TSTP Solution File: CAT010-10 by CiME---2.01
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%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : CAT010-10 : TPTP v7.3.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n184.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.5MB
% OS : Linux 3.10.0-862.11.6.el7.x86_64
% CPULimit : 300s
% DateTime : Wed Feb 27 11:42:43 EST 2019
% Result : Unsatisfiable 1.22s
% Output : Refutation 1.22s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CAT010-10 : TPTP v7.3.0. Released v7.3.0.
% 0.00/0.04 % Command : tptp2X_and_run_cime %s
% 0.03/0.25 % Computer : n184.star.cs.uiowa.edu
% 0.03/0.25 % Model : x86_64 x86_64
% 0.03/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.25 % Memory : 32218.5MB
% 0.03/0.25 % OS : Linux 3.10.0-862.11.6.el7.x86_64
% 0.03/0.25 % CPULimit : 300
% 0.03/0.25 % DateTime : Mon Feb 18 11:35:41 CST 2019
% 0.03/0.25 % CPUTime :
% 1.15/1.40 Processing problem /tmp/CiME_5567_n184.star.cs.uiowa.edu
% 1.15/1.40 #verbose 1;
% 1.15/1.40 let F = signature " b,a,true : constant; compose : 2; codomain : 1; domain : 1; there_exists : 1; equivalent : 2; ifeq : 4; ifeq2 : 4; ifeq3 : 4;";
% 1.15/1.40 let X = vars "A B C X Y Z";
% 1.15/1.40 let Axioms = equations F X "
% 1.15/1.40 compose(compose(A,B),C) = compose(A,compose(B,C));
% 1.15/1.40 ifeq3(A,A,B,C) = B;
% 1.15/1.40 ifeq2(A,A,B,C) = B;
% 1.15/1.40 ifeq(A,A,B,C) = B;
% 1.15/1.40 ifeq(equivalent(X,Y),true,there_exists(X),true) = true;
% 1.15/1.40 ifeq2(equivalent(X,Y),true,X,Y) = Y;
% 1.15/1.40 ifeq(there_exists(Y),true,equivalent(Y,Y),true) = true;
% 1.15/1.40 ifeq(there_exists(domain(X)),true,there_exists(X),true) = true;
% 1.15/1.40 ifeq(there_exists(codomain(X)),true,there_exists(X),true) = true;
% 1.15/1.40 ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true;
% 1.15/1.40 ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y);
% 1.15/1.40 ifeq(there_exists(domain(X)),true,ifeq3(domain(X),codomain(Y),there_exists(compose(X,Y)),true),true) = true;
% 1.15/1.40 compose(X,domain(X)) = X;
% 1.15/1.40 compose(codomain(X),X) = X;
% 1.15/1.40 there_exists(compose(a,b)) = true;
% 1.15/1.40 ";
% 1.15/1.40
% 1.15/1.40 let s1 = status F "
% 1.15/1.40 b lr_lex;
% 1.15/1.40 a lr_lex;
% 1.15/1.40 compose lr_lex;
% 1.15/1.40 codomain lr_lex;
% 1.15/1.40 domain lr_lex;
% 1.15/1.40 there_exists lr_lex;
% 1.15/1.40 true lr_lex;
% 1.15/1.40 equivalent lr_lex;
% 1.15/1.40 ifeq lr_lex;
% 1.15/1.40 ifeq2 lr_lex;
% 1.15/1.40 ifeq3 lr_lex;
% 1.15/1.40 ";
% 1.15/1.40
% 1.15/1.40 let p1 = precedence F "
% 1.15/1.40 ifeq3 > ifeq2 > ifeq > equivalent > compose > there_exists > domain > codomain > true > a > b";
% 1.15/1.40
% 1.15/1.40 let s2 = status F "
% 1.15/1.40 b mul;
% 1.15/1.40 a mul;
% 1.15/1.40 compose mul;
% 1.15/1.40 codomain mul;
% 1.15/1.40 domain mul;
% 1.15/1.40 there_exists mul;
% 1.15/1.40 true mul;
% 1.15/1.40 equivalent mul;
% 1.15/1.40 ifeq mul;
% 1.15/1.40 ifeq2 mul;
% 1.15/1.40 ifeq3 mul;
% 1.15/1.40 ";
% 1.15/1.40
% 1.15/1.40 let p2 = precedence F "
% 1.15/1.40 ifeq3 > ifeq2 > ifeq > equivalent > compose > there_exists > domain > codomain > true = a = b";
% 1.15/1.40
% 1.15/1.40 let o_auto = AUTO Axioms;
% 1.15/1.40
% 1.15/1.40 let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 1.15/1.40
% 1.15/1.40 let Conjectures = equations F X " codomain(compose(a,b)) = codomain(a);"
% 1.15/1.40 ;
% 1.15/1.40 (*
% 1.15/1.40 let Red_Axioms = normalize_equations Defining_rules Axioms;
% 1.15/1.40
% 1.15/1.40 let Red_Conjectures = normalize_equations Defining_rules Conjectures;
% 1.15/1.40 *)
% 1.15/1.40 #time on;
% 1.15/1.40
% 1.15/1.40 let res = prove_conj_by_ordered_completion o Axioms Conjectures;
% 1.15/1.40
% 1.15/1.40 #time off;
% 1.15/1.40
% 1.15/1.40
% 1.15/1.40 let status = if res then "unsatisfiable" else "satisfiable";
% 1.15/1.40 #quit;
% 1.15/1.40 Verbose level is now 1
% 1.15/1.40
% 1.15/1.40 F : signature = <signature>
% 1.15/1.40 X : variable_set = <variable set>
% 1.15/1.40
% 1.15/1.40 Axioms : (F,X) equations = { compose(compose(A,B),C) =
% 1.15/1.40 compose(A,compose(B,C)),
% 1.15/1.40 ifeq3(A,A,B,C) = B,
% 1.15/1.40 ifeq2(A,A,B,C) = B,
% 1.15/1.40 ifeq(A,A,B,C) = B,
% 1.15/1.40 ifeq(equivalent(X,Y),true,there_exists(X),true)
% 1.15/1.40 = true,
% 1.15/1.40 ifeq2(equivalent(X,Y),true,X,Y) = Y,
% 1.15/1.40 ifeq(there_exists(Y),true,equivalent(Y,Y),true)
% 1.15/1.40 = true,
% 1.15/1.40 ifeq(there_exists(domain(X)),true,there_exists(X),true)
% 1.15/1.40 = true,
% 1.15/1.40 ifeq(there_exists(codomain(X)),true,there_exists(X),true)
% 1.15/1.40 = true,
% 1.15/1.40 ifeq(there_exists(compose(X,Y)),true,there_exists(
% 1.15/1.40 domain(X)),true)
% 1.15/1.40 = true,
% 1.15/1.40 ifeq2(there_exists(compose(X,Y)),true,domain(X),
% 1.15/1.40 codomain(Y)) = codomain(Y),
% 1.15/1.40 ifeq(there_exists(domain(X)),true,ifeq3(
% 1.15/1.40 domain(X),
% 1.15/1.40 codomain(Y),
% 1.15/1.40 there_exists(
% 1.15/1.40 compose(X,Y)),true),true)
% 1.15/1.40 = true,
% 1.15/1.40 compose(X,domain(X)) = X,
% 1.15/1.40 compose(codomain(X),X) = X,
% 1.15/1.40 there_exists(compose(a,b)) = true }
% 1.15/1.40 (15 equation(s))
% 1.15/1.40 s1 : F status = <status>
% 1.15/1.40 p1 : F precedence = <precedence>
% 1.15/1.40 s2 : F status = <status>
% 1.15/1.40 p2 : F precedence = <precedence>
% 1.15/1.40 o_auto : F term_ordering = <term ordering>
% 1.15/1.41 o : F term_ordering = <term ordering>
% 1.15/1.41 Conjectures : (F,X) equations = { codomain(compose(a,b)) = codomain(a) }
% 1.15/1.41 (1 equation(s))
% 1.15/1.41 time is now on
% 1.15/1.41
% 1.15/1.41 Initializing completion ...
