%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT043-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 02:07:37 PM UTC 2026
% Result : Unsatisfiable 36.81s 6.18s
% Output : CNFRefutation 36.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 45
% Syntax : Number of clauses : 272 ( 106 unt; 80 nHn; 124 RR)
% Number of literals : 484 ( 217 equ; 154 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 10 con; 0-5 aty)
% Number of variables : 551 ( 193 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_linorder__neq__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_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/sandbox2/benchmark/theBenchmark.p',cls_Collect__neg__eq_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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(cls_CollectD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
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/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
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/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_ord_OatMost__iff_1) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_ord_OgreaterThan__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X4),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThan(X3,X4,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_1) ).
cnf(cls_ord_OgreaterThan__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X3),c_SetInterval_Oord_OgreaterThan(X1,X2,X4)))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_0) ).
cnf(cls_fun__upd__apply_0,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
cnf(cls_fun__upd__idem__iff_1,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 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))),hAPP(c_COMBC(hAPP(c_COMBC(hAPP(c_COMBB(c_Arrow__Order__Mirabelle_Obelow,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_P____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_not__Cons__self_0,axiom,
X1 != c_List_Olist_OCons(X2,X1,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
cnf(cls_sup__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(cls_sup__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
cnf(c_0_45,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_46,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_47,plain,
( ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_45 ).
cnf(c_0_48,plain,
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
c_0_46 ).
cnf(c_0_49,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_50,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_51,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_52,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_53,plain,
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder ).
cnf(c_0_55,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_56,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_57,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,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_59,axiom,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X1,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_60,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_51,c_0_50]),c_0_50]) ).
cnf(c_0_61,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_62,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_52 ).
cnf(c_0_63,plain,
c_lessequals(X1,X1,tc_nat),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
clsarity_nat__Lattices_Oupper__semilattice ).
cnf(c_0_65,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_55 ).
cnf(c_0_66,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,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_68,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_69,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_58,c_0_50]),c_0_50]) ).
cnf(c_0_70,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_71,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_59,c_0_60]) ).
cnf(c_0_72,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_73,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_61 ).
cnf(c_0_74,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_62,c_0_63]),c_0_64])]) ).
cnf(c_0_75,axiom,
class_Lattices_Olower__semilattice(tc_nat),
clsarity_nat__Lattices_Olower__semilattice ).
cnf(c_0_76,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_65,c_0_66]),c_0_66]) ).
cnf(c_0_77,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_78,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_79,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_67,c_0_50]) ).
cnf(c_0_80,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_68,c_0_69]) ).
cnf(c_0_81,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_70,c_0_69]),c_0_69]) ).
cnf(c_0_82,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_71]) ).
cnf(c_0_83,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_73,c_0_74]),c_0_75])]) ).
cnf(c_0_84,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_85,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_76,c_0_66]) ).
cnf(c_0_86,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3)))
| hBOOL(hAPP(X1,X2)) ),
c_0_77 ).
cnf(c_0_87,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_88,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_89,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_78,c_0_50]),c_0_79]) ).
cnf(c_0_90,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_91,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_80,c_0_66]) ).
cnf(c_0_92,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_81,c_0_60]),c_0_72]) ).
cnf(c_0_93,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_94,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_95,plain,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
c_0_84 ).
cnf(c_0_96,axiom,
class_Orderings_Obot(tc_nat),
clsarity_nat__Orderings_Obot ).
cnf(c_0_97,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_85,c_0_66]) ).
cnf(c_0_98,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_86,c_0_50]) ).
cnf(c_0_99,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_100,plain,
( ~ hBOOL(hAPP(X1,X3))
| c_Collect(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_87 ).
cnf(c_0_101,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_88,c_0_79]) ).
cnf(c_0_102,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_103,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_104,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_91,c_0_92]),c_0_71]),c_0_93]) ).
cnf(c_0_105,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_94 ).
cnf(c_0_106,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_107,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_97,c_0_66]) ).
cnf(c_0_108,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_109,plain,
( ~ hBOOL(hAPP(X1,X3))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(rw,[status(thm)],[c_0_100,c_0_50]) ).
cnf(c_0_110,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_fequal(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_90]),c_0_102]) ).
cnf(c_0_111,plain,
( hBOOL(X3)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = X3 ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_112,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_105,c_0_106]),c_0_64])]) ).
