19717
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%ID: $Id$
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%Author: Jia Meng, NICTA
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%typed combinator reduction for partial-types (no S)
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clause(
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forall([A, B, P, Q],
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or( equal(hAPP(hAPP(c_COMBK,P,tc_fun(A,tc_fun(B,A))),Q,tc_fun(B,A)),P))),
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a1 ).
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clause(
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forall([P, T],
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or( equal(hAPP(c_COMBI,P,tc_fun(T,T)),P))),
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a3 ).
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clause(
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forall([A, B, C, P, Q, R],
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or( equal(hAPP(hAPP(hAPP(c_COMBB,P,tc_fun(tc_fun(A,B),tc_fun(tc_fun(C,A),tc_fun(C,B)))),Q,tc_fun(tc_fun(C,A),tc_fun(C,B))),R,tc_fun(C,B)),hAPP(P,hAPP(Q,R,tc_fun(C,A)),tc_fun(A,B))))),
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a4 ).
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clause(
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forall([A, B, C, P, Q, R],
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or( equal(hAPP(hAPP(hAPP(c_COMBC,P,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(B,tc_fun(A,C)))),Q,tc_fun(B,tc_fun(A,C))),R,tc_fun(A,C)),hAPP(hAPP(P,R,tc_fun(A,tc_fun(B,C))),Q,tc_fun(B,C))))),
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a5 ).
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clause(
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forall([A, X, Y],
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or( not(hBOOL(hAPP(hAPP(fequal,X,tc_fun(A,tc_fun(A,tc_bool))),Y,tc_fun(A,tc_bool)))),
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equal(X,Y))),
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19969
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a6 ).
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clause(
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forall([A, X, Y],
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or( not(equal(X,Y)),
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hBOOL(hAPP(hAPP(fequal,X,tc_fun(A,tc_fun(A,tc_bool))),Y,tc_fun(A,tc_bool))))),
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19969
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a7 ).
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19717
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