% 1.15/1.41 New rule produced : [1] there_exists(compose(a,b)) -> true
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 14
% 1.15/1.41 Current number of rules: 1
% 1.15/1.41 New rule produced : [2] compose(X,domain(X)) -> X
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 13
% 1.15/1.41 Current number of rules: 2
% 1.15/1.41 New rule produced : [3] compose(codomain(X),X) -> X
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 12
% 1.15/1.41 Current number of rules: 3
% 1.15/1.41 New rule produced : [4] ifeq(A,A,B,C) -> B
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 11
% 1.15/1.41 Current number of rules: 4
% 1.15/1.41 New rule produced : [5] ifeq2(A,A,B,C) -> B
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 10
% 1.15/1.41 Current number of rules: 5
% 1.15/1.41 New rule produced : [6] ifeq3(A,A,B,C) -> B
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 9
% 1.15/1.41 Current number of rules: 6
% 1.15/1.41 New rule produced : [7] compose(compose(A,B),C) -> compose(A,compose(B,C))
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 8
% 1.15/1.41 Current number of rules: 7
% 1.15/1.41 New rule produced : [8] ifeq2(equivalent(X,Y),true,X,Y) -> Y
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 7
% 1.15/1.41 Current number of rules: 8
% 1.15/1.41 New rule produced :
% 1.15/1.41 [9] ifeq(there_exists(domain(X)),true,there_exists(X),true) -> true
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 6
% 1.15/1.41 Current number of rules: 9
% 1.15/1.41 New rule produced :
% 1.15/1.41 [10] ifeq(there_exists(Y),true,equivalent(Y,Y),true) -> true
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 5
% 1.15/1.41 Current number of rules: 10
% 1.15/1.41 New rule produced :
% 1.15/1.41 [11] ifeq(there_exists(codomain(X)),true,there_exists(X),true) -> true
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 4
% 1.15/1.41 Current number of rules: 11
% 1.15/1.41 New rule produced :
% 1.15/1.41 [12] ifeq(equivalent(X,Y),true,there_exists(X),true) -> true
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 3
% 1.15/1.41 Current number of rules: 12
% 1.15/1.41 New rule produced :
% 1.15/1.41 [13]
% 1.15/1.41 ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) -> true
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 2
% 1.15/1.41 Current number of rules: 13
% 1.15/1.41 New rule produced :
% 1.15/1.41 [14]
% 1.15/1.41 ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) -> codomain(Y)
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 1
% 1.15/1.41 Current number of rules: 14
% 1.15/1.41 New rule produced :
% 1.15/1.41 [15]
% 1.15/1.41 ifeq(there_exists(domain(X)),true,ifeq3(domain(X),codomain(Y),there_exists(
% 1.15/1.41 compose(X,Y)),true),true)
% 1.15/1.41 -> true
% 1.15/1.41 Current number of equations to process: 0
% 1.15/1.41 Current number of ordered equations: 0
% 1.15/1.41 Current number of rules: 15
% 1.15/1.41 New rule produced : [16] compose(A,compose(domain(A),B)) -> compose(A,B)
% 1.15/1.41 Current number of equations to process: 2
% 1.15/1.41 Current number of ordered equations: 0
% 1.15/1.41 Current number of rules: 16
% 1.15/1.41 New rule produced : [17] compose(codomain(A),compose(A,B)) -> compose(A,B)
% 1.15/1.41 Current number of equations to process: 1
% 1.15/1.41 Current number of ordered equations: 0
% 1.15/1.41 Current number of rules: 17
% 1.15/1.41 New rule produced : [18] equivalent(compose(a,b),compose(a,b)) -> true
% 1.15/1.41 Current number of equations to process: 2
% 1.15/1.41 Current number of ordered equations: 0
% 1.15/1.41 Current number of rules: 18
% 1.15/1.41 New rule produced :
% 1.15/1.41 [19] compose(A,compose(B,domain(compose(A,B)))) -> compose(A,B)
% 1.15/1.41 Current number of equations to process: 3
% 1.15/1.41 Current number of ordered equations: 0
% 1.15/1.41 Current number of rules: 19
% 1.15/1.41 New rule produced :
% 1.15/1.41 [20] ifeq(there_exists(domain(compose(a,b))),true,true,true) -> true
% 1.15/1.41 Current number of equations to process: 2
% 1.15/1.41 Current number of ordered equations: 0
% 1.15/1.41 Current number of rules: 20
% 1.15/1.41 New rule produced :
% 1.15/1.41 [21] ifeq(there_exists(codomain(compose(a,b))),true,true,true) -> true
% 1.15/1.41 Current number of equations to process: 1
% 1.15/1.42 Current number of ordered equations: 0
% 1.15/1.42 Current number of rules: 21
% 1.15/1.42 New rule produced :
% 1.15/1.42 [22] ifeq(equivalent(compose(a,b),A),true,true,true) -> true
% 1.15/1.42 Current number of equations to process: 0
% 1.15/1.42 Current number of ordered equations: 0
% 1.15/1.42 Current number of rules: 22
% 1.15/1.42 New rule produced : [23] there_exists(domain(a)) -> true
% 1.15/1.42 Current number of equations to process: 0
% 1.15/1.42 Current number of ordered equations: 0
% 1.15/1.42 Current number of rules: 23
% 1.15/1.42 New rule produced :
% 1.15/1.42 [24] ifeq(there_exists(A),true,there_exists(domain(A)),true) -> true
% 1.15/1.42 Current number of equations to process: 1
% 1.15/1.42 Current number of ordered equations: 0
% 1.15/1.42 Current number of rules: 24
% 1.15/1.42 New rule produced :
% 1.15/1.42 [25]
% 1.15/1.42 ifeq(there_exists(A),true,there_exists(domain(codomain(A))),true) -> true
% 1.15/1.42 Current number of equations to process: 1
% 1.15/1.42 Current number of ordered equations: 0
% 1.15/1.42 Current number of rules: 25
% 1.15/1.42 New rule produced : [26] domain(a) -> codomain(b)
% 1.15/1.42 Rule [23] there_exists(domain(a)) -> true collapsed.