cnf(c_0_113,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_107,c_0_108]) ).
cnf(c_0_114,plain,
hAPP(c_in(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_115,plain,
( hBOOL(X2)
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_111,c_0_111]) ).
cnf(c_0_116,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_117,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_76,c_0_112]) ).
cnf(c_0_118,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_113,c_0_71]),c_0_66]),c_0_66]),c_0_66]) ).
cnf(c_0_119,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_114,c_0_115]) ).
cnf(c_0_120,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_121,plain,
( ~ hBOOL(hAPP(hAPP(X3,X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OatMost(X3,X4,X1))) ),
c_0_116 ).
cnf(c_0_122,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_71]),c_0_112]) ).
cnf(c_0_123,plain,
( hBOOL(X1)
| X1 = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_118,c_0_115]) ).
cnf(c_0_124,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_119,c_0_93]) ).
cnf(c_0_125,plain,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_109,c_0_120]) ).
cnf(c_0_126,plain,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| hBOOL(hAPP(c_SetInterval_Oord_OatMost(X1,X2,X3),X4)) ),
inference(rw,[status(thm)],[c_0_121,c_0_66]) ).
cnf(c_0_127,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,X1) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_128,plain,
( hBOOL(c_Not)
| hBOOL(c_in(X1)) ),
inference(er,[status(thm)],[c_0_124]) ).
cnf(c_0_129,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_125,c_0_115]) ).
cnf(c_0_130,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_131,plain,
( ~ hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(c_SetInterval_Oord_OatMost(c_in(X1),X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_126,c_0_66]) ).
cnf(c_0_132,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_127,c_0_128]) ).
cnf(c_0_133,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_129,c_0_93]) ).
cnf(c_0_134,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_130 ).
cnf(c_0_135,plain,
hBOOL(hAPP(c_SetInterval_Oord_OatMost(c_in(X1),c_Arrow__Order__Mirabelle_OProf,X2),v_P____)),
inference(spm,[status(thm)],[c_0_131,c_0_108]) ).
cnf(c_0_136,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_93,c_0_132]),c_0_93]) ).
cnf(c_0_137,plain,
( hBOOL(c_Not)
| hBOOL(c_fequal(X1)) ),
inference(er,[status(thm)],[c_0_133]) ).
cnf(c_0_138,plain,
( ~ hBOOL(hAPP(c_SetInterval_Oord_OatMost(X1,X3,X4),X2))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(rw,[status(thm)],[c_0_134,c_0_66]) ).
cnf(c_0_139,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_135,c_0_136]) ).
cnf(c_0_140,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_141,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_127,c_0_137]) ).
cnf(c_0_142,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_138,c_0_139]) ).
cnf(c_0_143,plain,
( ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2))
| X1 = X2 ),
c_0_140 ).
cnf(c_0_144,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_93,c_0_141]),c_0_93]) ).
cnf(c_0_145,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_127,c_0_142]) ).
cnf(c_0_146,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_143,c_0_144]) ).
cnf(c_0_147,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_93,c_0_145]),c_0_93]) ).
cnf(c_0_148,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_146,c_0_147]),c_0_108])]) ).
cnf(c_0_149,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_127,c_0_148]) ).
cnf(c_0_150,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_76,c_0_120]) ).
cnf(c_0_151,plain,
( ~ hBOOL(hAPP(c_Not,c_Not))
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_149]),c_0_108])]) ).
cnf(c_0_152,plain,
~ hBOOL(hAPP(c_Not,hAPP(hAPP(c_fequal(X1),X2),X2))),
inference(rw,[status(thm)],[c_0_150,c_0_71]) ).
cnf(c_0_153,plain,
( hBOOL(X1)
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,c_Not) = X1 ),
inference(spm,[status(thm)],[c_0_151,c_0_115]) ).
cnf(c_0_154,plain,
( ~ hBOOL(hAPP(c_Not,hAPP(hAPP(X2,X3),X3)))
| hBOOL(X2)
| hBOOL(c_fequal(X1)) ),
inference(spm,[status(thm)],[c_0_152,c_0_115]) ).
cnf(c_0_155,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_93,c_0_149]),c_0_93]) ).
cnf(c_0_156,plain,
( ~ hBOOL(X1)
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,c_Not) = hAPP(c_Not,X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_153]) ).
