%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT043-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:08:14 PM UTC 2026
% Result : Unsatisfiable 71.52s 24.86s
% Output : CNFRefutation 71.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 53
% Syntax : Number of clauses : 323 ( 116 unt; 89 nHn; 152 RR)
% Number of literals : 590 ( 230 equ; 215 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 7 con; 0-5 aty)
% Number of variables : 636 ( 201 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_linorder__neq__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_not__leE_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
cnf(cls_Collect__neg__eq_0,axiom,
c_Collect(hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Collect(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_le__sup__iff_1,axiom,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(cls_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_vimage__Collect__eq_0,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(hAPP(c_COMBB(X2,X3,tc_bool,X4),X1),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X1,hAPP(X5,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_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/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
cnf(cls_vimage__const_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
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/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(cls_CollectD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_Collect__empty__eq_0,axiom,
( ~ hBOOL(hAPP(X1,X3))
| c_Collect(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_rev__bexI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_fun__upd__idem__iff_1,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
cnf(cls_ord_OatMost__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatMost(X3,X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatMost__iff_1) ).
cnf(cls_rev__bexI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X3,X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_ord_OatMost__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatMost__iff_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_CollectI_0,axiom,
( ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
cnf(cls_inf__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_diff__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_double__compl_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_not__Cons__self_0,axiom,
X1 != c_List_Olist_OCons(X2,X1,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
cnf(cls_compl__inf__bot_0,axiom,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_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/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_Diff__eq_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
( ~ class_Lattices_Oboolean__algebra(X2)
| class_Lattices_Oboolean__algebra(tc_fun(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
cnf(cls_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(c_0_53,plain,
( ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(fof_simplification,[status(thm)],[cls_linorder__neq__iff_1]) ).
cnf(c_0_54,plain,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_not__leE_0]) ).
cnf(c_0_55,plain,
( ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_53 ).
cnf(c_0_56,plain,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
c_0_54 ).
cnf(c_0_57,axiom,
c_Collect(hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Collect(X2,X1)),
cls_Collect__neg__eq_0 ).
cnf(c_0_58,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_59,plain,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_le__sup__iff_1]) ).
cnf(c_0_60,plain,
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder ).
cnf(c_0_62,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_63,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(hAPP(c_COMBB(X2,X3,tc_bool,X4),X1),X4),
cls_vimage__Collect__eq_0 ).
cnf(c_0_64,axiom,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X1,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_65,plain,
hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_58]) ).
cnf(c_0_66,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2 ),
inference(fof_simplification,[status(thm)],[cls_le__iff__inf_0]) ).
cnf(c_0_67,plain,
( ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_lessequals(X2,X3,X1) ),
c_0_59 ).
cnf(c_0_68,plain,
c_lessequals(X1,X1,tc_nat),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
clsarity_nat__Lattices_Oupper__semilattice ).
cnf(c_0_70,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_ComplD_0]) ).
cnf(c_0_71,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_72,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_62,c_0_58]) ).
cnf(c_0_73,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3)),X2),
cls_insert__def_0 ).
cnf(c_0_74,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_vimage__const_1 ).
cnf(c_0_75,plain,
c_Set_Ovimage(X1,X2,X4,X3) = hAPP(c_COMBB(X2,X3,tc_bool,X4),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_58]),c_0_58]) ).
cnf(c_0_76,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
cls_vimage__Compl_0 ).
cnf(c_0_77,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3) = hAPP(c_Not,hAPP(X2,X3)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_78,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_79,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2 ),
c_0_66 ).
cnf(c_0_80,plain,
c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X2),X1),tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_81,axiom,
class_Lattices_Olower__semilattice(tc_nat),
clsarity_nat__Lattices_Olower__semilattice ).
cnf(c_0_82,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_70 ).
cnf(c_0_83,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_84,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_85,plain,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1)),X2),
inference(rw,[status(thm)],[c_0_73,c_0_58]) ).
cnf(c_0_86,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X1),X4))
| hAPP(c_COMBB(X4,X2,tc_bool,X3),c_COMBK(X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_87,plain,
hAPP(c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X2,tc_bool,X4),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),hAPP(c_COMBB(X3,X2,tc_bool,X4),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_75]),c_0_75]) ).
cnf(c_0_88,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_77]) ).
cnf(c_0_89,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X2),X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_90,plain,
( ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_83]) ).
cnf(c_0_91,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_CollectD_0]) ).
cnf(c_0_92,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_bot__least_0]) ).
cnf(c_0_93,plain,
( ~ hBOOL(hAPP(X1,X3))
| c_Collect(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_Collect__empty__eq_0]) ).
cnf(c_0_94,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),
cls_singleton__iff_1 ).
cnf(c_0_95,plain,
hAPP(c_fequal(X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_58]),c_0_85]) ).
cnf(c_0_96,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Un__empty__right_0 ).
cnf(c_0_97,plain,
( hBOOL(hAPP(X1,X4))
| hAPP(c_COMBB(X1,X2,tc_bool,X3),c_COMBK(X4,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_86,c_0_83]) ).
