TSTP Solution File: GRP527-1 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : GRP527-1 : TPTP v6.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n098.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 00:23:24 EDT 2014
% Result : Unsatisfiable 4.37s
% Output : Refutation 4.37s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : GRP527-1 : TPTP v6.0.0. Released v2.6.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n098.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 16:48:28 CDT 2014
% % CPUTime : 4.37
% Processing problem /tmp/CiME_41215_n098.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " c3,b3,a3 : constant; inverse : 1; multiply : 2; divide : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% divide(A,divide(divide(A,B),divide(C,B))) = C;
% multiply(A,B) = divide(A,divide(divide(C,C),B));
% inverse(A) = divide(divide(B,B),A);
% ";
%
% let s1 = status F "
% c3 lr_lex;
% b3 lr_lex;
% a3 lr_lex;
% inverse lr_lex;
% multiply lr_lex;
% divide lr_lex;
% ";
%
% let p1 = precedence F "
% multiply > inverse > divide > a3 > b3 > c3";
%
% let s2 = status F "
% c3 mul;
% b3 mul;
% a3 mul;
% inverse mul;
% multiply mul;
% divide mul;
% ";
%
% let p2 = precedence F "
% multiply > inverse > divide > a3 = b3 = c3";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3));"
% ;
% (*
% 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(A,B),divide(C,B))) = C,
% 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(a3,b3),c3) =
% multiply(a3,multiply(b3,c3)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] inverse(A) <-> divide(divide(B,B),A)
% 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(c3,c3),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(c3,c3),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(a3,divide(divide(c3,c3),b3)),divide(divide(c3,c3),c3)) =
% divide(a3,divide(divide(c3,c3),divide(b3,divide(divide(c3,c3),c3))))
%
% 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(A,B),divide(C,B))) -> C
% Current number of equations to process: 2
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [6] divide(A,A) <-> divide(c3,c3)
% Rule [2] divide(divide(B,B),A) <-> divide(divide(c3,c3),A) collapsed.
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 5
% New rule produced : [7] divide(divide(A,divide(B,C)),C) -> divide(A,B)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [8] divide(A,divide(c3,c3)) -> A
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [9] divide(A,divide(B,B)) -> A
% Rule [8] divide(A,divide(c3,c3)) -> A collapsed.
% Current number of equations to process: 15
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [10] divide(A,divide(A,B)) -> B
% Current number of equations to process: 19
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced : [11] divide(A,A) <-> divide(B,B)
% Rule [3] divide(divide(c3,c3),A) <-> divide(divide(B,B),A) collapsed.
% Rule [6] divide(A,A) <-> divide(c3,c3) collapsed.
% Current number of equations to process: 21
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [12] divide(divide(c3,c3),A) <-> divide(divide(B,A),B)
% Current number of equations to process: 23
% Current number of ordered equations: 1
% Current number of rules: 8
% New rule produced : [13] divide(divide(B,A),B) <-> divide(divide(c3,c3),A)
% Current number of equations to process: 23
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [14] divide(divide(C,B),C) <-> divide(divide(A,A),B)
% Rule [13] divide(divide(B,A),B) <-> divide(divide(c3,c3),A) collapsed.
% Current number of equations to process: 22
% Current number of ordered equations: 1
% Current number of rules: 9
% New rule produced : [15] divide(divide(A,A),B) <-> divide(divide(C,B),C)
% Rule [12] divide(divide(c3,c3),A) <-> divide(divide(B,A),B) collapsed.
% Current number of equations to process: 22
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [16] divide(divide(A,B),divide(C,B)) -> divide(A,C)
% Rule [5] divide(A,divide(divide(A,B),divide(C,B))) -> C collapsed.
% Current number of equations to process: 38
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [17] divide(divide(A,B),C) <-> divide(divide(A,C),B)
% Rule [7] divide(divide(A,divide(B,C)),C) -> divide(A,B) collapsed.
% The conjecture has been reduced.
% Conjecture is now:
% divide(divide(a3,divide(divide(c3,c3),c3)),divide(divide(c3,c3),b3)) =
% divide(a3,divide(divide(c3,c3),divide(b3,divide(divide(c3,c3),c3))))
%
% Current number of equations to process: 46
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced : [18] divide(divide(A,B),A) <-> divide(divide(C,B),C)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [19] divide(A,B) <-> divide(divide(C,C),divide(B,A))
% Current number of equations to process: 64
% Current number of ordered equations: 1
% Current number of rules: 11
% New rule produced : [20] divide(divide(C,C),divide(B,A)) <-> divide(A,B)
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 12
% New rule produced : [21] divide(C,B) <-> divide(A,divide(B,divide(C,A)))
% The conjecture has been reduced.