cnf(c_0_157,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(c_fequal(X1))
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_93]),c_0_115]) ).
cnf(c_0_158,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,c_fequal(X1)) = hAPP(c_Not,c_Not) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_159,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| c_fequal(X1) = c_Not ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_158]),c_0_93]) ).
cnf(c_0_160,plain,
( hAPP(c_Not,X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_125,c_0_159]) ).
cnf(c_0_161,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_160,c_0_93]) ).
cnf(c_0_162,plain,
( ~ hBOOL(hAPP(hAPP(X3,X4),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThan(X3,X4,X1))) ),
inference(fof_simplification,[status(thm)],[cls_ord_OgreaterThan__iff_1]) ).
cnf(c_0_163,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(er,[status(thm)],[c_0_161]) ).
cnf(c_0_164,plain,
( ~ hBOOL(hAPP(hAPP(X3,X4),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OgreaterThan(X3,X4,X1))) ),
c_0_162 ).
cnf(c_0_165,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_127,c_0_163]) ).
cnf(c_0_166,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X3),c_SetInterval_Oord_OgreaterThan(X1,X2,X4)))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(fof_simplification,[status(thm)],[cls_ord_OgreaterThan__iff_0]) ).
cnf(c_0_167,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X4))
| hBOOL(hAPP(c_SetInterval_Oord_OgreaterThan(X1,X2,X3),X4)) ),
inference(rw,[status(thm)],[c_0_164,c_0_66]) ).
cnf(c_0_168,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = c_Arrow__Order__Mirabelle_OProf ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_165]),c_0_93]) ).
cnf(c_0_169,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X3),c_SetInterval_Oord_OgreaterThan(X1,X2,X4)))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_166 ).
cnf(c_0_170,plain,
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X2))
| hBOOL(hAPP(c_SetInterval_Oord_OgreaterThan(c_Arrow__Order__Mirabelle_OProf,v_P____,X1),X2))
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_171,plain,
( ~ hBOOL(hAPP(c_SetInterval_Oord_OgreaterThan(X1,X2,X4),X3))
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(rw,[status(thm)],[c_0_169,c_0_66]) ).
cnf(c_0_172,plain,
( hBOOL(hAPP(c_SetInterval_Oord_OgreaterThan(c_Arrow__Order__Mirabelle_OProf,v_P____,X1),v_P____))
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_168]),c_0_163]) ).
cnf(c_0_173,plain,
( hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),v_P____))
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_174,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,c_Not) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_156,c_0_163]) ).
cnf(c_0_175,plain,
( hBOOL(hAPP(c_Not,v_P____))
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_173,c_0_155]) ).
cnf(c_0_176,plain,
( ~ hBOOL(hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf))
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_151,c_0_174]) ).
cnf(c_0_177,plain,
( ~ hBOOL(v_P____)
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_122,c_0_175]) ).
cnf(c_0_178,plain,
( hBOOL(X1)
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) = X1 ),
inference(spm,[status(thm)],[c_0_176,c_0_115]) ).
cnf(c_0_179,plain,
( hBOOL(X1)
| v_P____ = X1
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_177,c_0_115]) ).
cnf(c_0_180,plain,
( ~ hBOOL(X1)
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) = hAPP(c_Not,X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_178]) ).
cnf(c_0_181,plain,
( ~ hBOOL(X1)
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,X1) = v_P____ ),
inference(spm,[status(thm)],[c_0_122,c_0_179]) ).
cnf(c_0_182,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf) = v_P____ ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_175]),c_0_93]) ).
cnf(c_0_183,plain,
( v_P____ = X1
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,X1) = v_P____ ),
inference(spm,[status(thm)],[c_0_181,c_0_179]) ).
cnf(c_0_184,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
cls_fun__upd__apply_0 ).
cnf(c_0_185,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,v_P____) = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_93,c_0_182]) ).
cnf(c_0_186,plain,
( v_P____ = X1
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Not,v_P____) = X1 ),
inference(spm,[status(thm)],[c_0_93,c_0_183]) ).
cnf(c_0_187,plain,
( ~ hBOOL(X3)
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) ),
inference(spm,[status(thm)],[c_0_109,c_0_184]) ).
cnf(c_0_188,plain,
( X1 = c_Arrow__Order__Mirabelle_OProf
| v_P____ = X1
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_189,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_109,c_0_108]) ).