% 1.15/1.42 Current number of equations to process: 2
% 1.15/1.42 Current number of ordered equations: 0
% 1.15/1.42 Current number of rules: 25
% 1.15/1.43 New rule produced : [27] there_exists(codomain(b)) -> true
% 1.15/1.43 Current number of equations to process: 1
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 26
% 1.15/1.43 New rule produced :
% 1.15/1.43 [28]
% 1.15/1.43 ifeq2(there_exists(A),true,domain(codomain(A)),codomain(A)) -> codomain(A)
% 1.15/1.43 Current number of equations to process: 3
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 27
% 1.15/1.43 New rule produced :
% 1.15/1.43 [29]
% 1.15/1.43 ifeq2(there_exists(A),true,domain(A),codomain(domain(A))) ->
% 1.15/1.43 codomain(domain(A))
% 1.15/1.43 Current number of equations to process: 2
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 28
% 1.15/1.43 New rule produced :
% 1.15/1.43 [30]
% 1.15/1.43 ifeq(there_exists(compose(A,compose(B,C))),true,there_exists(domain(compose(A,B))),true)
% 1.15/1.43 -> true
% 1.15/1.43 Current number of equations to process: 1
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 29
% 1.15/1.43 New rule produced :
% 1.15/1.43 [31]
% 1.15/1.43 ifeq2(there_exists(compose(A,compose(B,C))),true,domain(compose(A,B)),
% 1.15/1.43 codomain(C)) -> codomain(C)
% 1.15/1.43 Current number of equations to process: 0
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 30
% 1.15/1.43 New rule produced : [32] compose(A,domain(domain(A))) -> A
% 1.15/1.43 Current number of equations to process: 4
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 31
% 1.15/1.43 New rule produced :
% 1.15/1.43 [33] compose(A,compose(domain(domain(A)),B)) -> compose(A,B)
% 1.15/1.43 Current number of equations to process: 4
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 32
% 1.15/1.43 New rule produced : [34] compose(codomain(codomain(A)),A) -> A
% 1.15/1.43 Current number of equations to process: 7
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 33
% 1.15/1.43 New rule produced :
% 1.15/1.43 [35] compose(codomain(codomain(A)),compose(A,B)) -> compose(A,B)
% 1.15/1.43 Current number of equations to process: 7
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 34
% 1.15/1.43 New rule produced :
% 1.15/1.43 [36]
% 1.15/1.43 ifeq(there_exists(compose(A,B)),true,there_exists(domain(codomain(A))),true)
% 1.15/1.43 -> true
% 1.15/1.43 Current number of equations to process: 8
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 35
% 1.15/1.43 New rule produced :
% 1.15/1.43 [37]
% 1.15/1.43 compose(A,compose(B,compose(domain(compose(A,B)),C))) ->
% 1.15/1.43 compose(A,compose(B,C))
% 1.15/1.43 Current number of equations to process: 12
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 36
% 1.15/1.43 New rule produced :
% 1.15/1.43 [38]
% 1.15/1.43 compose(codomain(compose(A,B)),compose(A,compose(B,C))) ->
% 1.15/1.43 compose(A,compose(B,C))
% 1.15/1.43 Current number of equations to process: 11
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 37
% 1.15/1.43 New rule produced :
% 1.15/1.43 [39] compose(A,compose(B,domain(compose(domain(A),B)))) -> compose(A,B)
% 1.15/1.43 Current number of equations to process: 11
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 38
% 1.15/1.43 New rule produced : [40] there_exists(domain(compose(a,b))) -> true
% 1.15/1.43 Rule [20] ifeq(there_exists(domain(compose(a,b))),true,true,true) -> true
% 1.15/1.43 collapsed.