cnf(c_0_98,plain,
hAPP(c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),tc_bool,tc_bool,X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_65]),c_0_78]) ).
cnf(c_0_99,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_100,plain,
( ~ hBOOL(hAPP(X4,X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_in(X2),X3)),X4)) ),
inference(spm,[status(thm)],[c_0_90,c_0_83]) ).
cnf(c_0_101,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
c_0_91 ).
cnf(c_0_102,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
inference(fof_simplification,[status(thm)],[cls_le__iff__sup_0]) ).
cnf(c_0_103,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
c_0_92 ).
cnf(c_0_104,axiom,
class_Orderings_Obot(tc_nat),
clsarity_nat__Orderings_Obot ).
cnf(c_0_105,plain,
( ~ hBOOL(hAPP(X1,X3))
| c_Collect(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_93 ).
cnf(c_0_106,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))),
inference(rw,[status(thm)],[c_0_94,c_0_85]) ).
cnf(c_0_107,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_108,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_109,plain,
( hBOOL(X1)
| c_COMBK(X1,tc_bool,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_77]),c_0_99]) ).
cnf(c_0_110,plain,
( ~ hBOOL(hAPP(X3,X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_in(X2),X3)),hAPP(c_in(X4),X5))) ),
inference(spm,[status(thm)],[c_0_100,c_0_83]) ).
cnf(c_0_111,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_101,c_0_58]) ).
cnf(c_0_112,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
cls_CHAINED_0_01 ).
cnf(c_0_113,plain,
( ~ c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
c_0_102 ).
cnf(c_0_114,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_115,plain,
( ~ hBOOL(hAPP(X1,X3))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(rw,[status(thm)],[c_0_105,c_0_58]) ).
cnf(c_0_116,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_fequal(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_96]),c_0_107]) ).
cnf(c_0_117,plain,
( hBOOL(X3)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = X3 ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_118,plain,
( ~ hBOOL(hAPP(X6,X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_in(X2),hAPP(c_in(X3),X4))),hAPP(c_in(X5),X6))) ),
inference(spm,[status(thm)],[c_0_110,c_0_83]) ).
cnf(c_0_119,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_120,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_69])]) ).
cnf(c_0_121,plain,
hAPP(c_in(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_122,plain,
( hBOOL(X2)
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_117,c_0_117]) ).
cnf(c_0_123,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_in(X2),hAPP(c_in(X3),v_P____))),hAPP(c_in(X4),c_Arrow__Order__Mirabelle_OProf))),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_124,plain,
( ~ hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Orderings_Obot__class_Obot(tc_nat))),X2)) ),
inference(spm,[status(thm)],[c_0_90,c_0_120]) ).
cnf(c_0_125,plain,
( hAPP(X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(X2)
| hBOOL(c_in(X1)) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_126,plain,
~ hBOOL(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_77]),c_0_83]),c_0_83]),c_0_83]) ).
cnf(c_0_127,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_77]),c_0_120]) ).
cnf(c_0_128,plain,
( X2 != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_Not)
| hBOOL(c_in(X1)) ),
inference(spm,[status(thm)],[c_0_125,c_0_99]) ).
cnf(c_0_129,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
inference(fof_simplification,[status(thm)],[cls_rev__bexI_1]) ).
cnf(c_0_130,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
cls_ComplI_0 ).
cnf(c_0_131,plain,
( hBOOL(X1)
| X1 = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_126,c_0_122]) ).
cnf(c_0_132,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
cls_fun__upd__idem__iff_1 ).
cnf(c_0_133,plain,
( ~ hBOOL(X2)
| hBOOL(X1)
| X1 = hAPP(c_Not,X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_122]) ).
cnf(c_0_134,plain,
( hBOOL(c_Not)
| hBOOL(c_in(X1)) ),
inference(er,[status(thm)],[c_0_128]) ).
cnf(c_0_135,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
c_0_129 ).
cnf(c_0_136,plain,
( hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_83]),c_0_83]) ).
cnf(c_0_137,plain,
( ~ hBOOL(hAPP(hAPP(X3,X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatMost(X3,X4,X1))) ),
inference(fof_simplification,[status(thm)],[cls_ord_OatMost__iff_1]) ).
cnf(c_0_138,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,X1) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_127,c_0_131]) ).
cnf(c_0_139,plain,
c_Fun_Ofun__upd(c_Not,hAPP(c_Not,X1),X1,X2,X3) = c_Not,
inference(spm,[status(thm)],[c_0_132,c_0_99]) ).
cnf(c_0_140,plain,
( hBOOL(X1)
| hBOOL(c_Not)
| X1 = hAPP(c_Not,c_in(X2)) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_141,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X3,X1)),X2)) ),
inference(fof_simplification,[status(thm)],[cls_rev__bexI_0]) ).
cnf(c_0_142,plain,
( ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3))) ),
inference(rw,[status(thm)],[c_0_135,c_0_83]) ).
