TSTP Solution File: LCL745-1 by E-SAT---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : LCL745-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:33:44 EDT 2023
% Result : Unsatisfiable 1488.63s 190.65s
% Output : CNFRefutation 1488.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 70
% Syntax : Number of clauses : 297 ( 143 unt; 18 nHn; 131 RR)
% Number of literals : 508 ( 230 equ; 208 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 9 con; 0-5 aty)
% Number of variables : 726 ( 236 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf__sup__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf__sup__absorb_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_inf__bool__eq__raw_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(tc_bool) = c_and,
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf__bool__eq__raw_0) ).
cnf(cls_le__iff__inf_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_le__iff__inf_1) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_typing_OVar_0) ).
cnf(cls_le__iff__sup_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_le__iff__sup_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_le__iff__sup_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_le__iff__sup_1) ).
cnf(cls_sup__inf__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_sup__inf__absorb_0) ).
cnf(cls_var__app__type__eq_0,axiom,
( X1 = X2
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_var__app__type__eq_0) ).
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_foldl__Nil_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_COMBC__def_0) ).
cnf(cls_le__infI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_le__infI2_0) ).
cnf(cls_sup__absorb1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_sup__absorb1_0) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf__sup__aci_I8_J_0) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__Lattices_Olattice) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(cls_order__less__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_order__less__le__trans_0) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__Orderings_Opreorder) ).
cnf(cls_bot__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_bot__least_0) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__Orderings_Obot) ).
cnf(cls_le__infI1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_le__infI1_0) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf__sup__aci_I4_J_0) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_insert__def_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_Collect__def_0) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_order__less__irrefl_0) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_add__right__cancel_0) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_class__semiring_Oadd__0_0) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_order__le__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_order__le__less__trans_0) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_bool__Orderings_Opreorder) ).
cnf(cls_Collect__conj__eq_0,axiom,
c_Collect(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),X2),X1,tc_bool,tc_bool),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Collect(X2,X1)),c_Collect(X3,X1)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_Collect__conj__eq_0) ).
cnf(cls_Collect__conv__if2_1,axiom,
( c_Collect(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),hAPP(c_fequal(X1),X2)),X1,tc_bool,tc_bool),X3),X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_Collect__conv__if2_1) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_singleton__conv2_0) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(hAPP(c_COMBS(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),hAPP(X5,X6)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_COMBS__def_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_COMBB__def_0) ).
cnf(cls_Collect__disj__eq_0,axiom,
c_Collect(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_or),X2),X1,tc_bool,tc_bool),X3),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(X2,X1),c_Collect(X3,X1),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_Collect__disj__eq_0) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_Un__empty__right_0) ).
cnf(cls_gr0I_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_gr0I_0) ).
cnf(cls_Int__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_Int__empty__right_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X1),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf1E_1) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf1I_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_bot1E_0) ).
cnf(cls_exE__some_0,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_exE__some_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_xt1_I11_J_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_sup1CI_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_LeastI__ex_0,axiom,
( hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X2,X1)))
| ~ class_Orderings_Owellorder(X1)
| ~ hBOOL(hAPP(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_LeastI__ex_0) ).
cnf(cls_nat__neq__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_nat__neq__iff_0) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_add__nonneg__eq__0__iff_1) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(cls_Un__empty__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_Un__empty__left_0) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(cls_inf__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf__absorb2_0) ).
cnf(cls_IT_OVar_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB)) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_IT_OVar_0) ).
cnf(cls_listsp_ONil_0,axiom,
hBOOL(c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2)),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_listsp_ONil_0) ).
cnf(cls_bot__fun__eq_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_bot__fun__eq_0) ).
cnf(cls_inf__idem_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_inf__idem_0) ).
cnf(cls_sup__bot__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_sup__bot__right_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(clsarity_nat__Orderings_Owellorder,axiom,
class_Orderings_Owellorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',clsarity_nat__Orderings_Owellorder) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p',cls_nat__less__le_1) ).
cnf(c_0_70,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__absorb_0 ).
cnf(c_0_71,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_72,axiom,
c_Lattices_Olower__semilattice__class_Oinf(tc_bool) = c_and,
cls_inf__bool__eq__raw_0 ).
cnf(c_0_73,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
cls_le__iff__inf_1 ).
cnf(c_0_74,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_75,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I5_J_0 ).
cnf(c_0_76,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
cls_typing_OVar_0 ).
cnf(c_0_77,plain,
hAPP(hAPP(c_and,X1),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_78,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_le__iff__sup_0 ).
cnf(c_0_79,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),X2))
| hAPP(hAPP(c_and,X1),X2) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_72]),c_0_74])]) ).
cnf(c_0_80,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_81,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
cls_le__iff__sup_1 ).
cnf(c_0_82,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool),
inference(spm,[status(thm)],[c_0_75,c_0_71]) ).