% 1.15/1.43 Current number of equations to process: 11
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.43 Current number of rules: 38
% 1.15/1.43 New rule produced : [41] there_exists(domain(codomain(compose(a,b)))) -> true
% 1.15/1.43 Current number of equations to process: 11
% 1.15/1.43 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 39
% 1.15/1.44 New rule produced : [42] compose(a,codomain(b)) -> a
% 1.15/1.44 Current number of equations to process: 11
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 40
% 1.15/1.44 New rule produced : [43] there_exists(a) -> true
% 1.15/1.44 Current number of equations to process: 11
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 41
% 1.15/1.44 New rule produced :
% 1.15/1.44 [44] ifeq(there_exists(compose(a,A)),true,true,true) -> true
% 1.15/1.44 Current number of equations to process: 12
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 42
% 1.15/1.44 New rule produced : [45] equivalent(codomain(b),codomain(b)) -> true
% 1.15/1.44 Current number of equations to process: 15
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 43
% 1.15/1.44 New rule produced : [46] there_exists(b) -> true
% 1.15/1.44 Current number of equations to process: 16
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 44
% 1.15/1.44 New rule produced : [47] compose(a,compose(codomain(b),A)) -> compose(a,A)
% 1.15/1.44 Current number of equations to process: 16
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 45
% 1.15/1.44 New rule produced :
% 1.15/1.44 [48] ifeq(there_exists(domain(codomain(b))),true,true,true) -> true
% 1.15/1.44 Current number of equations to process: 15
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 46
% 1.15/1.44 New rule produced :
% 1.15/1.44 [49] ifeq(there_exists(codomain(codomain(b))),true,true,true) -> true
% 1.15/1.44 Current number of equations to process: 14
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 47
% 1.15/1.44 New rule produced :
% 1.15/1.44 [50] ifeq(equivalent(codomain(b),A),true,true,true) -> true
% 1.15/1.44 Current number of equations to process: 13
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 48
% 1.15/1.44 New rule produced : [51] there_exists(domain(codomain(b))) -> true
% 1.15/1.44 Rule [48] ifeq(there_exists(domain(codomain(b))),true,true,true) -> true
% 1.15/1.44 collapsed.
% 1.15/1.44 Current number of equations to process: 13
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 48
% 1.15/1.44 New rule produced : [52] there_exists(domain(codomain(codomain(b)))) -> true
% 1.15/1.44 Current number of equations to process: 13
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 49
% 1.15/1.44 New rule produced :
% 1.15/1.44 [53] domain(codomain(compose(a,b))) -> codomain(compose(a,b))
% 1.15/1.44 Rule [41] there_exists(domain(codomain(compose(a,b)))) -> true collapsed.
% 1.15/1.44 Current number of equations to process: 14
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 49
% 1.15/1.44 New rule produced : [54] there_exists(codomain(compose(a,b))) -> true
% 1.15/1.44 Rule [21] ifeq(there_exists(codomain(compose(a,b))),true,true,true) -> true
% 1.15/1.44 collapsed.
% 1.15/1.44 Current number of equations to process: 13
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 49
% 1.15/1.44 New rule produced :
% 1.15/1.44 [55] ifeq3(codomain(b),codomain(A),there_exists(compose(a,A)),true) -> true
% 1.15/1.44 Current number of equations to process: 12
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 50
% 1.15/1.44 New rule produced :
% 1.15/1.44 [56]
% 1.15/1.44 ifeq2(there_exists(compose(a,A)),true,codomain(b),codomain(A)) -> codomain(A)
% 1.15/1.44 Current number of equations to process: 11
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 51
% 1.15/1.44 New rule produced :
% 1.15/1.44 [57] domain(codomain(codomain(b))) -> codomain(codomain(b))
% 1.15/1.44 Rule [52] there_exists(domain(codomain(codomain(b)))) -> true collapsed.
% 1.15/1.44 Current number of equations to process: 12
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 51
% 1.15/1.44 New rule produced : [58] there_exists(codomain(codomain(b))) -> true
% 1.15/1.44 Rule [49] ifeq(there_exists(codomain(codomain(b))),true,true,true) -> true
% 1.15/1.44 collapsed.
% 1.15/1.44 Current number of equations to process: 11
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 51
% 1.15/1.44 New rule produced :
% 1.15/1.44 [59] codomain(domain(compose(a,b))) -> domain(compose(a,b))
% 1.15/1.44 Current number of equations to process: 11
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 52
% 1.15/1.44 New rule produced : [60] codomain(codomain(b)) -> codomain(b)
% 1.15/1.44 Rule [57] domain(codomain(codomain(b))) -> codomain(codomain(b)) collapsed.
% 1.15/1.44 Rule [58] there_exists(codomain(codomain(b))) -> true collapsed.
% 1.15/1.44 Current number of equations to process: 12
% 1.15/1.44 Current number of ordered equations: 0
% 1.15/1.44 Current number of rules: 51
% 1.15/1.44 New rule produced : [61] domain(codomain(b)) -> codomain(b)
% 1.22/1.45 Rule [51] there_exists(domain(codomain(b))) -> true collapsed.
% 1.22/1.45 Current number of equations to process: 11
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 51
% 1.22/1.45 New rule produced :
% 1.22/1.45 [62]
% 1.22/1.45 ifeq(there_exists(compose(A,B)),true,there_exists(domain(compose(A,codomain(B)))),true)
% 1.22/1.45 -> true
% 1.22/1.45 Current number of equations to process: 13
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 52
% 1.22/1.45 New rule produced :
% 1.22/1.45 [63]
% 1.22/1.45 compose(A,compose(B,compose(C,domain(compose(A,compose(B,C)))))) ->
% 1.22/1.45 compose(A,compose(B,C))
% 1.22/1.45 Current number of equations to process: 11
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 53
% 1.22/1.45 New rule produced :
% 1.22/1.45 [64]
% 1.22/1.45 ifeq2(there_exists(compose(A,B)),true,domain(codomain(A)),codomain(compose(A,B)))
% 1.22/1.45 -> codomain(compose(A,B))
% 1.22/1.45 Current number of equations to process: 10
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 54
% 1.22/1.45 New rule produced :
% 1.22/1.45 [65]