cnf(c_0_143,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Not,hAPP(X1,X2))) ),
inference(rw,[status(thm)],[c_0_136,c_0_77]) ).
cnf(c_0_144,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_145,plain,
( ~ hBOOL(hAPP(hAPP(X3,X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatMost(X3,X4,X1))) ),
c_0_137 ).
cnf(c_0_146,plain,
( hBOOL(c_Not)
| hAPP(c_Not,c_in(X1)) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_138,c_0_134]) ).
cnf(c_0_147,plain,
( hBOOL(c_Not)
| hAPP(c_Not,c_in(X1)) = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_139])]) ).
cnf(c_0_148,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X3,X1)),X2)) ),
c_0_141 ).
cnf(c_0_149,plain,
( ~ hBOOL(hAPP(X1,v_P____))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,X1,X2))) ),
inference(spm,[status(thm)],[c_0_142,c_0_119]) ).
cnf(c_0_150,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_143,c_0_108]) ).
cnf(c_0_151,plain,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_115,c_0_144]) ).
cnf(c_0_152,plain,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OatMost(X1,X2,X3),X4)) ),
inference(rw,[status(thm)],[c_0_145,c_0_83]) ).
cnf(c_0_153,plain,
( hBOOL(c_Not)
| c_in(X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_146]),c_0_99]) ).
cnf(c_0_154,plain,
( hBOOL(c_Not)
| c_in(X1) = hAPP(c_Not,c_Not) ),
inference(spm,[status(thm)],[c_0_99,c_0_147]) ).
cnf(c_0_155,plain,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,X2,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_83]),c_0_83]) ).
cnf(c_0_156,plain,
( hBOOL(v_P____)
| hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,c_Not,X1))) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_157,plain,
( hAPP(X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(X2)
| hBOOL(c_fequal(X1)) ),
inference(spm,[status(thm)],[c_0_151,c_0_122]) ).
cnf(c_0_158,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_ord_OatMost__iff_0]) ).
cnf(c_0_159,plain,
( ~ hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(c_SetInterval_Oord_OatMost(c_in(X1),X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_152,c_0_83]) ).
cnf(c_0_160,plain,
( hBOOL(c_Not)
| hAPP(c_Not,c_Not) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_161,plain,
( ~ hBOOL(hAPP(X1,v_P____))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,X1,X2))) ),
inference(spm,[status(thm)],[c_0_155,c_0_119]) ).
cnf(c_0_162,plain,
( ~ hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,c_Not,X1))
| hBOOL(v_P____) ),
inference(spm,[status(thm)],[c_0_127,c_0_156]) ).
cnf(c_0_163,plain,
( X2 != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_Not)
| hBOOL(c_fequal(X1)) ),
inference(spm,[status(thm)],[c_0_157,c_0_99]) ).
cnf(c_0_164,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_158 ).
cnf(c_0_165,plain,
hBOOL(hAPP(c_SetInterval_Oord_OatMost(c_in(X1),c_Arrow__Order__Mirabelle_OProf,X2),v_P____)),
inference(spm,[status(thm)],[c_0_159,c_0_119]) ).
cnf(c_0_166,plain,
( hAPP(c_Not,c_Not) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = hAPP(c_Not,c_Not) ),
inference(spm,[status(thm)],[c_0_138,c_0_160]) ).
cnf(c_0_167,plain,
( hBOOL(v_P____)
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,c_Not,X1))) ),
inference(spm,[status(thm)],[c_0_161,c_0_150]) ).
cnf(c_0_168,plain,
( hBOOL(v_P____)
| c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,c_Not,X1) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_162,c_0_131]) ).
cnf(c_0_169,plain,
( hBOOL(c_Not)
| hBOOL(c_fequal(X1)) ),
inference(er,[status(thm)],[c_0_163]) ).
cnf(c_0_170,plain,
( ~ hBOOL(hAPP(c_SetInterval_Oord_OatMost(X1,X3,X4),X2))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(rw,[status(thm)],[c_0_164,c_0_83]) ).
cnf(c_0_171,plain,
( hBOOL(c_Not)
| hBOOL(hAPP(c_SetInterval_Oord_OatMost(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),c_Arrow__Order__Mirabelle_OProf,X1),v_P____)) ),
inference(spm,[status(thm)],[c_0_165,c_0_153]) ).
cnf(c_0_172,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Not,c_Not) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_166]),c_0_99]) ).
cnf(c_0_173,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_115,c_0_136]) ).
cnf(c_0_174,plain,
( hBOOL(v_P____)
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)))) ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_175,plain,
( ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[cls_ATP__Linkup_Ofequal__imp__equal_0]) ).
cnf(c_0_176,plain,
( hBOOL(c_Not)
| hAPP(c_Not,c_fequal(X1)) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_138,c_0_169]) ).
cnf(c_0_177,plain,
( hBOOL(c_Not)
| hBOOL(hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),v_P____),c_Arrow__Order__Mirabelle_OProf)) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_178,plain,
( ~ hBOOL(c_Not)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_172]),c_0_119])]) ).