cnf(c_0_83,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_sup__inf__absorb_0 ).
cnf(c_0_84,axiom,
( X1 = X2
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)
| ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
cls_var__app__type__eq_0 ).
cnf(c_0_85,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
cls_foldl__Nil_0 ).
cnf(c_0_86,plain,
c_Type_Otyping(hAPP(c_and,X1),c_Lambda_OdB_OVar(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool)),X1),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_87,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X2
| hAPP(hAPP(c_and,X1),X2) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
cnf(c_0_88,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),X2))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_80])]) ).
cnf(c_0_89,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_and,X1),X2),tc_bool) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_71]),c_0_72]) ).
cnf(c_0_90,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I1_J_0 ).
cnf(c_0_91,plain,
( X1 = X2
| ~ c_Type_Otyping(X3,c_Lambda_OdB_OVar(X4),X2)
| ~ c_Type_Otyping(X3,c_Lambda_OdB_OVar(X4),X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
( c_Type_Otyping(hAPP(c_and,X1),c_Lambda_OdB_OVar(X2),X1)
| hAPP(hAPP(c_and,X1),X2) != X1 ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_94,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
cls_le__infI2_0 ).
cnf(c_0_95,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_and,X1),X2)),X1)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
hAPP(hAPP(c_and,X1),X2) = hAPP(hAPP(c_and,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_71]),c_0_72]),c_0_72]) ).
cnf(c_0_97,plain,
( X1 = X2
| hAPP(hAPP(c_and,X2),X3) != X2
| ~ c_Type_Otyping(hAPP(c_and,X2),c_Lambda_OdB_OVar(X3),X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,plain,
c_Type_Otyping(hAPP(X1,X2),c_Lambda_OdB_OVar(X3),hAPP(hAPP(c_COMBC(X1,X4,X5,X6),X3),X2)),
inference(spm,[status(thm)],[c_0_76,c_0_93]) ).
cnf(c_0_99,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_sup__absorb1_0 ).
cnf(c_0_100,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_and,X1),X2)),X3))
| hAPP(hAPP(c_and,X2),X3) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_79]),c_0_72]),c_0_74])]) ).
cnf(c_0_101,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I8_J_0 ).
cnf(c_0_102,axiom,
class_Lattices_Olattice(tc_nat),
clsarity_nat__Lattices_Olattice ).
cnf(c_0_103,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_and,X1),X2)),X2)),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_104,plain,
( hAPP(hAPP(c_COMBC(c_and,X1,X2,X3),X4),X5) = X5
| hAPP(hAPP(c_and,X5),X4) != X5 ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_and,X2),X3),tc_bool) = X1
| hAPP(hAPP(c_and,X3),X1) != X3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_80])]) ).
cnf(c_0_106,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
clsarity_nat__Lattices_Oupper__semilattice ).
cnf(c_0_108,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_COMBC(c_and,X1,X2,X3),X4),X5)),X4)),
inference(spm,[status(thm)],[c_0_103,c_0_93]) ).
cnf(c_0_109,plain,
( hAPP(hAPP(c_COMBC(c_and,X1,X2,X3),X4),X5) = X5
| hAPP(hAPP(c_and,X4),X5) != X5 ),
inference(spm,[status(thm)],[c_0_104,c_0_96]) ).
cnf(c_0_110,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X1
| hAPP(hAPP(c_and,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool)),X1) != c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool) ),
inference(spm,[status(thm)],[c_0_105,c_0_77]) ).
cnf(c_0_111,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__le__trans_0 ).
cnf(c_0_112,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_106]),c_0_107])]) ).
cnf(c_0_113,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder ).
cnf(c_0_114,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0 ).
cnf(c_0_115,axiom,
class_Orderings_Obot(tc_nat),
clsarity_nat__Orderings_Obot ).
cnf(c_0_116,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_le__infI1_0 ).
cnf(c_0_117,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),X2))
| hAPP(hAPP(c_and,X2),X1) != X1 ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_118,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I4_J_0 ).
cnf(c_0_119,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X1
| hAPP(hAPP(c_and,X3),X1) != X3
| hAPP(hAPP(c_and,X2),X3) != X2 ),
inference(spm,[status(thm)],[c_0_110,c_0_87]) ).
cnf(c_0_120,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
cls_insert__def_0 ).
cnf(c_0_121,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_122,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0 ).
cnf(c_0_123,plain,
( c_HOL_Oord__class_Oless(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113])]) ).
cnf(c_0_124,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X1)),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_125,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
cls_add__right__cancel_0 ).
cnf(c_0_126,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__semigroup__add ).
cnf(c_0_127,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0 ).
cnf(c_0_128,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_129,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_order__le__less__trans_0 ).
cnf(c_0_130,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_131,axiom,
c_Collect(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),X2),X1,tc_bool,tc_bool),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Collect(X2,X1)),c_Collect(X3,X1)),
cls_Collect__conj__eq_0 ).