cnf(c_0_190,plain,
( ~ hBOOL(X3)
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != v_P____
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_189]) ).
cnf(c_0_191,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
cls_fun__upd__idem__iff_1 ).
cnf(c_0_192,plain,
( ~ hBOOL(hAPP(X1,X2))
| X1 != v_P____
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_193,plain,
( hAPP(c_in(X1),X2) != v_P____
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_188]),c_0_189]) ).
cnf(c_0_194,plain,
( ~ hBOOL(hAPP(v_P____,X1))
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(er,[status(thm)],[c_0_192]) ).
cnf(c_0_195,plain,
( hAPP(v_P____,X2) != v_P____
| v_P____ = c_Arrow__Order__Mirabelle_OProf
| c_in(X1) = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_193,c_0_188]) ).
cnf(c_0_196,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(v_P____,X1) = v_P____ ),
inference(spm,[status(thm)],[c_0_194,c_0_179]) ).
cnf(c_0_197,negated_conjecture,
~ 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))),hAPP(c_COMBC(hAPP(c_COMBC(hAPP(c_COMBB(c_Arrow__Order__Mirabelle_Obelow,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_P____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_198,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| c_in(X1) = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_199,negated_conjecture,
~ 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))),hAPP(c_COMBC(hAPP(c_COMBC(hAPP(c_COMBB(c_Arrow__Order__Mirabelle_Obelow,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_P____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
c_0_197 ).
cnf(c_0_200,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,X1) != v_P____
| v_P____ = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_193,c_0_198]) ).
cnf(c_0_201,plain,
( ~ hBOOL(X2)
| hBOOL(X1)
| X1 = hAPP(c_Not,X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_115]) ).
cnf(c_0_202,negated_conjecture,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBC(hAPP(c_COMBC(hAPP(c_COMBB(c_Arrow__Order__Mirabelle_Obelow,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_P____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_b____))),
inference(rw,[status(thm)],[c_0_199,c_0_66]) ).
cnf(c_0_203,plain,
( v_P____ = c_Arrow__Order__Mirabelle_OProf
| hAPP(c_Arrow__Order__Mirabelle_OProf,X1) = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_200,c_0_188]) ).
cnf(c_0_204,plain,
c_Fun_Ofun__upd(c_Not,hAPP(c_Not,X1),X1,X2,X3) = c_Not,
inference(spm,[status(thm)],[c_0_191,c_0_93]) ).
cnf(c_0_205,plain,
( hBOOL(X1)
| hBOOL(c_Not)
| X1 = hAPP(c_Not,c_in(X2)) ),
inference(spm,[status(thm)],[c_0_201,c_0_128]) ).
cnf(c_0_206,negated_conjecture,
v_P____ = c_Arrow__Order__Mirabelle_OProf,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_163]) ).
cnf(c_0_207,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_204,c_0_205]),c_0_204])]) ).
cnf(c_0_208,plain,
( hBOOL(c_Not)
| c_in(X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) ),
inference(rw,[status(thm)],[c_0_136,c_0_206]) ).
cnf(c_0_209,plain,
( hBOOL(c_Not)
| c_in(X1) = hAPP(c_Not,c_Not) ),
inference(spm,[status(thm)],[c_0_93,c_0_207]) ).
cnf(c_0_210,plain,
( hBOOL(c_Not)
| hAPP(c_Not,c_Not) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_211,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_212,plain,
( hAPP(c_Not,c_Not) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf)) = hAPP(c_Not,c_Not) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_210]),c_0_206]) ).
cnf(c_0_213,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_211,c_0_66]),c_0_66]) ).
cnf(c_0_214,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not
| hAPP(c_Not,c_Not) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_212]),c_0_93]) ).
cnf(c_0_215,negated_conjecture,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf)),
inference(spm,[status(thm)],[c_0_108,c_0_206]) ).
cnf(c_0_216,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_109,c_0_213]) ).
cnf(c_0_217,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__idem_0]) ).
cnf(c_0_218,plain,
( ~ hBOOL(c_Not)
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_214]),c_0_215])]) ).
cnf(c_0_219,plain,
( ~ hBOOL(hAPP(c_Not,X2))
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_93,c_0_201]) ).
cnf(c_0_220,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_216,c_0_72]) ).
