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

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/const_comb_inclS.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,65 @@
+%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)]).
+
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/const_comb_noS.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,48 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%typed combinator reduction for const-types-only (no S)
+
+%K P Q --> P
+input_clause(a1,axiom,
+[++equal(hAPP(hAPP(c_COMBK(A,B),P),Q),P)]).
+
+%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(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(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(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)]).
+
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/const_helper1.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,10 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%extensionality for const-types-only
+
+input_clause(a18,axiom,
+[--equal(hAPP(F,hAPP(hAPP(hEXTENT(A,B),F),G)),hAPP(G,hAPP(hAPP(hEXTENT(A,B),F),G))),
+++equal(F,G)]).
+
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/full_comb_inclS.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,71 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%typed combinator reduction for full-types (include S)
+
+%K P Q --> P
+input_clause(a1,axiom,
+[++equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))),typeinfo(P,A)),tc_fun(B,A)),typeinfo(Q,B)),A),typeinfo(P,A))]).
+
+%S P Q R --> P R (Q R)
+input_clause(a2,axiom,
+[++equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBS,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(tc_fun(A,B),tc_fun(A,C)))),typeinfo(P,tc_fun(A,tc_fun(B,C)))),tc_fun(tc_fun(A,B),tc_fun(A,C))),typeinfo(Q,tc_fun(A,B))),tc_fun(A,C)),typeinfo(R,A)),C),typeinfo(hAPP(typeinfo(hAPP(typeinfo(P,tc_fun(A,tc_fun(B,C))),typeinfo(R,A)),tc_fun(B,C)),typeinfo(hAPP(typeinfo(Q,tc_fun(A,B)),typeinfo(R,A)),B)),C))]).
+
+%I P --> P
+input_clause(a3,axiom,
+[++equal(typeinfo(hAPP(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(P,T)),T),typeinfo(P,T))]).
+
+%B P Q R --> P(Q R)
+input_clause(a4,axiom,
+[++equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBB,tc_fun(tc_fun(A,B),tc_fun(tc_fun(C,A),tc_fun(C,B)))),typeinfo(P,tc_fun(A,B))),tc_fun(tc_fun(C,A),tc_fun(C,B))),typeinfo(Q,tc_fun(C,A))),tc_fun(C,B)),typeinfo(R,C)),B),typeinfo(hAPP(typeinfo(P,tc_fun(A,B)),typeinfo(hAPP(typeinfo(Q,tc_fun(C,A)),typeinfo(R,C)),A)),B))]).
+
+
+%C P Q R --> P R Q
+input_clause(a5,axiom,
+[++equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBC,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(B,tc_fun(A,C)))),typeinfo(P,tc_fun(A,tc_fun(B,C)))),tc_fun(B,tc_fun(A,C))),typeinfo(Q,B)),tc_fun(A,C)),typeinfo(R,A)),C),typeinfo(hAPP(typeinfo(hAPP(typeinfo(P,tc_fun(A,tc_fun(B,C))),typeinfo(R,A)),tc_fun(B,C)),typeinfo(Q,B)),C))]).
+
+%the combinators are all different
+input_clause(a6,axiom,
+[--equal(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))))]).
+
+input_clause(a7,axiom,
+[--equal(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(c_COMBS,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(tc_fun(A,B),tc_fun(A,C)))))]).
+
+
+input_clause(a8,axiom,
+[--equal(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(c_COMBB,tc_fun(tc_fun(A,B),tc_fun(tc_fun(C,A),tc_fun(C,B)))))]).
+
+
+input_clause(a9,axiom,
+[--equal(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(c_COMBC,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(B,tc_fun(A,C)))))]).
+
+
+input_clause(a10,axiom,
+[--equal(typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))),typeinfo(c_COMBS,tc_fun(tc_fun(A3,tc_fun(B3,C3)),tc_fun(tc_fun(A3,B3),tc_fun(A3,C3)))))]).