cnf(c_0_132,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_and,X1),X2)),X3))
| hAPP(hAPP(c_and,X3),X1) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_72]),c_0_74])]) ).
cnf(c_0_133,plain,
hAPP(hAPP(c_and,X1),hAPP(hAPP(c_and,X1),X2)) = hAPP(hAPP(c_and,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_71]),c_0_72]),c_0_72]),c_0_72]) ).
cnf(c_0_134,plain,
hAPP(hAPP(c_and,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool)) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_82]) ).
cnf(c_0_135,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),X3,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool)
| hAPP(hAPP(c_and,X3),X1) != X3 ),
inference(spm,[status(thm)],[c_0_119,c_0_77]) ).
cnf(c_0_136,axiom,
( c_Collect(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),hAPP(c_fequal(X1),X2)),X1,tc_bool,tc_bool),X3),X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(X3,X2)) ),
cls_Collect__conv__if2_1 ).
cnf(c_0_137,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
cls_singleton__conv2_0 ).
cnf(c_0_138,plain,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X2,tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_139,plain,
~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),X1,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_113])]) ).
cnf(c_0_140,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_124]),c_0_107])]) ).
cnf(c_0_141,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_142,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_143,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_and,X1),X2),X3,tc_bool)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_95]),c_0_130])]) ).
cnf(c_0_144,axiom,
hAPP(hAPP(c_COMBS(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),hAPP(X5,X6)),
cls_COMBS__def_0 ).
cnf(c_0_145,plain,
hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),X2),X1,tc_bool,tc_bool),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_131,c_0_121]),c_0_121]),c_0_121]) ).
cnf(c_0_146,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_147,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_and,X1),X2),X3,tc_bool) = X3
| hAPP(hAPP(c_and,X3),X1) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_132]),c_0_80])]) ).
cnf(c_0_148,plain,
hAPP(hAPP(c_and,X1),hAPP(hAPP(c_and,X2),X1)) = hAPP(hAPP(c_and,X2),X1),
inference(spm,[status(thm)],[c_0_133,c_0_96]) ).
cnf(c_0_149,plain,
( hAPP(hAPP(c_and,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool)) = X1
| hAPP(hAPP(c_and,X1),X2) != X1 ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_150,axiom,
c_Collect(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_or),X2),X1,tc_bool,tc_bool),X3),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(X2,X1),c_Collect(X3,X1),tc_fun(X1,tc_bool)),
cls_Collect__disj__eq_0 ).
cnf(c_0_151,plain,
( hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_and),hAPP(c_fequal(X1),X2)),X1,tc_bool,tc_bool),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(X3,X2)) ),
inference(rw,[status(thm)],[c_0_136,c_0_121]) ).
cnf(c_0_152,plain,
hAPP(c_fequal(X1),X2) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_121]),c_0_138]) ).
cnf(c_0_153,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Un__empty__right_0 ).
cnf(c_0_154,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),
inference(spm,[status(thm)],[c_0_75,c_0_102]) ).
cnf(c_0_155,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_156,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_gr0I_0 ).
cnf(c_0_157,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X2 ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_158,plain,
~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_and,X1),X2),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_143]),c_0_130])]) ).
cnf(c_0_159,plain,
hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4) = hAPP(hAPP(c_and,hAPP(X2,X4)),hAPP(X3,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_146]) ).
cnf(c_0_160,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Int__empty__right_0 ).
cnf(c_0_161,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_162,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_and,X1),X2),X3,tc_bool) = X3
| hAPP(hAPP(c_and,X3),X2) != X2 ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_163,plain,
( hAPP(hAPP(c_and,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool)),X3) = X3
| hAPP(hAPP(c_and,X3),X1) != X3 ),
inference(spm,[status(thm)],[c_0_96,c_0_149]) ).
cnf(c_0_164,plain,
hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_or),X2),X1,tc_bool,tc_bool),X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_121]),c_0_121]),c_0_121]) ).
cnf(c_0_165,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X1),X2)) ),
cls_inf1E_1 ).
cnf(c_0_166,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0 ).
cnf(c_0_167,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_inf1I_0 ).
cnf(c_0_168,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(X3,X2)) ),
inference(rw,[status(thm)],[c_0_151,c_0_145]) ).
cnf(c_0_169,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_170,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_171,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
cls_exE__some_0 ).
cnf(c_0_172,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_173,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),
inference(spm,[status(thm)],[c_0_106,c_0_154]) ).
cnf(c_0_174,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_124]),c_0_113])]) ).
cnf(c_0_175,plain,
c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_176,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X2,X3,X4),X5),X1) != hAPP(X5,X1) ),
inference(spm,[status(thm)],[c_0_157,c_0_144]) ).
cnf(c_0_177,plain,
~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_and,hAPP(hAPP(c_and,X1),X2)),X3),tc_bool),
inference(spm,[status(thm)],[c_0_158,c_0_143]) ).