% 1.22/1.45 ifeq2(there_exists(compose(A,B)),true,domain(compose(A,codomain(B))),
% 1.22/1.45 codomain(B)) -> codomain(B)
% 1.22/1.45 Current number of equations to process: 14
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 55
% 1.22/1.45 New rule produced :
% 1.22/1.45 [66]
% 1.22/1.45 ifeq2(there_exists(compose(A,B)),true,domain(compose(A,B)),codomain(domain(B)))
% 1.22/1.45 -> codomain(domain(B))
% 1.22/1.45 Current number of equations to process: 13
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 56
% 1.22/1.45 New rule produced :
% 1.22/1.45 [67]
% 1.22/1.45 ifeq(there_exists(domain(A)),true,ifeq3(domain(A),codomain(domain(A)),
% 1.22/1.45 there_exists(A),true),true) -> true
% 1.22/1.45 Current number of equations to process: 12
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 57
% 1.22/1.45 New rule produced :
% 1.22/1.45 [68]
% 1.22/1.45 ifeq2(there_exists(compose(A,B)),true,domain(A),codomain(compose(domain(A),B)))
% 1.22/1.45 -> codomain(compose(domain(A),B))
% 1.22/1.45 Current number of equations to process: 11
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 58
% 1.22/1.45 New rule produced :
% 1.22/1.45 [69]
% 1.22/1.45 ifeq(there_exists(compose(A,B)),true,there_exists(domain(compose(codomain(
% 1.22/1.45 compose(A,B)),A))),true)
% 1.22/1.45 -> true
% 1.22/1.45 Current number of equations to process: 10
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 59
% 1.22/1.45 New rule produced :
% 1.22/1.45 [70]
% 1.22/1.45 ifeq(there_exists(compose(A,compose(B,C))),true,there_exists(domain(compose(A,
% 1.22/1.45 codomain(B)))),true)
% 1.22/1.45 -> true
% 1.22/1.45 Current number of equations to process: 9
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 60
% 1.22/1.45 New rule produced :
% 1.22/1.45 [71] compose(A,compose(B,domain(domain(compose(A,B))))) -> compose(A,B)
% 1.22/1.45 Current number of equations to process: 13
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 61
% 1.22/1.45 New rule produced : [72] compose(A,domain(domain(domain(A)))) -> A
% 1.22/1.45 Current number of equations to process: 14
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 62
% 1.22/1.45 New rule produced :
% 1.22/1.45 [73] compose(A,compose(domain(domain(domain(domain(A)))),B)) -> compose(A,B)
% 1.22/1.45 Current number of equations to process: 17
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 63
% 1.22/1.45 New rule produced :
% 1.22/1.45 [74]
% 1.22/1.45 ifeq2(there_exists(A),true,domain(A),codomain(domain(domain(A)))) ->
% 1.22/1.45 codomain(domain(domain(A)))
% 1.22/1.45 Current number of equations to process: 16
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 64
% 1.22/1.45 New rule produced :
% 1.22/1.45 [75] compose(A,compose(domain(domain(domain(A))),B)) -> compose(A,B)
% 1.22/1.45 Current number of equations to process: 18
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 65
% 1.22/1.45 New rule produced :
% 1.22/1.45 [76]
% 1.22/1.45 compose(A,compose(B,domain(compose(domain(domain(A)),B)))) -> compose(A,B)
% 1.22/1.45 Current number of equations to process: 17
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 66
% 1.22/1.45 New rule produced : [77] compose(A,domain(domain(domain(domain(A))))) -> A
% 1.22/1.45 Current number of equations to process: 18
% 1.22/1.45 Current number of ordered equations: 0
% 1.22/1.45 Current number of rules: 67
% 1.22/1.45 New rule produced :
% 1.22/1.45 [78]
% 1.22/1.45 ifeq(there_exists(A),true,there_exists(domain(codomain(codomain(A)))),true)
% 1.22/1.45 -> true
% 1.22/1.45 Current number of equations to process: 19
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 68
% 1.22/1.48 New rule produced : [79] compose(codomain(codomain(codomain(A))),A) -> A
% 1.22/1.48 Current number of equations to process: 20
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 69
% 1.22/1.48 New rule produced :
% 1.22/1.48 [80]
% 1.22/1.48 compose(codomain(codomain(codomain(codomain(A)))),compose(A,B)) ->
% 1.22/1.48 compose(A,B)
% 1.22/1.48 Current number of equations to process: 27
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 70
% 1.22/1.48 New rule produced :
% 1.22/1.48 [81]
% 1.22/1.48 ifeq2(there_exists(A),true,domain(codomain(codomain(A))),codomain(A)) ->
% 1.22/1.48 codomain(A)
% 1.22/1.48 Current number of equations to process: 26
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 71
% 1.22/1.48 New rule produced :
% 1.22/1.48 [82] compose(codomain(codomain(codomain(A))),compose(A,B)) -> compose(A,B)
% 1.22/1.48 Current number of equations to process: 27
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 72
% 1.22/1.48 New rule produced :
% 1.22/1.48 [83] compose(codomain(codomain(codomain(codomain(A)))),A) -> A
% 1.22/1.48 Current number of equations to process: 29
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 73
% 1.22/1.48 New rule produced : [84] there_exists(domain(codomain(a))) -> true
% 1.22/1.48 Current number of equations to process: 29
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 74
% 1.22/1.48 New rule produced :
% 1.22/1.48 [85]
% 1.22/1.48 ifeq(there_exists(compose(A,B)),true,there_exists(domain(codomain(codomain(A)))),true)
% 1.22/1.48 -> true
% 1.22/1.48 Current number of equations to process: 29
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 75
% 1.22/1.48 New rule produced :
% 1.22/1.48 [86]
% 1.22/1.48 compose(A,compose(B,compose(domain(domain(compose(A,B))),C))) ->
% 1.22/1.48 compose(A,compose(B,C))
% 1.22/1.48 Current number of equations to process: 28
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 76
% 1.22/1.48 New rule produced :
% 1.22/1.48 [87]
% 1.22/1.48 compose(codomain(codomain(compose(A,B))),compose(A,compose(B,C))) ->
% 1.22/1.48 compose(A,compose(B,C))
% 1.22/1.48 Current number of equations to process: 27
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 77
% 1.22/1.48 New rule produced :
% 1.22/1.48 [88]
% 1.22/1.48 ifeq(there_exists(A),true,there_exists(domain(codomain(codomain(codomain(A))))),true)
% 1.22/1.48 -> true
% 1.22/1.48 Current number of equations to process: 28
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 78
% 1.22/1.48 New rule produced :
% 1.22/1.48 [89]