cnf(c_0_221,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2 ),
c_0_217 ).
cnf(c_0_222,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_223,plain,
( ~ hBOOL(X1)
| hAPP(c_Not,X1) = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not ),
inference(spm,[status(thm)],[c_0_218,c_0_201]) ).
cnf(c_0_224,plain,
( hBOOL(X1)
| X1 = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_214]),c_0_215])]) ).
cnf(c_0_225,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_220]) ).
cnf(c_0_226,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X1) = X1,
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_227,plain,
( X1 = c_Not
| hAPP(c_Not,X1) = c_Not
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not ),
inference(spm,[status(thm)],[c_0_223,c_0_224]) ).
cnf(c_0_228,plain,
hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(rw,[status(thm)],[c_0_225,c_0_71]) ).
cnf(c_0_229,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
inference(fof_simplification,[status(thm)],[cls_not__Cons__self_0]) ).
cnf(c_0_230,plain,
( ~ hBOOL(hAPP(c_Not,X2))
| hBOOL(c_fequal(X1))
| hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) ),
inference(spm,[status(thm)],[c_0_154,c_0_226]) ).
cnf(c_0_231,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_Not) ),
inference(spm,[status(thm)],[c_0_114,c_0_136]) ).
cnf(c_0_232,plain,
( X1 = c_Not
| hAPP(c_Not,c_Not) = X1
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not ),
inference(spm,[status(thm)],[c_0_93,c_0_227]) ).
cnf(c_0_233,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Not,
inference(spm,[status(thm)],[c_0_109,c_0_228]) ).
cnf(c_0_234,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
c_0_229 ).
cnf(c_0_235,plain,
( hBOOL(c_fequal(X1))
| hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) ),
inference(spm,[status(thm)],[c_0_230,c_0_228]) ).
cnf(c_0_236,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_152,c_0_144]) ).
cnf(c_0_237,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),X1) != hAPP(c_Not,c_Not)
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_206]),c_0_233]),c_0_218]) ).
cnf(c_0_238,plain,
( ~ hBOOL(X4)
| hAPP(c_Not,X4) != X2
| hBOOL(c_List_Olist_OCons(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_234,c_0_201]) ).
cnf(c_0_239,plain,
( hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool))
| hAPP(c_Not,c_fequal(X1)) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_235]),c_0_206]) ).
cnf(c_0_240,negated_conjecture,
( ~ hBOOL(hAPP(c_Not,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),X1),X1)))
| hBOOL(c_Not) ),
inference(spm,[status(thm)],[c_0_236,c_0_206]) ).
cnf(c_0_241,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not
| hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),X1) = c_Not ),
inference(spm,[status(thm)],[c_0_237,c_0_232]) ).
cnf(c_0_242,plain,
( ~ hBOOL(hAPP(c_Not,X2))
| hBOOL(c_List_Olist_OCons(X1,X2,X3)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_93])]) ).
cnf(c_0_243,plain,
( hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool))
| c_fequal(X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_239]),c_0_93]) ).
cnf(c_0_244,negated_conjecture,
( ~ hBOOL(X1)
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_93]),c_0_218]) ).
cnf(c_0_245,plain,
( hBOOL(c_List_Olist_OCons(X1,c_Not,X2))
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_214]),c_0_215])]) ).
cnf(c_0_246,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) ),
inference(spm,[status(thm)],[c_0_125,c_0_243]) ).
cnf(c_0_247,negated_conjecture,
hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = c_Not,
inference(spm,[status(thm)],[c_0_244,c_0_245]) ).
cnf(c_0_248,plain,
( hAPP(c_Not,X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) ),
inference(rw,[status(thm)],[c_0_246,c_0_247]) ).
cnf(c_0_249,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) ),
inference(spm,[status(thm)],[c_0_248,c_0_93]) ).
cnf(c_0_250,plain,
hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),
inference(er,[status(thm)],[c_0_249]) ).
cnf(c_0_251,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__bot__right_0]) ).
cnf(c_0_252,plain,
hAPP(c_Not,c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) = hAPP(c_Not,c_Not),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_250]),c_0_206]),c_0_247]) ).
cnf(c_0_253,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__bot__left_0]) ).
cnf(c_0_254,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2 ),
c_0_251 ).
cnf(c_0_255,plain,
c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = c_Not,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_252]),c_0_93]) ).