cnf(c_0_178,plain,
hAPP(hAPP(c_and,hAPP(X1,X2)),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_179,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_xt1_I11_J_0 ).
cnf(c_0_180,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1)),
inference(spm,[status(thm)],[c_0_114,c_0_161]) ).
cnf(c_0_181,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_182,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X2
| hAPP(hAPP(c_and,X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_bool) ),
inference(spm,[status(thm)],[c_0_162,c_0_134]) ).
cnf(c_0_183,plain,
hAPP(hAPP(c_and,X1),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),X3,tc_bool)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_77]),c_0_96]) ).
cnf(c_0_184,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_sup1CI_0 ).
cnf(c_0_185,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4) = hAPP(hAPP(c_or,hAPP(X1,X4)),hAPP(X2,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_164]),c_0_146]) ).
cnf(c_0_186,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_and,hAPP(X3,X2)),hAPP(X1,X2))) ),
inference(spm,[status(thm)],[c_0_165,c_0_159]) ).
cnf(c_0_187,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(spm,[status(thm)],[c_0_166,c_0_128]) ).
cnf(c_0_188,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0 ).
cnf(c_0_189,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_169]) ).
cnf(c_0_190,plain,
hAPP(hAPP(c_fequal(X1),X2),X3) = hAPP(hAPP(c_fequal(X1),X3),X2),
inference(spm,[status(thm)],[c_0_93,c_0_170]) ).
cnf(c_0_191,axiom,
( hBOOL(hAPP(X2,c_Orderings_Oord__class_OLeast(X2,X1)))
| ~ class_Orderings_Owellorder(X1)
| ~ hBOOL(hAPP(X2,X3)) ),
cls_LeastI__ex_0 ).
cnf(c_0_192,plain,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),c_Hilbert__Choice_OEps(hAPP(c_fequal(X1),X2),X3))),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_193,plain,
~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),X2,tc_nat),
inference(spm,[status(thm)],[c_0_139,c_0_173]) ).
cnf(c_0_194,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat) = X1,
inference(spm,[status(thm)],[c_0_83,c_0_102]) ).
cnf(c_0_195,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(rw,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_196,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_nat__neq__iff_0 ).
cnf(c_0_197,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_add__nonneg__eq__0__iff_1 ).
cnf(c_0_198,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(rw,[status(thm)],[c_0_140,c_0_175]) ).
cnf(c_0_199,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__comm__monoid__add ).
cnf(c_0_200,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1)),
inference(spm,[status(thm)],[c_0_124,c_0_175]) ).
cnf(c_0_201,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_COMBC(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X2,X3,X4),X5,X6,X7),X1),X8) != hAPP(X8,X1) ),
inference(spm,[status(thm)],[c_0_176,c_0_93]) ).
cnf(c_0_202,plain,
~ c_HOL_Oord__class_Oless(X1,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),tc_bool),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_203,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181])]) ).
cnf(c_0_204,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X2
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool),X1,tc_bool) != X2 ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_205,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),X3,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool)
| hAPP(hAPP(c_and,X3),X2) != X3 ),
inference(spm,[status(thm)],[c_0_119,c_0_134]) ).
cnf(c_0_206,plain,
( hBOOL(hAPP(hAPP(c_or,hAPP(X1,X2)),hAPP(X3,X2)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_207,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_and,hAPP(X2,c_HOL_Ozero__class_Ozero(tc_nat))),X1)) ),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_208,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
inference(spm,[status(thm)],[c_0_188,c_0_128]) ).
cnf(c_0_209,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_210,plain,
( hBOOL(hAPP(hAPP(c_fequal(X1),X2),c_Orderings_Oord__class_OLeast(hAPP(c_fequal(X1),X2),X3)))
| ~ class_Orderings_Owellorder(X3) ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_211,plain,
~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_212,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_213,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_112]),c_0_198]),c_0_198]),c_0_199]),c_0_200])]) ).
cnf(c_0_214,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_COMBC(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X2,X3,X4),X5,X6,X7),X1),hAPP(c_COMBS(X8,X9,X10,X11),X12)) != hAPP(hAPP(X8,X1),hAPP(X12,X1)) ),
inference(spm,[status(thm)],[c_0_201,c_0_144]) ).
cnf(c_0_215,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
cls_Un__empty__left_0 ).
cnf(c_0_216,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_217,plain,
hAPP(hAPP(c_COMBC(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1,X2,X3),X4),X5) = hAPP(X5,X4),
inference(spm,[status(thm)],[c_0_93,c_0_142]) ).
cnf(c_0_218,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X2
| hAPP(hAPP(c_and,X1),X3) != X1
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool) != X2 ),
inference(spm,[status(thm)],[c_0_204,c_0_205]) ).
cnf(c_0_219,plain,
( hBOOL(hAPP(hAPP(c_or,hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_206,c_0_187]) ).