cnf(c_0_179,plain,
( ~ hBOOL(hAPP(c_Not,X2))
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_99,c_0_133]) ).
cnf(c_0_180,plain,
( X2 != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(spm,[status(thm)],[c_0_173,c_0_78]) ).
cnf(c_0_181,plain,
( hBOOL(v_P____)
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)))) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_138,c_0_174]) ).
cnf(c_0_182,plain,
( ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2))
| X1 = X2 ),
c_0_175 ).
cnf(c_0_183,plain,
( hBOOL(c_Not)
| c_fequal(X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_176]),c_0_99]) ).
cnf(c_0_184,plain,
( hBOOL(c_Not)
| hAPP(c_Not,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),v_P____),c_Arrow__Order__Mirabelle_OProf)) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_138,c_0_177]) ).
cnf(c_0_185,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,X1) = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_178,c_0_133]) ).
cnf(c_0_186,plain,
( hBOOL(X1)
| X1 = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_172]),c_0_119])]) ).
cnf(c_0_187,plain,
hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X3)),
inference(er,[status(thm)],[c_0_180]) ).
cnf(c_0_188,plain,
( hBOOL(v_P____)
| hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_181]),c_0_99]) ).
cnf(c_0_189,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = c_Not ),
inference(spm,[status(thm)],[c_0_99,c_0_172]) ).
cnf(c_0_190,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),X1),X2))
| hBOOL(c_Not)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_191,plain,
( hBOOL(c_Not)
| hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),v_P____),c_Arrow__Order__Mirabelle_OProf) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_184]),c_0_99]) ).
cnf(c_0_192,plain,
( X1 = c_Not
| hAPP(c_Not,X1) = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_193,plain,
hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(rw,[status(thm)],[c_0_187,c_0_77]) ).
cnf(c_0_194,plain,
( hBOOL(v_P____)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not) ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_195,plain,
( hBOOL(c_Not)
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_119])]) ).
cnf(c_0_196,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_115,c_0_119]) ).
cnf(c_0_197,plain,
( X1 = c_Not
| hAPP(c_Not,c_Not) = X1
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_99,c_0_192]) ).
cnf(c_0_198,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Not,
inference(spm,[status(thm)],[c_0_115,c_0_193]) ).
cnf(c_0_199,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Not,v_P____) = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not) ),
inference(spm,[status(thm)],[c_0_185,c_0_194]) ).
cnf(c_0_200,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = hAPP(c_Not,c_Not) ),
inference(spm,[status(thm)],[c_0_138,c_0_195]) ).
cnf(c_0_201,plain,
( ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1))) ),
inference(fof_simplification,[status(thm)],[cls_CollectI_0]) ).
cnf(c_0_202,plain,
( hAPP(c_Not,c_Not) != c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_198]) ).
cnf(c_0_203,plain,
( hAPP(c_Not,c_Not) = v_P____
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not) ),
inference(spm,[status(thm)],[c_0_99,c_0_199]) ).
cnf(c_0_204,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_200]),c_0_99]) ).
cnf(c_0_205,plain,
( ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1))) ),
c_0_201 ).
cnf(c_0_206,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_204]) ).
cnf(c_0_207,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_DiffE_1]) ).
cnf(c_0_208,plain,
( ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(rw,[status(thm)],[c_0_205,c_0_58]) ).
cnf(c_0_209,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not),v_P____),c_Arrow__Order__Mirabelle_OProf))
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_206]),c_0_178]) ).
cnf(c_0_210,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_207 ).
cnf(c_0_211,plain,
hBOOL(hAPP(hAPP(c_in(X1),v_P____),c_Arrow__Order__Mirabelle_OProf)),
inference(spm,[status(thm)],[c_0_208,c_0_119]) ).
cnf(c_0_212,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2 ),
inference(fof_simplification,[status(thm)],[cls_inf__idem_0]) ).
cnf(c_0_213,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not),v_P____)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_115,c_0_209]) ).
cnf(c_0_214,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),v_P____),c_HOL_Ominus__class_Ominus(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(X1,tc_bool)))),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_215,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
inference(fof_simplification,[status(thm)],[cls_diff__eq_0]) ).
cnf(c_0_216,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2 ),
c_0_212 ).
cnf(c_0_217,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_218,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not),v_P____) != hAPP(c_Not,c_Not)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_197]),c_0_198]) ).
cnf(c_0_219,plain,
~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,c_Arrow__Order__Mirabelle_OProf,tc_fun(X2,tc_bool)),v_P____)),
inference(rw,[status(thm)],[c_0_214,c_0_83]) ).
cnf(c_0_220,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) ),
c_0_215 ).
cnf(c_0_221,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X1) = X1,
inference(spm,[status(thm)],[c_0_216,c_0_217]) ).
cnf(c_0_222,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_223,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not),v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_218,c_0_197]) ).
cnf(c_0_224,plain,
( ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,c_Arrow__Order__Mirabelle_OProf,X2),v_P____))
| hBOOL(X2)
| hBOOL(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_219,c_0_122]) ).
