 and 2
% [9] divide(divide(A,A),divide(B,divide(divide(C,divide(a2,a2)),inverse(B))))
% -> C; trace = Cp of 5 and 2
% [10] divide(divide(A,A),divide(B,divide(divide(C,C),inverse(D)))) <->
% divide(D,B); trace = Cp of 8 and 4
% [11] divide(divide(A,A),divide(B,divide(divide(C,divide(D,D)),inverse(B))))
% -> C; trace = Cp of 9 and 4
% [12] divide(divide(A,A),divide(a2,a2)) <->
% divide(B,divide(divide(C,C),inverse(B))); trace = Cp of 10 and 5
% [14] divide(A,A) <-> divide(B,B); trace = Cp of 11 and 5
% [18] divide(A,divide(divide(B,B),inverse(A))) <-> divide(C,C); trace = Cp of 14 and 12
% [24] divide(A,divide(divide(B,B),divide(inverse(A),divide(divide(a2,a2),
% inverse(divide(C,C))))))
% <-> divide(D,D); trace = Cp of 18 and 7
% [25] divide(A,divide(divide(B,B),divide(inverse(A),divide(divide(C,C),
% inverse(divide(D,D))))))
% <-> divide(V_4,V_4); trace = Cp of 24 and 14
% [47] divide(divide(B,B),divide(divide(C,divide(divide(A,divide(D,C)),
% inverse(D))),divide(divide(a2,a2),
% inverse(divide(V_4,V_4)))))
% -> A; trace = Cp of 7 and 2
% [49] divide(divide(A,A),divide(inverse(B),divide(divide(C,C),inverse(
% divide(D,D)))))
% -> B; trace = Cp of 47 and 25
% [57] divide(divide(A,A),inverse(B)) -> B; trace = Cp of 49 and 7
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 1.970000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------