cnf(c_0_220,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_and,X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_208]),c_0_142]) ).
cnf(c_0_221,plain,
( hBOOL(hAPP(X1,c_Orderings_Oord__class_OLeast(hAPP(c_fequal(X2),X3),X4)))
| ~ hBOOL(hAPP(X1,X3))
| ~ class_Orderings_Owellorder(X4) ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_222,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X1) = c_Orderings_Obot__class_Obot(tc_nat),
inference(spm,[status(thm)],[c_0_140,c_0_194]) ).
cnf(c_0_223,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_224,axiom,
class_Lattices_Olower__semilattice(tc_nat),
clsarity_nat__Lattices_Olower__semilattice ).
cnf(c_0_225,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(spm,[status(thm)],[c_0_213,c_0_208]) ).
cnf(c_0_226,plain,
c_COMBS(c_COMBC(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X1,X2,X3),X4,X5,X6),X7,X8,X9) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(er,[status(thm)],[c_0_214]) ).
cnf(c_0_227,plain,
hAPP(hAPP(c_or,c_Orderings_Obot__class_Obot(tc_bool)),hAPP(X1,X2)) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_215]),c_0_216]) ).
cnf(c_0_228,plain,
hAPP(c_COMBS(hAPP(hAPP(c_COMBC(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),tc_bool,tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),hAPP(hAPP(c_COMBC(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),tc_bool,tc_bool,tc_bool),c_or),c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1))),X1,tc_bool,tc_bool),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_164]),c_0_217]),c_0_217]) ).
cnf(c_0_229,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X2
| c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_bool),tc_bool) != X2 ),
inference(spm,[status(thm)],[c_0_218,c_0_134]) ).
cnf(c_0_230,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_and,X2),X1),tc_bool) = X1,
inference(spm,[status(thm)],[c_0_89,c_0_96]) ).
cnf(c_0_231,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Orderings_Oord__class_OLeast(hAPP(c_fequal(X3),X2),X4)))
| ~ class_Orderings_Owellorder(X4) ),
inference(spm,[status(thm)],[c_0_189,c_0_210]) ).
cnf(c_0_232,plain,
( hBOOL(hAPP(hAPP(c_or,X1),X2))
| ~ hBOOL(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_208]),c_0_142]) ).
cnf(c_0_233,plain,
( hBOOL(c_Orderings_Oord__class_OLeast(hAPP(c_fequal(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_and,X4),X2))
| ~ class_Orderings_Owellorder(X3) ),
inference(spm,[status(thm)],[c_0_220,c_0_221]) ).
cnf(c_0_234,plain,
hAPP(hAPP(c_COMBC(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_nat)) = c_Orderings_Obot__class_Obot(tc_nat),
inference(spm,[status(thm)],[c_0_93,c_0_222]) ).
cnf(c_0_235,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_inf__absorb2_0 ).
cnf(c_0_236,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_223]),c_0_224])]) ).
cnf(c_0_237,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X2,X3,X4),X5),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(spm,[status(thm)],[c_0_225,c_0_144]) ).
cnf(c_0_238,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_nat),X2),X1) != hAPP(hAPP(X2,X1),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_144]),c_0_226]) ).
cnf(c_0_239,plain,
hAPP(hAPP(c_or,c_Orderings_Obot__class_Obot(tc_bool)),X1) = X1,
inference(spm,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_240,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_and,X1),X2),X3,tc_bool) = X3
| c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_bool) != X3 ),
inference(spm,[status(thm)],[c_0_229,c_0_230]) ).
cnf(c_0_241,plain,
( hBOOL(hAPP(hAPP(c_or,X1),X2))
| ~ hBOOL(c_Orderings_Oord__class_OLeast(hAPP(c_fequal(X3),X2),X4))
| ~ class_Orderings_Owellorder(X4) ),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_242,plain,
( hBOOL(c_Orderings_Oord__class_OLeast(hAPP(c_fequal(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool)),X4))
| ~ hBOOL(X2)
| ~ class_Orderings_Owellorder(X4) ),
inference(spm,[status(thm)],[c_0_233,c_0_77]) ).
cnf(c_0_243,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB)) ),
cls_IT_OVar_0 ).
cnf(c_0_244,axiom,
hBOOL(c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2)),
cls_listsp_ONil_0 ).
cnf(c_0_245,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_234,c_0_175]),c_0_93]),c_0_175]) ).
cnf(c_0_246,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_224])]) ).
cnf(c_0_247,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_COMBC(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X2,X3,X4),X5,X6,X7),X1),X8) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(spm,[status(thm)],[c_0_237,c_0_93]) ).
cnf(c_0_248,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_or,c_Orderings_Obot__class_Obot(tc_bool))),X1) != hAPP(X1,X1) ),
inference(spm,[status(thm)],[c_0_238,c_0_239]) ).