cnf(c_0_225,plain,
c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),X1,tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_222])]) ).
cnf(c_0_226,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_double__compl_0]) ).
cnf(c_0_227,plain,
( hBOOL(hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf))
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_209,c_0_223]) ).
cnf(c_0_228,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf),v_P____))
| hBOOL(tc_bool)
| hBOOL(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_229,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2 ),
c_0_226 ).
cnf(c_0_230,plain,
( ~ hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_127,c_0_227]) ).
cnf(c_0_231,plain,
( ~ hBOOL(hAPP(X2,v_P____))
| hBOOL(X2)
| hBOOL(tc_bool)
| hBOOL(tc_fun(X1,tc_bool))
| hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf)) ),
inference(spm,[status(thm)],[c_0_228,c_0_122]) ).
cnf(c_0_232,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = X1,
inference(spm,[status(thm)],[c_0_229,c_0_222]) ).
cnf(c_0_233,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,X1) = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_230,c_0_133]) ).
cnf(c_0_234,plain,
( hBOOL(X1)
| X1 = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_227]),c_0_99]) ).
cnf(c_0_235,plain,
( hBOOL(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(tc_fun(X1,tc_bool))
| hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Arrow__Order__Mirabelle_OProf)) ),
inference(spm,[status(thm)],[c_0_231,c_0_119]) ).
cnf(c_0_236,plain,
( ~ hBOOL(X2)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(tc_bool) ),
inference(spm,[status(thm)],[c_0_115,c_0_232]) ).
cnf(c_0_237,plain,
( X1 = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,X1) = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_238,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_235]),c_0_236]),c_0_236]),c_0_236]) ).
cnf(c_0_239,plain,
( X1 = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) = X1
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_99,c_0_237]) ).
cnf(c_0_240,plain,
( X2 != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1))
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(spm,[status(thm)],[c_0_125,c_0_232]) ).
cnf(c_0_241,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) != hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_196]) ).
cnf(c_0_242,plain,
( hBOOL(c_in(X1))
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(er,[status(thm)],[c_0_240]) ).
cnf(c_0_243,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_241,c_0_239]) ).
cnf(c_0_244,plain,
( hBOOL(c_in(X1))
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_230]) ).
cnf(c_0_245,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Not,c_in(X1)) = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_233,c_0_244]) ).
cnf(c_0_246,plain,
( hAPP(c_in(X1),X2) != hAPP(c_Not,c_Not)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_197]),c_0_198]) ).
cnf(c_0_247,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| c_in(X1) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_99,c_0_245]) ).
cnf(c_0_248,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = c_Arrow__Order__Mirabelle_OProf ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_227]),c_0_99]) ).
cnf(c_0_249,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
inference(fof_simplification,[status(thm)],[cls_not__Cons__self_0]) ).
cnf(c_0_250,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_fequal(X2),X3)),X3)),
inference(spm,[status(thm)],[c_0_90,c_0_144]) ).
cnf(c_0_251,plain,
( hAPP(hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf),X1) != hAPP(c_Not,c_Not)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_246,c_0_247]) ).
cnf(c_0_252,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(spm,[status(thm)],[c_0_99,c_0_248]) ).
cnf(c_0_253,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
c_0_249 ).
cnf(c_0_254,plain,
~ hBOOL(hAPP(c_Not,hAPP(hAPP(c_fequal(X1),X2),X2))),
inference(rw,[status(thm)],[c_0_250,c_0_77]) ).
cnf(c_0_255,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),X1) != hAPP(c_Not,c_Not)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(spm,[status(thm)],[c_0_251,c_0_252]) ).
cnf(c_0_256,plain,
( ~ hBOOL(X4)
| hAPP(c_Not,X4) != X2
| hBOOL(c_List_Olist_OCons(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_253,c_0_133]) ).
cnf(c_0_257,plain,
( ~ hBOOL(hAPP(c_Not,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),X1),X1)))
| hBOOL(c_Not) ),
inference(spm,[status(thm)],[c_0_254,c_0_183]) ).
cnf(c_0_258,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not
| hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),X1) = c_Not ),
inference(spm,[status(thm)],[c_0_255,c_0_197]) ).
cnf(c_0_259,plain,
( ~ hBOOL(hAPP(c_Not,X2))
| hBOOL(c_List_Olist_OCons(X1,X2,X3)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_99])]) ).
cnf(c_0_260,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Obot__class_Obot(X1) ),
inference(fof_simplification,[status(thm)],[cls_compl__inf__bot_0]) ).
cnf(c_0_261,plain,
( ~ hBOOL(X1)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_258]),c_0_99]),c_0_178]) ).
cnf(c_0_262,plain,
( hBOOL(c_List_Olist_OCons(X1,c_Not,X2))
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_172]),c_0_119])]) ).
cnf(c_0_263,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Obot__class_Obot(X1) ),
c_0_260 ).
cnf(c_0_264,plain,
hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Not,
inference(spm,[status(thm)],[c_0_261,c_0_262]) ).