% 1.22/1.48 ifeq(there_exists(compose(A,B)),true,there_exists(domain(codomain(codomain(
% 1.22/1.48 codomain(A))))),true)
% 1.22/1.48 -> true
% 1.22/1.48 Current number of equations to process: 31
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 79
% 1.22/1.48 New rule produced :
% 1.22/1.48 [90]
% 1.22/1.48 compose(A,compose(B,domain(compose(B,domain(compose(A,B)))))) -> compose(A,B)
% 1.22/1.48 Current number of equations to process: 34
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 80
% 1.22/1.48 New rule produced :
% 1.22/1.48 [91]
% 1.22/1.48 compose(A,compose(B,compose(domain(compose(domain(A),B)),C))) ->
% 1.22/1.48 compose(A,compose(B,C))
% 1.22/1.48 Current number of equations to process: 33
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 81
% 1.22/1.48 New rule produced :
% 1.22/1.48 [92]
% 1.22/1.48 compose(A,compose(B,domain(domain(domain(compose(A,B)))))) -> compose(A,B)
% 1.22/1.48 Current number of equations to process: 37
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 82
% 1.22/1.48 New rule produced :
% 1.22/1.48 [93] compose(codomain(compose(A,codomain(B))),compose(A,B)) -> compose(A,B)
% 1.22/1.48 Current number of equations to process: 41
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 83
% 1.22/1.48 New rule produced :
% 1.22/1.48 [94]
% 1.22/1.48 compose(codomain(compose(codomain(compose(A,B)),A)),compose(A,B)) ->
% 1.22/1.48 compose(A,B)
% 1.22/1.48 Current number of equations to process: 42
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 84
% 1.22/1.48 New rule produced :
% 1.22/1.48 [95]
% 1.22/1.48 compose(codomain(compose(A,codomain(B))),compose(A,compose(B,C))) ->
% 1.22/1.48 compose(A,compose(B,C))
% 1.22/1.48 Current number of equations to process: 45
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 85
% 1.22/1.48 New rule produced :
% 1.22/1.48 [96]
% 1.22/1.48 compose(codomain(compose(A,codomain(codomain(B)))),compose(A,B)) ->
% 1.22/1.48 compose(A,B)
% 1.22/1.48 Current number of equations to process: 50
% 1.22/1.48 Current number of ordered equations: 0
% 1.22/1.48 Current number of rules: 86
% 1.22/1.48 New rule produced : [97] compose(A,domain(compose(domain(A),domain(A)))) -> A
% 1.22/1.48 Current number of equations to process: 56
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 87
% 1.22/1.50 New rule produced :
% 1.22/1.50 [98] compose(A,domain(compose(domain(codomain(A)),A))) -> A
% 1.22/1.50 Current number of equations to process: 56
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 88
% 1.22/1.50 New rule produced :
% 1.22/1.50 [99] compose(a,compose(A,domain(compose(codomain(b),A)))) -> compose(a,A)
% 1.22/1.50 Current number of equations to process: 56
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 89
% 1.22/1.50 New rule produced :
% 1.22/1.50 [100] compose(A,domain(compose(domain(codomain(codomain(A))),A))) -> A
% 1.22/1.50 Current number of equations to process: 59
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 90
% 1.22/1.50 New rule produced :
% 1.22/1.50 [101] equivalent(domain(compose(a,b)),domain(compose(a,b))) -> true
% 1.22/1.50 Current number of equations to process: 63
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 91
% 1.22/1.50 New rule produced :
% 1.22/1.50 [102] ifeq(there_exists(domain(domain(compose(a,b)))),true,true,true) -> true
% 1.22/1.50 Current number of equations to process: 62
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 92
% 1.22/1.50 New rule produced :
% 1.22/1.50 [103] ifeq(equivalent(domain(compose(a,b)),A),true,true,true) -> true
% 1.22/1.50 Current number of equations to process: 61
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 93
% 1.22/1.50 New rule produced : [104] there_exists(domain(domain(compose(a,b)))) -> true
% 1.22/1.50 Rule
% 1.22/1.50 [102] ifeq(there_exists(domain(domain(compose(a,b)))),true,true,true) -> true
% 1.22/1.50 collapsed.
% 1.22/1.50 Current number of equations to process: 61
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 93
% 1.22/1.50 New rule produced :
% 1.22/1.50 [105] domain(domain(compose(a,b))) -> domain(compose(a,b))
% 1.22/1.50 Rule [104] there_exists(domain(domain(compose(a,b)))) -> true collapsed.
% 1.22/1.50 Current number of equations to process: 61
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 93
% 1.22/1.50 New rule produced : [106] equivalent(a,a) -> true
% 1.22/1.50 Current number of equations to process: 62
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 94
% 1.22/1.50 New rule produced :
% 1.22/1.50 [107] ifeq(there_exists(codomain(a)),true,true,true) -> true
% 1.22/1.50 Current number of equations to process: 63
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 95
% 1.22/1.50 New rule produced : [108] ifeq(equivalent(a,A),true,true,true) -> true
% 1.22/1.50 Current number of equations to process: 62
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 96
% 1.22/1.50 New rule produced : [109] domain(codomain(a)) -> codomain(a)
% 1.22/1.50 Rule [84] there_exists(domain(codomain(a))) -> true collapsed.
% 1.22/1.50 Current number of equations to process: 63
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 96
% 1.22/1.50 New rule produced : [110] there_exists(codomain(a)) -> true
% 1.22/1.50 Rule [107] ifeq(there_exists(codomain(a)),true,true,true) -> true collapsed.
% 1.22/1.50 Current number of equations to process: 62
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 96
% 1.22/1.50 New rule produced : [111] equivalent(b,b) -> true
% 1.22/1.50 Current number of equations to process: 63
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 97
% 1.22/1.50 New rule produced :
% 1.22/1.50 [112] ifeq(there_exists(domain(b)),true,true,true) -> true
% 1.22/1.50 Current number of equations to process: 63
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 98
% 1.22/1.50 New rule produced : [113] ifeq(equivalent(b,A),true,true,true) -> true
% 1.22/1.50 Current number of equations to process: 62
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 99
% 1.22/1.50 New rule produced : [114] there_exists(domain(b)) -> true
% 1.22/1.50 Rule [112] ifeq(there_exists(domain(b)),true,true,true) -> true collapsed.