cnf(c_0_256,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_257,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2 ),
c_0_253 ).
cnf(c_0_258,plain,
hAPP(hAPP(c_Not,X1),c_Orderings_Obot__class_Obot(tc_bool)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_256])]) ).
cnf(c_0_259,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1) = X1,
inference(spm,[status(thm)],[c_0_257,c_0_256]) ).
cnf(c_0_260,plain,
hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_Not,X1),
inference(spm,[status(thm)],[c_0_258,c_0_93]) ).
cnf(c_0_261,negated_conjecture,
~ hBOOL(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf))),
inference(spm,[status(thm)],[c_0_118,c_0_206]) ).
cnf(c_0_262,plain,
hAPP(hAPP(c_Not,c_Not),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_259,c_0_260]),c_0_255]) ).
cnf(c_0_263,negated_conjecture,
~ hBOOL(hAPP(c_Not,c_Not)),
inference(spm,[status(thm)],[c_0_261,c_0_247]) ).
cnf(c_0_264,plain,
( X2 != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_262]),c_0_263]) ).
cnf(c_0_265,plain,
hBOOL(c_in(X1)),
inference(er,[status(thm)],[c_0_264]) ).
cnf(c_0_266,plain,
hAPP(c_Not,c_in(X1)) = hAPP(c_Not,c_Not),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_265]),c_0_206]),c_0_247]) ).
cnf(c_0_267,plain,
c_in(X1) = c_Not,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_266]),c_0_93]) ).
cnf(c_0_268,plain,
hAPP(c_Not,X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[c_0_114,c_0_267]) ).
cnf(c_0_269,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_270,plain,
X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_268,c_0_93]) ).
cnf(c_0_271,plain,
$false,
inference(sr,[status(thm)],[c_0_269,c_0_270]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT043-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.66 % Computer : n015.cluster.edu
% 0.18/0.66 % Model : x86_64 x86_64
% 0.18/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.66 % Memory : 8046.5625MB
% 0.18/0.66 % OS : Linux 6.8.0-71-generic
% 0.18/0.66 % CPULimit : 300
% 0.18/0.66 % WCLimit : 300
% 0.18/0.66 % DateTime : Mon Sep 21 04:31:07 UTC 2026
% 0.18/0.67 % CPUTime :
% 0.18/0.67 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.73 Running first-order theorem proving
% 0.23/0.73 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 36.81/6.18 % Version: 3.5.1
% 36.81/6.18 % Preprocessing class: FSLMSMSMSSSNFFN.
% 36.81/6.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 36.81/6.18 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 36.81/6.18 % Starting new_bool_3 with 600s (2) cores
% 36.81/6.18 % Starting new_bool_1 with 300s (1) cores
% 36.81/6.18 % Starting sh5l with 300s (1) cores
% 36.81/6.18 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 556917 completed with status 0
% 36.81/6.18 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 36.81/6.18 % Preprocessing class: FSLMSMSMSSSNFFN.
% 36.81/6.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 36.81/6.18 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 36.81/6.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 36.81/6.18 % No SInE strategy applied
% 36.81/6.18 % Search class: FGHSM-FSLM33-DFFFFFNN
% 36.81/6.18 % Scheduled 11 strats onto 4 cores with 1200 seconds (1200 total)
% 36.81/6.18 % Starting SubtermCWHack with 109s (1) cores
% 36.81/6.18 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 36.81/6.18 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 109s (1) cores
% 36.81/6.18 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 109s (1) cores
% 36.81/6.18 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 556926 completed with status 0
% 36.81/6.18 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 36.81/6.18 % Preprocessing class: FSLMSMSMSSSNFFN.
% 36.81/6.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 36.81/6.18 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 36.81/6.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 36.81/6.18 % No SInE strategy applied
% 36.81/6.18 % Search class: FGHSM-FSLM33-DFFFFFNN
% 36.81/6.18 % Scheduled 11 strats onto 4 cores with 1200 seconds (1200 total)
% 36.81/6.18 % Starting SubtermCWHack with 109s (1) cores
% 36.81/6.18 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 36.81/6.18 % Preprocessing time : 0.010 s
% 36.81/6.18 % Presaturation interreduction done
% 36.81/6.18
% 36.81/6.18 % Proof found!