cnf(c_0_265,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_263]) ).
cnf(c_0_266,plain,
( X2 != c_Arrow__Order__Mirabelle_OProf
| hBOOL(X2)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(spm,[status(thm)],[c_0_196,c_0_122]) ).
cnf(c_0_267,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,X1) = hAPP(c_Not,c_Not) ),
inference(rw,[status(thm)],[c_0_138,c_0_264]) ).
cnf(c_0_268,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(X1))
| ~ hBOOL(hAPP(c_Not,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2)))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(rw,[status(thm)],[c_0_265,c_0_77]) ).
cnf(c_0_269,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(er,[status(thm)],[c_0_266]) ).
cnf(c_0_270,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_271,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2)),
cls_Diff__eq_0 ).
cnf(c_0_272,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__cancel_0 ).
cnf(c_0_273,plain,
( ~ class_Lattices_Oboolean__algebra(X2)
| class_Lattices_Oboolean__algebra(tc_fun(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clsarity_fun__Lattices_Oboolean__algebra]) ).
cnf(c_0_274,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| hAPP(c_Not,c_in(X1)) = hAPP(c_Not,c_Not) ),
inference(spm,[status(thm)],[c_0_267,c_0_242]) ).
cnf(c_0_275,plain,
( ~ hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ class_Lattices_Oboolean__algebra(tc_fun(X1,tc_bool))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268,c_0_269]),c_0_270]),c_0_271]),c_0_272]) ).
cnf(c_0_276,plain,
( ~ class_Lattices_Oboolean__algebra(X2)
| class_Lattices_Oboolean__algebra(tc_fun(X1,X2)) ),
c_0_273 ).
cnf(c_0_277,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__absorb_0]) ).
cnf(c_0_278,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__inf__absorb_0]) ).
cnf(c_0_279,plain,
( hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool))
| c_in(X1) = c_Not ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_274]),c_0_99]) ).
cnf(c_0_280,plain,
( ~ hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_222])]) ).
cnf(c_0_281,plain,
( hBOOL(X1)
| X1 = hAPP(c_Not,c_Not) ),
inference(rw,[status(thm)],[c_0_131,c_0_264]) ).
cnf(c_0_282,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2 ),
c_0_277 ).
cnf(c_0_283,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2 ),
c_0_278 ).
cnf(c_0_284,plain,
( hAPP(c_Not,X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(spm,[status(thm)],[c_0_121,c_0_279]) ).
cnf(c_0_285,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = hAPP(c_Not,c_Not) ),
inference(spm,[status(thm)],[c_0_280,c_0_281]) ).
cnf(c_0_286,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2 ),
inference(spm,[status(thm)],[c_0_282,c_0_283]) ).
cnf(c_0_287,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)) ),
inference(spm,[status(thm)],[c_0_284,c_0_99]) ).
cnf(c_0_288,plain,
hBOOL(c_Arrow__Order__Mirabelle_OProf),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_285]),c_0_99]),c_0_198]) ).
cnf(c_0_289,plain,
( ~ class_Lattices_Olattice(X2)
| ~ hBOOL(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3)),X3)) ),
inference(spm,[status(thm)],[c_0_90,c_0_286]) ).
cnf(c_0_290,plain,
hBOOL(c_HOL_Ouminus__class_Ouminus(tc_bool)),
inference(er,[status(thm)],[c_0_287]) ).
cnf(c_0_291,plain,
hAPP(c_Not,c_Not) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf),
inference(spm,[status(thm)],[c_0_267,c_0_288]) ).
cnf(c_0_292,plain,
( ~ class_Lattices_Olattice(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(c_Not,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2))) ),
inference(rw,[status(thm)],[c_0_289,c_0_77]) ).
cnf(c_0_293,plain,
hAPP(c_Not,c_HOL_Ouminus__class_Ouminus(tc_bool)) = hAPP(c_Not,c_Not),
inference(spm,[status(thm)],[c_0_267,c_0_290]) ).
cnf(c_0_294,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[cls_bot1E_0]) ).
cnf(c_0_295,plain,
c_Not = c_Arrow__Order__Mirabelle_OProf,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_291]),c_0_99]) ).
cnf(c_0_296,plain,
( ~ class_Lattices_Olattice(X1)
| ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ hBOOL(hAPP(c_Not,c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1)))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(spm,[status(thm)],[c_0_292,c_0_220]) ).
cnf(c_0_297,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Not,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_293]),c_0_99]) ).
cnf(c_0_298,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_299,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_294 ).
cnf(c_0_300,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1)) ),
inference(spm,[status(thm)],[c_0_127,c_0_295]) ).
cnf(c_0_301,plain,
hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Arrow__Order__Mirabelle_OProf,
inference(rw,[status(thm)],[c_0_264,c_0_295]) ).
cnf(c_0_302,plain,
( ~ hBOOL(hAPP(c_Not,X1))
| ~ hBOOL(hAPP(c_Not,c_HOL_Ominus__class_Ominus(hAPP(c_Not,X1),X1,tc_bool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297]),c_0_222]),c_0_298])]) ).