% Conjecture is now:
% divide(c3,divide(divide(c3,a3),divide(b3,divide(divide(c3,c3),c3)))) =
% divide(a3,divide(divide(c3,c3),divide(b3,divide(divide(c3,c3),c3))))
%
% Current number of equations to process: 75
% Current number of ordered equations: 3
% Current number of rules: 13
% New rule produced : [22] divide(C,B) <-> divide(divide(A,B),divide(A,C))
% Current number of equations to process: 75
% Current number of ordered equations: 2
% Current number of rules: 14
% New rule produced : [23] divide(A,divide(B,divide(C,A))) <-> divide(C,B)
% Current number of equations to process: 75
% Current number of ordered equations: 1
% Current number of rules: 15
% New rule produced : [24] divide(divide(A,B),divide(A,C)) <-> divide(C,B)
% Current number of equations to process: 75
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced : [25] divide(C,divide(B,A)) <-> divide(A,divide(B,C))
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [26] divide(divide(A,divide(B,C)),A) -> divide(C,B)
% Current number of equations to process: 178
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced : [27] divide(A,divide(divide(c3,c3),divide(B,A))) -> B
% Current number of equations to process: 185
% Current number of ordered equations: 0
% Current number of rules: 19
% New rule produced : [28] divide(A,divide(B,divide(C,divide(A,B)))) -> C
% Current number of equations to process: 205
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [29] divide(A,divide(divide(B,B),divide(C,A))) -> C
% Rule [27] divide(A,divide(divide(c3,c3),divide(B,A))) -> B collapsed.
% Current number of equations to process: 237
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced : [30] divide(divide(A,C),divide(divide(B,C),B)) -> A
% Current number of equations to process: 259
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced : [31] divide(divide(c3,c3),divide(divide(B,B),A)) -> A
% Current number of equations to process: 285
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced : [32] divide(divide(B,B),divide(divide(C,C),A)) -> A
% Rule [31] divide(divide(c3,c3),divide(divide(B,B),A)) -> A collapsed.
% Current number of equations to process: 292
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [33] divide(divide(A,divide(B,C)),V_3) -> divide(A,divide(B,divide(C,V_3)))
% Rule [26] divide(divide(A,divide(B,C)),A) -> divide(C,B) collapsed.
% Current number of equations to process: 284
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [34]
% divide(divide(divide(A,A),B),C) <->
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,C),B)))
% Current number of equations to process: 336
% Current number of ordered equations: 1
% Current number of rules: 23
% New rule produced :
% [35]
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,C),B))) <->
% divide(divide(divide(A,A),B),C)
% Current number of equations to process: 336
% Current number of ordered equations: 0
% Current number of rules: 24
% New rule produced :
% [36] divide(A,divide(B,divide(V_3,C))) <-> divide(divide(A,B),divide(C,V_3))
% Current number of equations to process: 444
% Current number of ordered equations: 3
% Current number of rules: 25
% New rule produced :
% [37] divide(A,divide(C,divide(V_3,B))) <-> divide(divide(A,B),divide(C,V_3))
% Current number of equations to process: 444
% Current number of ordered equations: 2
% Current number of rules: 26
% New rule produced :
% [38] divide(divide(A,B),divide(C,V_3)) <-> divide(A,divide(B,divide(V_3,C)))
% Rule [16] divide(divide(A,B),divide(C,B)) -> divide(A,C) collapsed.
% Rule [30] divide(divide(A,C),divide(divide(B,C),B)) -> A collapsed.
% Current number of equations to process: 444
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [39] divide(divide(A,B),divide(A,C)) <-> divide(divide(V_3,V_3),divide(B,C))
% Current number of equations to process: 619
% Current number of ordered equations: 1
% Current number of rules: 26
% New rule produced :
% [40] divide(divide(V_3,V_3),divide(B,C)) <-> divide(divide(A,B),divide(A,C))
% Current number of equations to process: 619
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [41] divide(divide(divide(A,B),C),V_3) <-> divide(divide(divide(A,C),V_3),B)
% Current number of equations to process: 722
% Current number of ordered equations: 1
% Current number of rules: 28
% New rule produced :
% [42] divide(divide(divide(A,C),V_3),B) <-> divide(divide(divide(A,B),C),V_3)
% Current number of equations to process: 722
% Current number of ordered equations: 0
% Current number of rules: 29
% Rule [35]
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,C),B))) <->
% divide(divide(divide(A,A),B),C) is composed into [35]
% divide(divide(c3,V_3),
% divide(c3,divide(
% divide(V_3,C),B)))
% <->
% divide(divide(c3,c3),
% divide(c3,divide(
% divide(c3,B),C)))
% New rule produced :
% [43]
% divide(divide(divide(A,A),B),C) <->
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,B),C)))
% Rule
% [34]
% divide(divide(divide(A,A),B),C) <->
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,C),B))) collapsed.