% 36.81/6.18 % SZS status Unsatisfiable
% 36.81/6.18 % SZS output start CNFRefutation
% See solution above
% 36.81/6.18 % Parsed axioms : 688
% 36.81/6.18 % Removed by relevancy pruning/SinE : 0
% 36.81/6.18 % Initial clauses : 688
% 36.81/6.18 % Removed in clause preprocessing : 3
% 36.81/6.18 % Initial clauses in saturation : 685
% 36.81/6.18 % Processed clauses : 11434
% 36.81/6.18 % ...of these trivial : 287
% 36.81/6.18 % ...subsumed : 5948
% 36.81/6.18 % ...remaining for further processing : 5199
% 36.81/6.18 % Other redundant clauses eliminated : 125
% 36.81/6.18 % Clauses deleted for lack of memory : 0
% 36.81/6.18 % Backward-subsumed : 1105
% 36.81/6.18 % Backward-rewritten : 1784
% 36.81/6.18 % Generated clauses : 268550
% 36.81/6.18 % ...of the previous two non-redundant : 258673
% 36.81/6.18 % ...aggressively subsumed : 0
% 36.81/6.18 % Contextual simplify-reflections : 58
% 36.81/6.18 % Paramodulations : 268327
% 36.81/6.18 % Factorizations : 19
% 36.81/6.18 % NegExts : 0
% 36.81/6.18 % Equation resolutions : 190
% 36.81/6.18 % Disequality decompositions : 0
% 36.81/6.18 % Total rewrite steps : 36282
% 36.81/6.18 % ...of those cached : 32393
% 36.81/6.18 % Propositional unsat checks : 0
% 36.81/6.18 % Propositional check models : 0
% 36.81/6.18 % Propositional check unsatisfiable : 0
% 36.81/6.18 % Propositional clauses : 0
% 36.81/6.18 % Propositional clauses after purity: 0
% 36.81/6.18 % Propositional unsat core size : 0
% 36.81/6.18 % Propositional preprocessing time : 0.000
% 36.81/6.18 % Propositional encoding time : 0.000
% 36.81/6.18 % Propositional solver time : 0.000
% 36.81/6.18 % Success case prop preproc time : 0.000
% 36.81/6.18 % Success case prop encoding time : 0.000
% 36.81/6.18 % Success case prop solver time : 0.000
% 36.81/6.18 % Current number of processed clauses : 1755
% 36.81/6.18 % Positive orientable unit clauses : 291
% 36.81/6.18 % Positive unorientable unit clauses: 11
% 36.81/6.18 % Negative unit clauses : 143
% 36.81/6.18 % Non-unit-clauses : 1310
% 36.81/6.18 % Current number of unprocessed clauses: 242364
% 36.81/6.18 % ...number of literals in the above : 741867
% 36.81/6.18 % Current number of archived formulas : 0
% 36.81/6.18 % Current number of archived clauses : 3447
% 36.81/6.18 % Clause-clause subsumption calls (NU) : 788178
% 36.81/6.18 % Rec. Clause-clause subsumption calls : 531423
% 36.81/6.18 % Non-unit clause-clause subsumptions : 4256
% 36.81/6.18 % Unit Clause-clause subsumption calls : 91899
% 36.81/6.18 % Rewrite failures with RHS unbound : 209
% 36.81/6.18 % BW rewrite match attempts : 6267
% 36.81/6.18 % BW rewrite match successes : 523
% 36.81/6.18 % Condensation attempts : 0
% 36.81/6.18 % Condensation successes : 0
% 36.81/6.18 % Termbank termtop insertions : 4951353
% 36.81/6.18 % Search garbage collected termcells : 1281
% 36.81/6.18
% 36.81/6.18 % -------------------------------------------------
% 36.81/6.18 % User time : 5.039 s
% 36.81/6.18 % System time : 0.205 s
% 36.81/6.18 % Total time : 5.244 s
% 36.81/6.18 % Maximum resident set size: 4976 pages
% 36.81/6.18
% 36.81/6.18 % -------------------------------------------------
% 36.81/6.18 % User time : 19.931 s
% 36.81/6.18 % System time : 0.681 s
% 36.81/6.18 % Total time : 20.612 s
% 36.81/6.18 % Maximum resident set size: 5120 pages
% 36.81/6.18 % E exiting
%------------------------------------------------------------------------------