% 1.22/1.50 Current number of equations to process: 62
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 99
% 1.22/1.50 New rule produced : [115] codomain(domain(b)) -> domain(b)
% 1.22/1.50 Current number of equations to process: 62
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 100
% 1.22/1.50 New rule produced :
% 1.22/1.50 [116]
% 1.22/1.50 compose(codomain(compose(a,b)),codomain(compose(a,b))) ->
% 1.22/1.50 codomain(compose(a,b))
% 1.22/1.50 Current number of equations to process: 66
% 1.22/1.50 Current number of ordered equations: 0
% 1.22/1.50 Current number of rules: 101
% 1.22/1.50 New rule produced :
% 1.22/1.50 [117]
% 1.22/1.50 ifeq(there_exists(compose(codomain(compose(a,b)),A)),true,true,true) -> true
% 1.22/1.53 Current number of equations to process: 65
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 102
% 1.22/1.53 New rule produced :
% 1.22/1.53 [118] codomain(codomain(compose(a,b))) -> codomain(compose(a,b))
% 1.22/1.53 Current number of equations to process: 67
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 103
% 1.22/1.53 New rule produced :
% 1.22/1.53 [119] equivalent(codomain(compose(a,b)),codomain(compose(a,b))) -> true
% 1.22/1.53 Current number of equations to process: 68
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 104
% 1.22/1.53 New rule produced :
% 1.22/1.53 [120] ifeq(equivalent(codomain(compose(a,b)),A),true,true,true) -> true
% 1.22/1.53 Current number of equations to process: 67
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 105
% 1.22/1.53 New rule produced :
% 1.22/1.53 [121]
% 1.22/1.53 compose(A,compose(B,domain(compose(domain(domain(domain(A))),B)))) ->
% 1.22/1.53 compose(A,B)
% 1.22/1.53 Current number of equations to process: 68
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 106
% 1.22/1.53 New rule produced :
% 1.22/1.53 [122]
% 1.22/1.53 ifeq2(there_exists(compose(A,a)),true,domain(compose(A,a)),codomain(b)) ->
% 1.22/1.53 codomain(b)
% 1.22/1.53 Current number of equations to process: 67
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 107
% 1.22/1.53 New rule produced :
% 1.22/1.53 [123]
% 1.22/1.53 compose(codomain(compose(codomain(codomain(compose(A,B))),A)),compose(A,B))
% 1.22/1.53 -> compose(A,B)
% 1.22/1.53 Current number of equations to process: 69
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 108
% 1.22/1.53 New rule produced :
% 1.22/1.53 [124]
% 1.22/1.53 compose(A,compose(B,domain(compose(domain(B),domain(compose(A,B)))))) ->
% 1.22/1.53 compose(A,B)
% 1.22/1.53 Current number of equations to process: 68
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 109
% 1.22/1.53 New rule produced :
% 1.22/1.53 [125]
% 1.22/1.53 compose(a,compose(A,compose(domain(compose(codomain(b),A)),B))) ->
% 1.22/1.53 compose(a,compose(A,B))
% 1.22/1.53 Current number of equations to process: 67
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 110
% 1.22/1.53 New rule produced :
% 1.22/1.53 [126]
% 1.22/1.53 ifeq3(codomain(b),codomain(compose(codomain(b),A)),there_exists(compose(a,A)),true)
% 1.22/1.53 -> true
% 1.22/1.53 Current number of equations to process: 66
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 111
% 1.22/1.53 New rule produced :
% 1.22/1.53 [127]
% 1.22/1.53 compose(domain(compose(a,b)),domain(compose(a,b))) -> domain(compose(a,b))
% 1.22/1.53 Current number of equations to process: 68
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 112
% 1.22/1.53 New rule produced : [128] compose(codomain(b),codomain(b)) -> codomain(b)
% 1.22/1.53 Current number of equations to process: 74
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 113
% 1.22/1.53 New rule produced :
% 1.22/1.53 [129] compose(codomain(b),compose(codomain(b),A)) -> compose(codomain(b),A)
% 1.22/1.53 Current number of equations to process: 76
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 114
% 1.22/1.53 New rule produced :
% 1.22/1.53 [130] ifeq(there_exists(compose(codomain(b),A)),true,true,true) -> true
% 1.22/1.53 Current number of equations to process: 78
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 115
% 1.22/1.53 New rule produced :
% 1.22/1.53 [131] ifeq(there_exists(compose(b,A)),true,true,true) -> true
% 1.22/1.53 Current number of equations to process: 79
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 116
% 1.22/1.53 New rule produced :
% 1.22/1.53 [132]
% 1.22/1.53 ifeq(there_exists(compose(domain(compose(a,b)),A)),true,true,true) -> true
% 1.22/1.53 Current number of equations to process: 78
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 117
% 1.22/1.53 New rule produced :
% 1.22/1.53 [133]
% 1.22/1.53 ifeq3(codomain(b),codomain(A),there_exists(compose(codomain(b),A)),true) ->
% 1.22/1.53 true
% 1.22/1.53 Current number of equations to process: 77
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 118
% 1.22/1.53 New rule produced :
% 1.22/1.53 [134]
% 1.22/1.53 ifeq2(there_exists(compose(A,codomain(b))),true,domain(A),codomain(b)) ->
% 1.22/1.53 codomain(b)
% 1.22/1.53 Current number of equations to process: 76
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 119
% 1.22/1.53 New rule produced :
% 1.22/1.53 [135]
% 1.22/1.53 ifeq2(there_exists(compose(codomain(b),A)),true,codomain(b),codomain(A)) ->
% 1.22/1.53 codomain(A)
% 1.22/1.53 Current number of equations to process: 75
% 1.22/1.53 Current number of ordered equations: 0
% 1.22/1.53 Current number of rules: 120
% 1.22/1.53 New rule produced :
% 1.22/1.53 [136]
% 1.22/1.53 ifeq(there_exists(A),true,there_exists(domain(compose(A,codomain(domain(A))))),true)
% 1.22/1.53 -> true
% 1.22/1.53 Current number of equations to process: 79
