src/HOL/Tools/atp-inputs/par_comb_inclS.tptp
author haftmann
Tue, 25 Jul 2006 16:51:26 +0200
changeset 20192 956cd30ef3be
parent 19969 c72e2110c026
permissions -rw-r--r--
renamed Name.give_names to Name.names and moved Name.alphanum to Symbol.alphanum
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%ID: $Id$
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%Author: Jia Meng, NICTA
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%typed combinator reduction for partial-types (include S)
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%K P Q --> P
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input_clause(a1,axiom,
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[++equal(hAPP(hAPP(c_COMBK,P,tc_fun(A,tc_fun(B,A))),Q,tc_fun(B,A)),P)]).
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%S P Q R --> P R (Q R)
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input_clause(a2,axiom,
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[++equal(hAPP(hAPP(hAPP(c_COMBS,P,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(tc_fun(A,B),tc_fun(A,C)))),Q,tc_fun(tc_fun(A,B),tc_fun(A,C))),R,tc_fun(A,C)),hAPP(hAPP(P,R,tc_fun(A,tc_fun(B,C))),hAPP(Q,R,tc_fun(A,B)),tc_fun(B,C)))]).
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%I P --> P
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input_clause(a3,axiom,
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[++equal(hAPP(c_COMBI,P,tc_fun(T,T)),P)]).
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%B P Q R --> P(Q R)
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input_clause(a4,axiom,
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[++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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%C P Q R --> P R Q
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input_clause(a5,axiom,
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[++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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input_clause(a6,axiom,
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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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++equal(X,Y)]).
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input_clause(a7,axiom,
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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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--equal(X,Y)]).
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