+
+input_clause(a11,axiom,
+[--equal(typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))),typeinfo(c_COMBB,tc_fun(tc_fun(A1,B1),tc_fun(tc_fun(C1,A1),tc_fun(C1,B1)))))]).
+
+
+input_clause(a12,axiom,
+[--equal(typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))),typeinfo(c_COMBC,tc_fun(tc_fun(A2,tc_fun(B2,C2)),tc_fun(B2,tc_fun(A2,C2)))))]).
+
+
+input_clause(a13,axiom,
+[--equal(typeinfo(c_COMBS,tc_fun(tc_fun(A3,tc_fun(B3,C3)),tc_fun(tc_fun(A3,B3),tc_fun(A3,C3)))),typeinfo(c_COMBB,tc_fun(tc_fun(A1,B1),tc_fun(tc_fun(C1,A1),tc_fun(C1,B1)))))]).
+
+
+input_clause(a14,axiom,
+[--equal(typeinfo(c_COMBS,tc_fun(tc_fun(A3,tc_fun(B3,C3)),tc_fun(tc_fun(A3,B3),tc_fun(A3,C3)))),typeinfo(c_COMBC,tc_fun(tc_fun(A2,tc_fun(B2,C2)),tc_fun(B2,tc_fun(A2,C2)))))]).
+
+input_clause(a15,axiom,
+[--equal(typeinfo(c_COMBB,tc_fun(tc_fun(A1,B1),tc_fun(tc_fun(C1,A1),tc_fun(C1,B1)))),typeinfo(c_COMBC,tc_fun(tc_fun(A2,tc_fun(B2,C2)),tc_fun(B2,tc_fun(A2,C2)))))]).
+
+input_clause(a16,axiom,
+[--hBOOL(typeinfo(hAPP(typeinfo(hAPP(typeinfo(fequal,tc_fun(A,tc_fun(A,tc_bool))),typeinfo(X,A)),tc_fun(A,tc_bool)),typeinfo(Y,A)),tc_bool)),
+++equal(typeinfo(X,A),typeinfo(Y,A))]).
+
+input_clause(a17,axiom,
+[++hBOOL(typeinfo(hAPP(typeinfo(hAPP(typeinfo(fequal,tc_fun(A,tc_fun(A,tc_bool))),typeinfo(X,A)),tc_fun(A,tc_bool)),typeinfo(Y,A)),tc_bool)),
+--equal(typeinfo(X,A),typeinfo(Y,A))]).
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/full_comb_noS.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,52 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%typed combinator reduction for full-types (no S)
+
+%K P Q --> P
+input_clause(a1,axiom,
+[++equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))),typeinfo(P,A)),tc_fun(B,A)),typeinfo(Q,B)),A),typeinfo(P,A))]).
+
+%I P --> P
+input_clause(a3,axiom,
+[++equal(typeinfo(hAPP(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(P,T)),T),typeinfo(P,T))]).
+
+%B P Q R --> P(Q R)
+input_clause(a4,axiom,
+[++equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBB,tc_fun(tc_fun(A,B),tc_fun(tc_fun(C,A),tc_fun(C,B)))),typeinfo(P,tc_fun(A,B))),tc_fun(tc_fun(C,A),tc_fun(C,B))),typeinfo(Q,tc_fun(C,A))),tc_fun(C,B)),typeinfo(R,C)),B),typeinfo(hAPP(typeinfo(P,tc_fun(A,B)),typeinfo(hAPP(typeinfo(Q,tc_fun(C,A)),typeinfo(R,C)),A)),B))]).
+
+
+%C P Q R --> P R Q
+input_clause(a5,axiom,
+[++equal(typeinfo(hAPP(typeinfo(hAPP(typeinfo(hAPP(typeinfo(c_COMBC,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(B,tc_fun(A,C)))),typeinfo(P,tc_fun(A,tc_fun(B,C)))),tc_fun(B,tc_fun(A,C))),typeinfo(Q,B)),tc_fun(A,C)),typeinfo(R,A)),C),typeinfo(hAPP(typeinfo(hAPP(typeinfo(P,tc_fun(A,tc_fun(B,C))),typeinfo(R,A)),tc_fun(B,C)),typeinfo(Q,B)),C))]).
