%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL823-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:45:10 PM UTC 2026
% Result : Unsatisfiable 4.45s 3.36s
% Output : CNFRefutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 15 unt; 0 nHn; 10 RR)
% Number of literals : 21 ( 7 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 28 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 13 con; 0-3 aty)
% Number of variables : 27 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Collect__conj__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),X2)),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),hAPP(c_Collect(X1),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__conj__eq_0) ).
cnf(cls_Collect__def_0,axiom,
hAPP(c_Collect(X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_rs____,tc_Lambda_OdB)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_listsp__infI_0,axiom,
( hBOOL(c_List_Olistsp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,X1))
| ~ hBOOL(c_List_Olistsp(X3,X4,X1))
| ~ hBOOL(c_List_Olistsp(X2,X4,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp__infI_0) ).
cnf(cls_CHAINED_0_01,axiom,
hBOOL(c_List_Olistsp(hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))),v_rs____,tc_Lambda_OdB)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(c_List_Olistsp(hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____))),v_rs____,tc_Lambda_OdB)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(c_0_7,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),X2)),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),hAPP(c_Collect(X1),X3)),
cls_Collect__conj__eq_0 ).
cnf(c_0_8,axiom,
hAPP(c_Collect(X1),X2) = X2,
cls_Collect__def_0 ).
cnf(c_0_9,negated_conjecture,
~ hBOOL(c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_rs____,tc_Lambda_OdB)),
cls_conjecture_0 ).
cnf(c_0_10,plain,
hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),X2)),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]),c_0_8]) ).
cnf(c_0_11,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
cls_Int__commute_0 ).
cnf(c_0_12,negated_conjecture,
~ hBOOL(c_List_Olistsp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst))))))))),v_rs____,tc_Lambda_OdB)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,axiom,
( hBOOL(c_List_Olistsp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,X1))
| ~ hBOOL(c_List_Olistsp(X3,X4,X1))
| ~ hBOOL(c_List_Olistsp(X2,X4,X1)) ),
cls_listsp__infI_0 ).
cnf(c_0_14,axiom,
hBOOL(c_List_Olistsp(hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))),v_rs____,tc_Lambda_OdB)),
cls_CHAINED_0_01 ).
cnf(c_0_15,axiom,
hBOOL(c_List_Olistsp(hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____))),v_rs____,tc_Lambda_OdB)),
cls_CHAINED_0 ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL823-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n018.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 23:12:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 4.45/3.36 % Version : CSE_E---1.7
% 4.45/3.36 % Problem : theBenchmark.p
% 4.45/3.36 % SZS status Unsatisfiable for theBenchmark.p
% 4.45/3.36 % SZS output start CNFRefutation
% See solution above
% 4.45/3.37 % Total time : 2.480s
%------------------------------------------------------------------------------