src/HOL/Tools/atp-inputs/const_comb_inclS.tptp

added some helper files for HOL goals/lemmas. Clauses have TPTP format.

%ID: $Id$
%Author: Jia Meng, NICTA
%typed combinator reduction for const-types-only (include S)

%K P Q --> P
input_clause(a1,axiom,
[++equal(hAPP(hAPP(c_COMBK(A,B),P),Q),P)]).

%S P Q R --> P R (Q R)
input_clause(a2,axiom,
[++equal(hAPP(hAPP(hAPP(c_COMBS(A,B,C),P),Q),R),hAPP(hAPP(P,R),hAPP(Q,R)))]).


%I P --> P
input_clause(a3,axiom,
[++equal(hAPP(c_COMBI(T),P),P)]).

%B P Q R --> P(Q R)
input_clause(a4,axiom,
[++equal(hAPP(hAPP(hAPP(c_COMBB(A,B,C),P),Q),R),hAPP(P,hAPP(Q,R)))]).


%C P Q R --> P R Q
input_clause(a5,axiom,
[++equal(hAPP(hAPP(hAPP(c_COMBC(A,B,C),P),Q),R),hAPP(hAPP(P,R),Q))]).

%the combinators are all different
input_clause(a6,axiom,
[--equal(c_COMBI(T),c_COMBK(A,B))]).

input_clause(a7,axiom,
[--equal(c_COMBI(T),c_COMBS(A,B,C))]).

input_clause(a8,axiom,
[--equal(c_COMBI(T),c_COMBB(A,B,C))]).

input_clause(a9,axiom,
[--equal(c_COMBI(T),c_COMBC(A,B,C))]).

input_clause(a10,axiom,
[--equal(c_COMBK(A,B),c_COMBS(A3,B3,C3))]).

input_clause(a11,axiom,
[--equal(c_COMBK(A,B),c_COMBB(A1,B1,C1))]).

input_clause(a12,axiom,
[--equal(c_COMBK(A,B),c_COMBC(A2,B2,C2))]).

input_clause(a13,axiom,
[--equal(c_COMBS(A3,B3,C3),c_COMBB(A1,B1,C1))]).

input_clause(a14,axiom,
[--equal(c_COMBS(A3,B3,C3),c_COMBC(A2,B2,C2))]).

input_clause(a15,axiom,
[--equal(c_COMBB(A1,B1,C1),c_COMBC(A2,B2,C2))]).

input_clause(a16,axiom,
[--hBOOL(hAPP(hAPP(fequal(A),X),Y)),++equal(X,Y)]).

input_clause(a17,axiom,
[++hBOOL(hAPP(hAPP(fequal(A),X),Y)),--equal(X,Y)]).