cnf(c_0_249,plain,
( hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_220,c_0_77]) ).
cnf(c_0_250,plain,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_and,X1),X2),X3,tc_bool) = X3
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool) != X3 ),
inference(spm,[status(thm)],[c_0_240,c_0_82]) ).
cnf(c_0_251,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__fun__eq_0 ).
cnf(c_0_252,plain,
( hBOOL(hAPP(hAPP(c_or,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool)))
| ~ hBOOL(X2)
| ~ class_Orderings_Owellorder(X4) ),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_253,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_244]),c_0_85]) ).
cnf(c_0_254,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(X3,X2)) != hAPP(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X4,X5,X6),X3),X2) ),
inference(spm,[status(thm)],[c_0_141,c_0_144]) ).
cnf(c_0_255,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__idem_0 ).
cnf(c_0_256,plain,
hAPP(hAPP(c_COMBC(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1,X2,X3),X4),X5) = hAPP(c_HOL_Ozero__class_Ozero(tc_nat),X4),
inference(spm,[status(thm)],[c_0_93,c_0_245]) ).
cnf(c_0_257,plain,
( hAPP(hAPP(c_COMBC(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2,X3,X4),X5),X6) = hAPP(X6,X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
inference(spm,[status(thm)],[c_0_93,c_0_246]) ).
cnf(c_0_258,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_144]),c_0_226]) ).
cnf(c_0_259,plain,
hAPP(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_or,c_Orderings_Obot__class_Obot(tc_bool))) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(er,[status(thm)],[c_0_248]) ).
cnf(c_0_260,plain,
( hBOOL(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool) != X1
| ~ hBOOL(hAPP(hAPP(c_and,X3),X2)) ),
inference(spm,[status(thm)],[c_0_249,c_0_250]) ).
cnf(c_0_261,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0 ).
cnf(c_0_262,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_263,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_251,c_0_161]) ).
cnf(c_0_264,plain,
( hBOOL(hAPP(hAPP(c_or,X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2)),X3,tc_bool)))
| ~ class_Orderings_Owellorder(X4) ),
inference(spm,[status(thm)],[c_0_252,c_0_253]) ).
cnf(c_0_265,axiom,
class_Orderings_Owellorder(tc_nat),
clsarity_nat__Orderings_Owellorder ).
cnf(c_0_266,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_COMBC(c_and,X2,X3,X4),X1),X5),tc_bool) = X1,
inference(spm,[status(thm)],[c_0_230,c_0_93]) ).
cnf(c_0_267,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_and,X2),X3)) != hAPP(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X4,X5,X6),hAPP(c_and,X3)),X2) ),
inference(spm,[status(thm)],[c_0_254,c_0_96]) ).
cnf(c_0_268,plain,
hAPP(hAPP(c_COMBS(c_COMBC(X1,X2,X3,X4),X5,X6,X7),X8),X9) = hAPP(hAPP(X1,hAPP(X8,X9)),X9),
inference(spm,[status(thm)],[c_0_93,c_0_144]) ).
cnf(c_0_269,plain,
hAPP(hAPP(c_and,X1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_74]),c_0_72]) ).
cnf(c_0_270,plain,
( hAPP(X1,X2) = hAPP(c_HOL_Ozero__class_Ozero(tc_nat),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(spm,[status(thm)],[c_0_256,c_0_257]) ).
cnf(c_0_271,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(spm,[status(thm)],[c_0_258,c_0_259]) ).
cnf(c_0_272,plain,
( hBOOL(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool),X1,tc_bool) != X1
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_260,c_0_77]) ).
cnf(c_0_273,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X1,
inference(spm,[status(thm)],[c_0_261,c_0_262]) ).
cnf(c_0_274,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_169,c_0_263]) ).
cnf(c_0_275,plain,
hBOOL(hAPP(hAPP(c_or,X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2)),X3,tc_bool))),
inference(spm,[status(thm)],[c_0_264,c_0_265]) ).
cnf(c_0_276,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X1
| hAPP(hAPP(c_and,X1),X2) != X2 ),
inference(spm,[status(thm)],[c_0_266,c_0_109]) ).
cnf(c_0_277,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_nat),c_and),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_268]),c_0_269]),c_0_226]) ).
cnf(c_0_278,plain,
( hAPP(c_HOL_Ozero__class_Ozero(tc_nat),X1) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_or,c_Orderings_Obot__class_Obot(tc_bool)),tc_nat) ),
inference(spm,[status(thm)],[c_0_239,c_0_270]) ).
cnf(c_0_279,plain,
hAPP(c_or,c_Orderings_Obot__class_Obot(tc_bool)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(spm,[status(thm)],[c_0_271,c_0_259]) ).
cnf(c_0_280,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_nat__less__le_1 ).
cnf(c_0_281,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_273]),c_0_274]) ).