+
+%the combinators are all different
+input_clause(a6,axiom,
+[--equal(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))))]).
+
+input_clause(a8,axiom,
+[--equal(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(c_COMBB,tc_fun(tc_fun(A,B),tc_fun(tc_fun(C,A),tc_fun(C,B)))))]).
+
+
+input_clause(a9,axiom,
+[--equal(typeinfo(c_COMBI,tc_fun(T,T)),typeinfo(c_COMBC,tc_fun(tc_fun(A,tc_fun(B,C)),tc_fun(B,tc_fun(A,C)))))]).
+
+input_clause(a11,axiom,
+[--equal(typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))),typeinfo(c_COMBB,tc_fun(tc_fun(A1,B1),tc_fun(tc_fun(C1,A1),tc_fun(C1,B1)))))]).
+
+
+input_clause(a12,axiom,
+[--equal(typeinfo(c_COMBK,tc_fun(A,tc_fun(B,A))),typeinfo(c_COMBC,tc_fun(tc_fun(A2,tc_fun(B2,C2)),tc_fun(B2,tc_fun(A2,C2)))))]).
+
+
+input_clause(a15,axiom,
+[--equal(typeinfo(c_COMBB,tc_fun(tc_fun(A1,B1),tc_fun(tc_fun(C1,A1),tc_fun(C1,B1)))),typeinfo(c_COMBC,tc_fun(tc_fun(A2,tc_fun(B2,C2)),tc_fun(B2,tc_fun(A2,C2)))))]).
+
+input_clause(a16,axiom,
+[--hBOOL(typeinfo(hAPP(typeinfo(hAPP(typeinfo(fequal,tc_fun(A,tc_fun(A,tc_bool))),typeinfo(X,A)),tc_fun(A,tc_bool)),typeinfo(Y,A)),tc_bool)),
+++equal(typeinfo(X,A),typeinfo(Y,A))]).
+
+input_clause(a17,axiom,
+[++hBOOL(typeinfo(hAPP(typeinfo(hAPP(typeinfo(fequal,tc_fun(A,tc_fun(A,tc_bool))),typeinfo(X,A)),tc_fun(A,tc_bool)),typeinfo(Y,A)),tc_bool)),
+--equal(typeinfo(X,A),typeinfo(Y,A))]).
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/full_helper1.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,7 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%extensionality for full-types
+
+input_clause(a18,axiom,
+[--equal(typeinfo(hAPP(typeinfo(F,tc_fun(A,B)),typeinfo(hAPP(typeinfo(hAPP(typeinfo(hEXTENT,tc_fun(tc_fun(A,B),tc_fun(tc_fun(A,B),A))),typeinfo(F,tc_fun(A,B))),tc_fun(tc_fun(A,B),A)),typeinfo(G,tc_fun(A,B))),A)),B),typeinfo(hAPP(typeinfo(G,tc_fun(A,B)),typeinfo(hAPP(typeinfo(hAPP(typeinfo(hEXTENT,tc_fun(tc_fun(A,B),tc_fun(tc_fun(A,B),A))),typeinfo(F,tc_fun(A,B))),tc_fun(tc_fun(A,B),A)),typeinfo(G,tc_fun(A,B))),A)),B)),
+++equal(typeinfo(F,tc_fun(A,B)),typeinfo(G,tc_fun(A,B)))]).

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/par_comb_inclS.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,67 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%typed combinator reduction for partial-types (include S)
+
+%K P Q --> P
+input_clause(a1,axiom,
+[++equal(hAPP(hAPP(c_COMBK,P,tc_fun(A,tc_fun(B,A))),Q,tc_fun(B,A)),P)]).
+
+
+%S P Q R --> P R (Q R)
+input_clause(a2,axiom,
+[++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)))]).
+
+%I P --> P
+input_clause(a3,axiom,
+[++equal(hAPP(c_COMBI,P,tc_fun(T,T)),P)]).