cnf(c_0_303,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)),
inference(spm,[status(thm)],[c_0_299,c_0_131]) ).
cnf(c_0_304,plain,
~ hBOOL(v_P____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_301]),c_0_288])]) ).
cnf(c_0_305,plain,
~ hBOOL(hAPP(c_Not,c_HOL_Ominus__class_Ominus(c_Not,hAPP(c_Not,c_Not),tc_bool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_302,c_0_193]),c_0_303]),c_0_264]),c_0_99]),c_0_303]),c_0_264]) ).
cnf(c_0_306,plain,
( hBOOL(X1)
| v_P____ = X1 ),
inference(spm,[status(thm)],[c_0_304,c_0_122]) ).
cnf(c_0_307,plain,
( ~ hBOOL(c_HOL_Ominus__class_Ominus(X2,X4,X1))
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(spm,[status(thm)],[c_0_115,c_0_220]) ).
cnf(c_0_308,plain,
hBOOL(c_HOL_Ominus__class_Ominus(c_Not,hAPP(c_Not,c_Not),tc_bool)),
inference(spm,[status(thm)],[c_0_305,c_0_150]) ).
cnf(c_0_309,plain,
( ~ hBOOL(X1)
| hAPP(c_Arrow__Order__Mirabelle_OProf,X1) = v_P____ ),
inference(spm,[status(thm)],[c_0_300,c_0_306]) ).
cnf(c_0_310,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Not),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_307,c_0_308]),c_0_222])]) ).
cnf(c_0_311,plain,
hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Arrow__Order__Mirabelle_OProf,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_295]),c_0_295]) ).
cnf(c_0_312,plain,
( v_P____ = X1
| hAPP(c_Arrow__Order__Mirabelle_OProf,X1) = v_P____ ),
inference(spm,[status(thm)],[c_0_309,c_0_306]) ).
cnf(c_0_313,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Arrow__Order__Mirabelle_OProf),
inference(rw,[status(thm)],[c_0_310,c_0_295]) ).
cnf(c_0_314,plain,
( c_Arrow__Order__Mirabelle_OProf = X1
| v_P____ = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_311,c_0_312]),c_0_264]),c_0_295]) ).
cnf(c_0_315,plain,
( hBOOL(X1)
| X1 = hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_133,c_0_288]) ).
cnf(c_0_316,plain,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ hBOOL(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3)),X3)) ),
inference(spm,[status(thm)],[c_0_90,c_0_216]) ).
cnf(c_0_317,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Arrow__Order__Mirabelle_OProf) != v_P____,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_314]),c_0_196]) ).
cnf(c_0_318,plain,
( hBOOL(X1)
| X1 = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) ),
inference(rw,[status(thm)],[c_0_315,c_0_295]) ).
cnf(c_0_319,plain,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP(c_Not,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2))) ),
inference(rw,[status(thm)],[c_0_316,c_0_77]) ).
cnf(c_0_320,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Arrow__Order__Mirabelle_OProf) = c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_317,c_0_314]) ).
cnf(c_0_321,plain,
hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = v_P____,
inference(spm,[status(thm)],[c_0_304,c_0_318]) ).
cnf(c_0_322,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_320]),c_0_295]),c_0_321]),c_0_264]),c_0_295]),c_0_288]),c_0_288]),c_0_217])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT043-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/15.60 % CPULimit : 300
% 0.10/15.60 % WCLimit : 300
% 0.10/15.60 % DateTime : Mon Sep 21 04:27:50 UTC 2026
% 0.52/15.60 % CPUTime :
% 0.52/15.60 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.52/15.67 Running first-order theorem proving
% 0.52/15.67 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.52/24.86 % Version: 3.5.1
% 71.52/24.86 % Preprocessing class: FSLMSMSMSSSNFFN.
% 71.52/24.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 71.52/24.86 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 71.52/24.86 % Starting new_bool_3 with 600s (2) cores
% 71.52/24.86 % Starting new_bool_1 with 300s (1) cores
% 71.52/24.86 % Starting sh5l with 300s (1) cores
% 71.52/24.86 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 4132854 completed with status 0
% 71.52/24.86 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 71.52/24.86 % Preprocessing class: FSLMSMSMSSSNFFN.
% 71.52/24.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 71.52/24.86 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 71.52/24.86 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 71.52/24.86 % No SInE strategy applied
% 71.52/24.86 % Search class: FGHSM-FSLM33-DFFFFFNN
% 71.52/24.86 % Scheduled 11 strats onto 4 cores with 1200 seconds (1200 total)
% 71.52/24.86 % Starting SubtermCWHack with 109s (1) cores
% 71.52/24.86 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 71.52/24.86 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 109s (1) cores
% 71.52/24.86 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 109s (1) cores
% 71.52/24.86 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 4132862 completed with status 0
% 71.52/24.86 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 71.52/24.86 % Preprocessing class: FSLMSMSMSSSNFFN.