% Current number of equations to process: 871
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [44]
% divide(divide(c3,c3),divide(c3,divide(divide(c3,B),C))) <->
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,B),C)))
% Current number of equations to process: 870
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced :
% [45]
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,B),C))) <->
% divide(divide(c3,c3),divide(c3,divide(divide(c3,B),C)))
% Current number of equations to process: 870
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [46]
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,C),B))) <->
% divide(divide(divide(A,B),A),C)
% Current number of equations to process: 1076
% Current number of ordered equations: 1
% Current number of rules: 32
% New rule produced :
% [47]
% divide(divide(divide(A,B),A),C) <->
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,C),B)))
% Current number of equations to process: 1076
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [48] divide(divide(A,B),divide(A,C)) <-> divide(V_3,divide(B,divide(C,V_3)))
% Current number of equations to process: 1233
% Current number of ordered equations: 1
% Current number of rules: 34
% New rule produced :
% [49] divide(V_3,divide(B,divide(C,V_3))) <-> divide(divide(A,B),divide(A,C))
% Current number of equations to process: 1233
% Current number of ordered equations: 0
% Current number of rules: 35
% New rule produced :
% [50]
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,B),C))) <->
% divide(divide(divide(A,B),A),C)
% Current number of equations to process: 1411
% Current number of ordered equations: 1
% Current number of rules: 36
% Rule [50]
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,B),C))) <->
% divide(divide(divide(A,B),A),C) is composed into [50]
% divide(divide(c3,V_3),
% divide(c3,divide(
% divide(V_3,B),C)))
% <->
% divide(divide(c3,c3),
% divide(c3,divide(
% divide(c3,B),C)))
% Rule [46]
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,C),B))) <->
% divide(divide(divide(A,B),A),C) is composed into [46]
% divide(divide(c3,V_3),
% divide(c3,divide(
% divide(V_3,C),B)))
% <->
% divide(divide(c3,c3),
% divide(c3,divide(
% divide(c3,B),C)))
% New rule produced :
% [51]
% divide(divide(divide(A,B),A),C) <->
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,B),C)))
% Rule
% [47]
% divide(divide(divide(A,B),A),C) <->
% divide(divide(c3,V_3),divide(c3,divide(divide(V_3,C),B))) collapsed.
% Current number of equations to process: 1411
% Current number of ordered equations: 0
% Current number of rules: 36
% New rule produced :
% [52] divide(V_3,divide(B,divide(C,V_3))) <-> divide(divide(A,A),divide(B,C))
% Current number of equations to process: 1557
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [53] divide(divide(A,A),divide(B,C)) <-> divide(V_3,divide(B,divide(C,V_3)))
% Current number of equations to process: 1557
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [54] divide(A,divide(divide(B,B),C)) <-> divide(V_3,divide(divide(V_3,A),C))
% Current number of equations to process: 1685
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [55] divide(V_3,divide(divide(V_3,A),C)) <-> divide(A,divide(divide(B,B),C))
% The conjecture has been reduced.
% Conjecture is now:
% Trivial
%
% Current number of equations to process: 1685
% Current number of ordered equations: 0
% Current number of rules: 40
% The current conjecture is true and the solution is the identity
% % SZS output start Refutation
%
% The following 13 rules have been used:
% [3]
% divide(divide(c3,c3),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(A,B),divide(C,B))) -> C; trace = in the starting set
% [7] divide(divide(A,divide(B,C)),C) -> divide(A,B); trace = Self cp of 5
% [9] divide(A,divide(B,B)) -> A; trace = Cp of 7 and 3
% [10] divide(A,divide(A,B)) -> B; trace = Cp of 9 and 5
% [11] divide(A,A) <-> divide(B,B); trace = Cp of 10 and 7
% [14] divide(divide(C,B),C) <-> divide(divide(A,A),B); trace = Cp of 11 and 7
% [16] divide(divide(A,B),divide(C,B)) -> divide(A,C); trace = Cp of 10 and 7
% [17] divide(divide(A,B),C) <-> divide(divide(A,C),B); trace = Cp of 16 and 7
% [21] divide(C,B) <-> divide(A,divide(B,divide(C,A))); trace = Cp of 16 and 10
% [23] divide(A,divide(B,divide(C,A))) <-> divide(C,B); trace = Cp of 16 and 10
% [55] divide(V_3,divide(divide(V_3,A),C)) <-> divide(A,divide(divide(B,B),C)); trace = Cp of 23 and 14
% % SZS output end Refutation
% All conjectures have been proven
%
% Execution time: 3.250000 sec
% res : bool = true
% time is now off
%
% status : string = "unsatisfiable"
% % SZS status Unsatisfiable
% CiME interrupted
%
% EOF
%------------------------------------------------------------------------------