+
+
+%B P Q R --> P(Q R)
+input_clause(a4,axiom,
+[++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)))]).
+
+
+%C P Q R --> P R Q
+input_clause(a5,axiom,
+[++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)))]).
+
+%the combinators are all different
+input_clause(a6,axiom,
+[--equal(c_COMBI,c_COMBK)]).
+
+input_clause(a7,axiom,
+[--equal(c_COMBI,c_COMBS)]).
+
+input_clause(a8,axiom,
+[--equal(c_COMBI,c_COMBB)]).
+
+input_clause(a9,axiom,
+[--equal(c_COMBI,c_COMBC)]).
+
+input_clause(a10,axiom,
+[--equal(c_COMBK,c_COMBS)]).
+
+input_clause(a11,axiom,
+[--equal(c_COMBK,c_COMBB)]).
+
+input_clause(a12,axiom,
+[--equal(c_COMBK,c_COMBC)]).
+
+input_clause(a13,axiom,
+[--equal(c_COMBS,c_COMBB)]).
+
+input_clause(a14,axiom,
+[--equal(c_COMBS,c_COMBC)]).
+
+input_clause(a15,axiom,
+[--equal(c_COMBB,c_COMBC)]).
+
+input_clause(a16,axiom,
+[--hBOOL(hAPP(hAPP(fequal,X,tc_fun(A,tc_fun(A,tc_bool))),Y,tc_fun(A,tc_bool))),
+++equal(X,Y)]).
+
+input_clause(a17,axiom,
+[++hBOOL(hAPP(hAPP(fequal,X,tc_fun(A,tc_fun(A,tc_bool))),Y,tc_fun(A,tc_bool))),
+--equal(X,Y)]).
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/par_comb_noS.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,50 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%typed combinator reduction for partial-types (no S)
+
+%K P Q --> P
+input_clause(a1,axiom,
+[++equal(hAPP(hAPP(c_COMBK,P,tc_fun(A,tc_fun(B,A))),Q,tc_fun(B,A)),P)]).
+
+%I P --> P
+input_clause(a3,axiom,
+[++equal(hAPP(c_COMBI,P,tc_fun(T,T)),P)]).
+
+
+%B P Q R --> P(Q R)
+input_clause(a4,axiom,
+[++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)))]).
+
+
+%C P Q R --> P R Q
+input_clause(a5,axiom,
+[++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)))]).
+
+%the combinators are all different
+input_clause(a6,axiom,
+[--equal(c_COMBI,c_COMBK)]).
+
+input_clause(a8,axiom,
+[--equal(c_COMBI,c_COMBB)]).
+
+input_clause(a9,axiom,
+[--equal(c_COMBI,c_COMBC)]).
+
+input_clause(a11,axiom,
+[--equal(c_COMBK,c_COMBB)]).
+
+input_clause(a12,axiom,
+[--equal(c_COMBK,c_COMBC)]).
+
+input_clause(a15,axiom,
+[--equal(c_COMBB,c_COMBC)]).
+
+input_clause(a16,axiom,
+[--hBOOL(hAPP(hAPP(fequal,X,tc_fun(A,tc_fun(A,tc_bool))),Y,tc_fun(A,tc_bool))),
+++equal(X,Y)]).
+
+input_clause(a17,axiom,
+[++hBOOL(hAPP(hAPP(fequal,X,tc_fun(A,tc_fun(A,tc_bool))),Y,tc_fun(A,tc_bool))),
+--equal(X,Y)]).
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/par_helper1.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,9 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%extensionality for partial types
+
+input_clause(a18,axiom,
+[--equal(hAPP(F,hAPP(hAPP(hEXTENT,F,tc_fun(tc_fun(A,B),tc_fun(tc_fun(A,B),A))),G,tc_fun(tc_fun(A,B),A)),tc_fun(A,B)),hAPP(G,hAPP(hAPP(hEXTENT,F,tc_fun(tc_fun(A,B),tc_fun(tc_fun(A,B),A))),G,tc_fun(tc_fun(A,B),A)),tc_fun(A,B))),
+++equal(F,G)]).