% 71.52/24.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 71.52/24.86 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 71.52/24.86 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 71.52/24.86 % No SInE strategy applied
% 71.52/24.86 % Search class: FGHSM-FSLM33-DFFFFFNN
% 71.52/24.86 % Scheduled 11 strats onto 4 cores with 1200 seconds (1200 total)
% 71.52/24.86 % Starting SubtermCWHack with 109s (1) cores
% 71.52/24.86 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 71.52/24.86 % Preprocessing time : 0.018 s
% 71.52/24.86 % Presaturation interreduction done
% 71.52/24.86
% 71.52/24.86 % Proof found!
% 71.52/24.86 % SZS status Unsatisfiable
% 71.52/24.86 % SZS output start CNFRefutation
% See solution above
% 71.52/24.86 % Parsed axioms : 688
% 71.52/24.86 % Removed by relevancy pruning/SinE : 0
% 71.52/24.86 % Initial clauses : 688
% 71.52/24.86 % Removed in clause preprocessing : 3
% 71.52/24.86 % Initial clauses in saturation : 685
% 71.52/24.86 % Processed clauses : 9914
% 71.52/24.86 % ...of these trivial : 278
% 71.52/24.86 % ...subsumed : 5046
% 71.52/24.86 % ...remaining for further processing : 4590
% 71.52/24.86 % Other redundant clauses eliminated : 134
% 71.52/24.86 % Clauses deleted for lack of memory : 0
% 71.52/24.86 % Backward-subsumed : 1025
% 71.52/24.86 % Backward-rewritten : 995
% 71.52/24.86 % Generated clauses : 257258
% 71.52/24.86 % ...of the previous two non-redundant : 246423
% 71.52/24.86 % ...aggressively subsumed : 0
% 71.52/24.86 % Contextual simplify-reflections : 52
% 71.52/24.86 % Paramodulations : 257019
% 71.52/24.86 % Factorizations : 24
% 71.52/24.86 % NegExts : 0
% 71.52/24.86 % Equation resolutions : 198
% 71.52/24.86 % Disequality decompositions : 0
% 71.52/24.86 % Total rewrite steps : 28197
% 71.52/24.86 % ...of those cached : 24643
% 71.52/24.86 % Propositional unsat checks : 0
% 71.52/24.86 % Propositional check models : 0
% 71.52/24.86 % Propositional check unsatisfiable : 0
% 71.52/24.86 % Propositional clauses : 0
% 71.52/24.86 % Propositional clauses after purity: 0
% 71.52/24.86 % Propositional unsat core size : 0
% 71.52/24.86 % Propositional preprocessing time : 0.000
% 71.52/24.86 % Propositional encoding time : 0.000
% 71.52/24.86 % Propositional solver time : 0.000
% 71.52/24.86 % Success case prop preproc time : 0.000
% 71.52/24.86 % Success case prop encoding time : 0.000
% 71.52/24.86 % Success case prop solver time : 0.000
% 71.52/24.86 % Current number of processed clauses : 2012
% 71.52/24.86 % Positive orientable unit clauses : 297
% 71.52/24.86 % Positive unorientable unit clauses: 11
% 71.52/24.86 % Negative unit clauses : 207
% 71.52/24.86 % Non-unit-clauses : 1497
% 71.52/24.86 % Current number of unprocessed clauses: 232894
% 71.52/24.86 % ...number of literals in the above : 707920
% 71.52/24.86 % Current number of archived formulas : 0
% 71.52/24.86 % Current number of archived clauses : 2581
% 71.52/24.86 % Clause-clause subsumption calls (NU) : 646562
% 71.52/24.86 % Rec. Clause-clause subsumption calls : 415051
% 71.52/24.86 % Non-unit clause-clause subsumptions : 3541
% 71.52/24.86 % Unit Clause-clause subsumption calls : 94432
% 71.52/24.86 % Rewrite failures with RHS unbound : 233
% 71.52/24.86 % BW rewrite match attempts : 6214
% 71.52/24.86 % BW rewrite match successes : 511
% 71.52/24.86 % Condensation attempts : 0
% 71.52/24.86 % Condensation successes : 0
% 71.52/24.86 % Termbank termtop insertions : 4683241
% 71.52/24.86 % Search garbage collected termcells : 1281
% 71.52/24.86
% 71.52/24.86 % -------------------------------------------------
% 71.52/24.86 % User time : 8.491 s
% 71.52/24.86 % System time : 0.348 s
% 71.52/24.86 % Total time : 8.839 s
% 71.52/24.86 % Maximum resident set size: 4976 pages
% 71.52/24.86
% 71.52/24.86 % -------------------------------------------------
% 71.52/24.86 % User time : 33.653 s
% 71.52/24.86 % System time : 1.222 s
% 71.52/24.86 % Total time : 34.876 s
% 71.52/24.86 % Maximum resident set size: 5376 pages
% 71.52/24.86 % E exiting
%------------------------------------------------------------------------------