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 121
% 1.22/1.56 New rule produced :
% 1.22/1.56 [137]
% 1.22/1.56 ifeq(there_exists(A),true,there_exists(domain(compose(codomain(A),codomain(A)))),true)
% 1.22/1.56 -> true
% 1.22/1.56 Current number of equations to process: 78
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 122
% 1.22/1.56 New rule produced :
% 1.22/1.56 [138]
% 1.22/1.56 compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),A)) ->
% 1.22/1.56 compose(codomain(compose(a,b)),A)
% 1.22/1.56 Current number of equations to process: 77
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 123
% 1.22/1.56 New rule produced :
% 1.22/1.56 [139]
% 1.22/1.56 compose(domain(compose(a,b)),compose(domain(compose(a,b)),A)) ->
% 1.22/1.56 compose(domain(compose(a,b)),A)
% 1.22/1.56 Current number of equations to process: 76
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 124
% 1.22/1.56 New rule produced :
% 1.22/1.56 [140]
% 1.22/1.56 ifeq(there_exists(compose(A,B)),true,there_exists(domain(compose(A,codomain(
% 1.22/1.56 codomain(B))))),true)
% 1.22/1.56 -> true
% 1.22/1.56 Current number of equations to process: 75
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 125
% 1.22/1.56 New rule produced :
% 1.22/1.56 [141]
% 1.22/1.56 compose(A,compose(B,compose(domain(domain(domain(compose(A,B)))),C))) ->
% 1.22/1.56 compose(A,compose(B,C))
% 1.22/1.56 Current number of equations to process: 73
% 1.22/1.56 Current number of ordered equations: 1
% 1.22/1.56 Current number of rules: 126
% 1.22/1.56 New rule produced :
% 1.22/1.56 [142]
% 1.22/1.56 compose(A,compose(B,compose(domain(compose(domain(domain(A)),B)),C))) ->
% 1.22/1.56 compose(A,compose(B,C))
% 1.22/1.56 Current number of equations to process: 73
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 127
% 1.22/1.56 New rule produced :
% 1.22/1.56 [143]
% 1.22/1.56 compose(codomain(compose(A,codomain(codomain(B)))),compose(A,compose(B,C)))
% 1.22/1.56 -> compose(A,compose(B,C))
% 1.22/1.56 Current number of equations to process: 71
% 1.22/1.56 Current number of ordered equations: 1
% 1.22/1.56 Current number of rules: 128
% 1.22/1.56 New rule produced :
% 1.22/1.56 [144]
% 1.22/1.56 compose(codomain(codomain(codomain(compose(A,B)))),compose(A,compose(B,C)))
% 1.22/1.56 -> compose(A,compose(B,C))
% 1.22/1.56 Current number of equations to process: 71
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 129
% 1.22/1.56 New rule produced :
% 1.22/1.56 [145]
% 1.22/1.56 ifeq(there_exists(A),true,there_exists(domain(compose(A,codomain(domain(
% 1.22/1.56 domain(A)))))),true)
% 1.22/1.56 -> true
% 1.22/1.56 Current number of equations to process: 78
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 130
% 1.22/1.56 New rule produced :
% 1.22/1.56 [146]
% 1.22/1.56 ifeq2(there_exists(compose(A,B)),true,domain(compose(A,codomain(codomain(B)))),
% 1.22/1.56 codomain(B)) -> codomain(B)
% 1.22/1.56 Current number of equations to process: 84
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 131
% 1.22/1.56 New rule produced : [147] codomain(compose(a,b)) -> codomain(a)
% 1.22/1.56 Rule [53] domain(codomain(compose(a,b))) -> codomain(compose(a,b)) collapsed.
% 1.22/1.56 Rule [54] there_exists(codomain(compose(a,b))) -> true collapsed.
% 1.22/1.56 Rule
% 1.22/1.56 [116]
% 1.22/1.56 compose(codomain(compose(a,b)),codomain(compose(a,b))) ->
% 1.22/1.56 codomain(compose(a,b)) collapsed.
% 1.22/1.56 Rule
% 1.22/1.56 [117]
% 1.22/1.56 ifeq(there_exists(compose(codomain(compose(a,b)),A)),true,true,true) -> true
% 1.22/1.56 collapsed.
% 1.22/1.56 Rule [118] codomain(codomain(compose(a,b))) -> codomain(compose(a,b))
% 1.22/1.56 collapsed.
% 1.22/1.56 Rule [119] equivalent(codomain(compose(a,b)),codomain(compose(a,b))) -> true
% 1.22/1.56 collapsed.
% 1.22/1.56 Rule [120] ifeq(equivalent(codomain(compose(a,b)),A),true,true,true) -> true
% 1.22/1.56 collapsed.
% 1.22/1.56 Rule
% 1.22/1.56 [138]
% 1.22/1.56 compose(codomain(compose(a,b)),compose(codomain(compose(a,b)),A)) ->
% 1.22/1.56 compose(codomain(compose(a,b)),A) collapsed.
% 1.22/1.56 The conjecture has been reduced.
% 1.22/1.56 Conjecture is now:
% 1.22/1.56 Trivial
% 1.22/1.56
% 1.22/1.56 Current number of equations to process: 100
% 1.22/1.56 Current number of ordered equations: 0
% 1.22/1.56 Current number of rules: 124
% 1.22/1.56 The current conjecture is true and the solution is the identity
% 1.22/1.56 % SZS output start Refutation
% 1.22/1.56
% 1.22/1.56 The following 7 rules have been used:
% 1.22/1.56 [1]
% 1.22/1.56 there_exists(compose(a,b)) -> true; trace = in the starting set
% 1.22/1.56 [3] compose(codomain(X),X) -> X; trace = in the starting set
% 1.22/1.56 [7] compose(compose(A,B),C) -> compose(A,compose(B,C)); trace = in the starting set
% 1.22/1.56 [14] ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) ->
% 1.22/1.56 codomain(Y); trace = in the starting set
% 1.22/1.56 [17] compose(codomain(A),compose(A,B)) -> compose(A,B); trace = Cp of 7 and 3
% 1.22/1.56 [64] ifeq2(there_exists(compose(A,B)),true,domain(codomain(A)),codomain(
% 1.22/1.56 compose(A,B)))
% 1.22/1.56 -> codomain(compose(A,B)); trace = Cp of 17 and 14
% 1.22/1.56 [147] codomain(compose(a,b)) -> codomain(a); trace = Cp of 64 and 1
% 1.22/1.56 % SZS output end Refutation
% 1.22/1.56 All conjectures have been proven
% 1.22/1.56
% 1.22/1.56 Execution time: 0.150000 sec
% 1.22/1.56 res : bool = true
% 1.22/1.56 time is now off
% 1.22/1.56
% 1.22/1.56 status : string = "unsatisfiable"
% 1.22/1.56 % SZS status Unsatisfiable
% 1.22/1.56 CiME interrupted
%------------------------------------------------------------------------------