cnf(c_0_282,plain,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,X2),hAPP(hAPP(c_COMBS(c_and,X3,X4,X5),X1),X2),tc_bool) = hAPP(X1,X2),
inference(spm,[status(thm)],[c_0_230,c_0_144]) ).
cnf(c_0_283,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),c_Orderings_Obot__class_Obot(tc_nat)) = c_Orderings_Obot__class_Obot(tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_124]),c_0_224])]) ).
cnf(c_0_284,plain,
hBOOL(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1)),X2,tc_bool)),
inference(spm,[status(thm)],[c_0_275,c_0_239]) ).
cnf(c_0_285,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool) = X2
| hAPP(hAPP(c_and,X2),X1) != X1 ),
inference(spm,[status(thm)],[c_0_82,c_0_276]) ).
cnf(c_0_286,plain,
hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_nat),c_and),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_187])]) ).
cnf(c_0_287,plain,
hAPP(c_HOL_Ozero__class_Ozero(tc_nat),X1) = X1,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_278,c_0_279]),c_0_280]) ).
cnf(c_0_288,plain,
( hAPP(X1,X2) != c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_281,c_0_282]) ).
cnf(c_0_289,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_283,c_0_175]),c_0_175]) ).
cnf(c_0_290,plain,
( hBOOL(X1)
| hAPP(hAPP(c_and,X1),hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2))) != hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2)) ),
inference(spm,[status(thm)],[c_0_284,c_0_285]) ).
cnf(c_0_291,plain,
hAPP(c_and,c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[c_0_286,c_0_287]) ).
cnf(c_0_292,plain,
( c_Orderings_Obot__class_Obot(tc_bool) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(spm,[status(thm)],[c_0_288,c_0_289]) ).
cnf(c_0_293,plain,
hBOOL(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_290,c_0_291]),c_0_287])]) ).
cnf(c_0_294,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(X2,X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rw,[status(thm)],[c_0_258,c_0_287]) ).
cnf(c_0_295,plain,
c_Orderings_Obot__class_Obot(tc_bool) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_292,c_0_293])]) ).
cnf(c_0_296,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_279]),c_0_295]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL745-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 2400
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Oct 2 12:09:08 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.35/0.55 Running first-order model finding
% 0.35/0.55 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.U7WVLizuEA/E---3.1_18566.p
% 1488.63/190.65 # Version: 3.1pre001
% 1488.63/190.65 # Preprocessing class: FSLMSMSMSSSNFFN.
% 1488.63/190.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1488.63/190.65 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 1488.63/190.65 # Starting new_bool_3 with 600s (2) cores
% 1488.63/190.65 # Starting new_bool_1 with 300s (1) cores
% 1488.63/190.65 # Starting sh5l with 300s (1) cores
% 1488.63/190.65 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 18643 completed with status 0
% 1488.63/190.65 # Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 1488.63/190.65 # Preprocessing class: FSLMSMSMSSSNFFN.
% 1488.63/190.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1488.63/190.65 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 1488.63/190.65 # No SInE strategy applied
% 1488.63/190.65 # Search class: FGHSM-FSLM32-DFFFFFNN
% 1488.63/190.65 # Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 1488.63/190.65 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 90s (1) cores
% 1488.63/190.65 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 1488.63/190.65 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 1488.63/190.65 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1488.63/190.65 # U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 18654 completed with status 7
% 1488.63/190.65 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 90s (1) cores
% 1488.63/190.65 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 18653 completed with status 7
% 1488.63/190.65 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 90s (1) cores
% 1488.63/190.65 # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 18651 completed with status 7
% 1488.63/190.65 # Starting U----_206d_02_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1488.63/190.65 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 18652 completed with status 7
% 1488.63/190.65 # Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1488.63/190.65 # G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with pid 18710 completed with status 7
% 1488.63/190.65 # Starting U----_207c_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1488.63/190.65 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with pid 18711 completed with status 7
% 1488.63/190.65 # Starting G----_0021_C18_F1_SE_CS_SP_S4S with 90s (1) cores
% 1488.63/190.65 # U----_206d_02_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 18712 completed with status 7
% 1488.63/190.65 # Starting C12_02_nc_SAT001_MinMin_p005000_rr with 90s (1) cores
% 1488.63/190.65 # U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 18715 completed with status 0
% 1488.63/190.65 # Result found by U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 1488.63/190.65 # Preprocessing class: FSLMSMSMSSSNFFN.
% 1488.63/190.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1488.63/190.65 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 1488.63/190.65 # No SInE strategy applied
% 1488.63/190.65 # Search class: FGHSM-FSLM32-DFFFFFNN
% 1488.63/190.65 # Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 1488.63/190.65 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 90s (1) cores
% 1488.63/190.65 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 1488.63/190.65 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 1488.63/190.65 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1488.63/190.65 # U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 18654 completed with status 7
% 1488.63/190.65 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 90s (1) cores
% 1488.63/190.65 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 18653 completed with status 7
% 1488.63/190.65 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 90s (1) cores
% 1488.63/190.65 # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 18651 completed with status 7
% 1488.63/190.65 # Starting U----_206d_02_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1488.63/190.65 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 18652 completed with status 7
% 1488.63/190.65 # Starting U----_206d_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 1488.63/190.65 # Preprocessing time : 0.005 s
% 1488.63/190.65 # Presaturation interreduction done
% 1488.63/190.65
% 1488.63/190.65 # Proof found!