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/u_comb_inclS.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,61 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%untyped combinator reduction (include S)
+
+input_clause(a1,axiom,
+[++equal(hAPP(hAPP(c_COMBK,P),Q),P)]).
+
+%S P Q R
+input_clause(a2,axiom,
+[++equal(hAPP(hAPP(hAPP(c_COMBS,P),Q),R),hAPP(hAPP(P,R),hAPP(Q,R)))]).
+
+input_clause(a3,axiom,
+[++equal(hAPP(c_COMBI,P),P)]).
+
+%B P Q R --> P(Q R)
+input_clause(a4,axiom,
+[++equal(hAPP(hAPP(hAPP(c_COMBB,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,P),Q),R),hAPP(hAPP(P,R),Q))]).
+
+%the combinators are all different
+input_clause(a6,axiom,
+[--equal(c_COMBI,c_COMBK)]).
+
+input_clause(a7,axiom,
+[--equal(c_COMBI,c_COMBS)]).
+
+input_clause(a8,axiom,
+[--equal(c_COMBI,c_COMBB)]).
+
+input_clause(a9,axiom,
+[--equal(c_COMBI,c_COMBC)]).
+
+input_clause(a10,axiom,
+[--equal(c_COMBK,c_COMBS)]).
+
+input_clause(a11,axiom,
+[--equal(c_COMBK,c_COMBB)]).
+
+input_clause(a12,axiom,
+[--equal(c_COMBK,c_COMBC)]).
+
+input_clause(a13,axiom,
+[--equal(c_COMBS,c_COMBB)]).
+
+input_clause(a14,axiom,
+[--equal(c_COMBS,c_COMBC)]).
+
+input_clause(a15,axiom,
+[--equal(c_COMBB,c_COMBC)]).
+
+input_clause(a16,axiom,
+[--hBOOL(hAPP(hAPP(fequal,X),Y)),++equal(X,Y)]).
+
+input_clause(a17,axiom,
+[++hBOOL(hAPP(hAPP(fequal,X),Y)),--equal(X,Y)]).
+
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/u_comb_noS.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,45 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%untyped combinator reduction (no S)
+
+input_clause(a1,axiom,
+[++equal(hAPP(hAPP(c_COMBK,P),Q),P)]).
+
+input_clause(a3,axiom,
+[++equal(hAPP(c_COMBI,P),P)]).
+
+%B P Q R --> P(Q R)
+input_clause(a4,axiom,
+[++equal(hAPP(hAPP(hAPP(c_COMBB,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,P),Q),R),hAPP(hAPP(P,R),Q))]).
+
+%the combinators are all different
+input_clause(a6,axiom,
+[--equal(c_COMBI,c_COMBK)]).
+
+input_clause(a8,axiom,
+[--equal(c_COMBI,c_COMBB)]).
+
+input_clause(a9,axiom,
+[--equal(c_COMBI,c_COMBC)]).
+
+input_clause(a11,axiom,
+[--equal(c_COMBK,c_COMBB)]).
+
+input_clause(a12,axiom,
+[--equal(c_COMBK,c_COMBC)]).
+
+input_clause(a15,axiom,
+[--equal(c_COMBB,c_COMBC)]).
+
+input_clause(a16,axiom,
+[--hBOOL(hAPP(hAPP(fequal,X),Y)),++equal(X,Y)]).
+
+input_clause(a17,axiom,
+[++hBOOL(hAPP(hAPP(fequal,X),Y)),--equal(X,Y)]).
+
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/atp-inputs/u_helper1.tptp	Fri Apr 28 06:05:19 2006 +0200
@@ -0,0 +1,8 @@
+%ID: $Id$
+%Author: Jia Meng, NICTA
+%extensionality, untyped
+
+input_clause(a18,axiom,
+[--equal(hAPP(F,hAPP(hAPP(hEXTENT,F),G)),hAPP(G,hAPP(hAPP(hEXTENT,F),G))),
+++equal(F,G)]).
+