% 1488.63/190.65 # SZS status Unsatisfiable
% 1488.63/190.65 # SZS output start CNFRefutation
% See solution above
% 1488.63/190.65 # Parsed axioms : 569
% 1488.63/190.65 # Removed by relevancy pruning/SinE : 0
% 1488.63/190.65 # Initial clauses : 569
% 1488.63/190.65 # Removed in clause preprocessing : 3
% 1488.63/190.65 # Initial clauses in saturation : 566
% 1488.63/190.65 # Processed clauses : 63417
% 1488.63/190.65 # ...of these trivial : 2607
% 1488.63/190.65 # ...subsumed : 51710
% 1488.63/190.65 # ...remaining for further processing : 9100
% 1488.63/190.65 # Other redundant clauses eliminated : 105522
% 1488.63/190.65 # Clauses deleted for lack of memory : 592593
% 1488.63/190.65 # Backward-subsumed : 501
% 1488.63/190.65 # Backward-rewritten : 999
% 1488.63/190.65 # Generated clauses : 3884245
% 1488.63/190.65 # ...of the previous two non-redundant : 3660055
% 1488.63/190.65 # ...aggressively subsumed : 0
% 1488.63/190.65 # Contextual simplify-reflections : 6
% 1488.63/190.65 # Paramodulations : 3778522
% 1488.63/190.65 # Factorizations : 155
% 1488.63/190.65 # NegExts : 0
% 1488.63/190.65 # Equation resolutions : 105566
% 1488.63/190.65 # Total rewrite steps : 616600
% 1488.63/190.65 # Propositional unsat checks : 0
% 1488.63/190.65 # Propositional check models : 0
% 1488.63/190.65 # Propositional check unsatisfiable : 0
% 1488.63/190.65 # Propositional clauses : 0
% 1488.63/190.65 # Propositional clauses after purity: 0
% 1488.63/190.65 # Propositional unsat core size : 0
% 1488.63/190.65 # Propositional preprocessing time : 0.000
% 1488.63/190.65 # Propositional encoding time : 0.000
% 1488.63/190.65 # Propositional solver time : 0.000
% 1488.63/190.65 # Success case prop preproc time : 0.000
% 1488.63/190.65 # Success case prop encoding time : 0.000
% 1488.63/190.65 # Success case prop solver time : 0.000
% 1488.63/190.65 # Current number of processed clauses : 7146
% 1488.63/190.65 # Positive orientable unit clauses : 1134
% 1488.63/190.65 # Positive unorientable unit clauses: 272
% 1488.63/190.65 # Negative unit clauses : 723
% 1488.63/190.65 # Non-unit-clauses : 5017
% 1488.63/190.65 # Current number of unprocessed clauses: 1206554
% 1488.63/190.65 # ...number of literals in the above : 3193901
% 1488.63/190.65 # Current number of archived formulas : 0
% 1488.63/190.65 # Current number of archived clauses : 1955
% 1488.63/190.65 # Clause-clause subsumption calls (NU) : 2686887
% 1488.63/190.65 # Rec. Clause-clause subsumption calls : 2165179
% 1488.63/190.65 # Non-unit clause-clause subsumptions : 36768
% 1488.63/190.65 # Unit Clause-clause subsumption calls : 190027
% 1488.63/190.65 # Rewrite failures with RHS unbound : 0
% 1488.63/190.65 # BW rewrite match attempts : 220420
% 1488.63/190.65 # BW rewrite match successes : 11957
% 1488.63/190.65 # Condensation attempts : 0
% 1488.63/190.65 # Condensation successes : 0
% 1488.63/190.65 # Termbank termtop insertions : 96191560
% 1488.63/190.65
% 1488.63/190.65 # -------------------------------------------------
% 1488.63/190.65 # User time : 714.742 s
% 1488.63/190.65 # System time : 12.622 s
% 1488.63/190.65 # Total time : 727.364 s
% 1488.63/190.65 # Maximum resident set size: 2864 pages
% 1488.63/190.65
% 1488.63/190.65 # -------------------------------------------------
% 1488.63/190.65 # User time : 731.198 s
% 1488.63/190.65 # System time : 13.112 s
% 1488.63/190.65 # Total time : 744.310 s
% 1488.63/190.65 # Maximum resident set size: 2144 pages
% 1488.63/190.65 % E---3.1 exiting
%------------------------------------------------------------------------------